add lab3 exercises
This commit is contained in:
Mariano Sciacco
18
lab3/README.md
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lab3/README.md
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# CPS Lab 3 Exercise (2021-12-22)
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- Mariano Sciacco
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- Federico Carboni
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- Giuseppe Rossano
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- Alessandro Benetti
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## Notes
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> Note 1: requires `gnuplot` and `phaverlite` (see https://www.cs.unipr.it/~zaffanella/PPLite/PHAVerLite)
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> Note 2: all credits to `phaver` executable in this folder goes to Enea Zaffanella
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> Note 3: execute `./phaver <filename.pha>` to compile the `.pha` file
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> Note 4: execute `gnuplot --persist -c phaverplot.gp filename.txt` to generate the graph
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> Note 5: results of the plot are inside the respective folders as pdf files.
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57
lab3/examples/bouncing.pha
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57
lab3/examples/bouncing.pha
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// ----------------------------------------------------------
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// Hybrid System Example: Bouncing Ball
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// ----------------------------------------------------------
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// ----------------------------------------------------------
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// Constants
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// ----------------------------------------------------------
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g:=1; // constant for gravity
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// ----------------------------------------------------------
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// System Description
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// ----------------------------------------------------------
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automaton bouncing_ball
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contr_var: v, x;
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synclabs: jump;
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loc state: while x>=0 & x<=10 & v<=10 & v>=-10 wait {x'==v & v'==-g}
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when x==0 & v<0 sync jump do {v'==-v*0.5 & x'==x} goto state;
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initially: state & x==2 & v==0;
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end
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// ----------------------------------------------------------
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// Define Partitioning
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// ----------------------------------------------------------
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// Add a new label for the transitions that are introduced
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// between partitions
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bouncing_ball.add_label(tau);
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// Define the directions of the partitions
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// here: in both axes with a min. threshold of partition size 0.2
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bouncing_ball.set_refine_constraints((x, 0.2),(v,0.2),tau);
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// With this partitioning we can use convex hull overapproximations,
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// resulting in fewer polyhedra (one per partition)
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//REACH_USE_CONVEX_HULL=true;
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// ----------------------------------------------------------
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// Define Partitioning (alternative)
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// ----------------------------------------------------------
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// We can also just partition in the v-direction, but then we must turn off
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// the convex hull (try it...)
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// bouncing_ball.set_refine_constraints((v,0.2),tau);
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// REACH_USE_CONVEX_HULL=false;
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// ----------------------------------------------------------
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// Analysis Commands
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// ----------------------------------------------------------
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reg=bouncing_ball.reachable;
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// ----------------------------------------------------------
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// Saving Data for Graphical Output
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// ----------------------------------------------------------
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reg.print("out_reach",2); // output as a list of vertices
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// for display with graph use, e.g.:
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// graph -T X -C -B -q0.5 out_reach
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// for display with matlab use, e.g.:
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// plot_2d_vertices('out_m_reach')
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81
lab3/examples/bouncing_timed.pha
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lab3/examples/bouncing_timed.pha
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// ----------------------------------------------------------
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// Hybrid System Example: Bouncing Ball
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// ----------------------------------------------------------
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// This version produces a plot of position over time.
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// A clock is added to the system to model time explicitly.
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// This gives us a another choice of partitioning: along
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// the time-axis. It's fast, but doesn't work with convex
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// hull.
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//
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// The complexity of this example requires us to put limits
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// on the bits used in polyhedral computations.
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// Otherwise, it may take very long or not terminate at all.
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REACH_CONSTRAINT_LIMIT = 48;
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REACH_CONSTRAINT_TRIGGER = 96;
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CONSTRAINT_BITSIZE = 24;
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REACH_BITSIZE_TRIGGER = 200;
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// ----------------------------------------------------------
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// Constants
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// ----------------------------------------------------------
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g:=1; // constant for gravity
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// ----------------------------------------------------------
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// System Description
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// ----------------------------------------------------------
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automaton bouncing_ball
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contr_var: t, x, v;
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synclabs: jump;
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loc state: while x>=0 & x<=10 & v<=10 & v>=-10 & t<=5 & t>=0 wait {x'==v & v'==-g & t'==1}
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when x==0 & v<0 sync jump do {v'==-v*0.5 & x'==x & t'==t} goto state;
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initially: state & x==2 & v==0 & t==0;
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end
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// ----------------------------------------------------------
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// Define Partitioning
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// ----------------------------------------------------------
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// Add a new label for the transitions that are introduced
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// between partitions
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bouncing_ball.add_label(tau);
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// Define the directions of the partitions
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// here: in both axes with a min. threshold of partition size 0.2
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bouncing_ball.set_refine_constraints((x, 0.2),(v,0.2),tau);
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// With this partitioning we can use convex hull overapproximations,
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// resulting in fewer polyhedra (one per partition)
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//REACH_USE_CONVEX_HULL=true;
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// ----------------------------------------------------------
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// Define Partitioning (alternative 1)
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// ----------------------------------------------------------
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// We can also just partition in the v-direction, but then
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// we must turn off convex hull (try it...)
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// bouncing_ball.set_refine_constraints((v,0.2),tau);
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// REACH_USE_CONVEX_HULL=false;
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// ----------------------------------------------------------
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// Define Partitioning (alternative 2)
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// ----------------------------------------------------------
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// We can also just partition in the t-direction, but then
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// we must turn off convex hull
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// and refine the time-elapse operator at least twice
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// at every step (try it...)
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//TIME_POST_ITER=2;
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//bouncing_ball.set_refine_constraints((t, 0.1),tau);
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//REACH_USE_CONVEX_HULL=false;
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// ----------------------------------------------------------
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// Analysis Commands
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// ----------------------------------------------------------
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reg=bouncing_ball.reachable;
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// ----------------------------------------------------------
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// Saving Data for Graphical Output
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// ----------------------------------------------------------
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reg.project_to(t, x); // remove v to get a 2-dim output
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reg.print("out_reach",2); // output as a list of vertices
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// for display with graph use, e.g.:
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// graph -T X -C -B -q0.5 out_reach
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// for display with matlab use, e.g.:
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// plot_2d_vertices('out_m_reach')
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63
lab3/examples/evader.pha
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63
lab3/examples/evader.pha
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// Constants definition
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//
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// Automaton definition
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//
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automaton evader
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contr_var: e, p, x; // e position of the evader
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// p position of the pursuer
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// x timer
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synclabs: jump;
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loc ClkW:
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while 0 <= e <= 40 & 0 <= p <= 40 & x <= 2 wait
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{e'==5 & -0.5 <= p' <= 6 & x'==1}
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when (p == 0) sync jump do {e'==e & p'==40 & x'==x} goto ClkW;
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when (p == 40) sync jump do {e'==e & p'==0 & x'==x} goto ClkW;
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when (x >= 2) & (0 < e < 40) & (6*e - 5*p > 40) sync jump do
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{e'==e & p'==p & x'==0} goto ClkW;
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when (x >= 2) & (0 < e < 40) & (6*e - 5*p <= 40) sync jump do
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{e'==e & p'==p & x'==0} goto CntrClkW;
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when (e == 0) sync jump do {e'==e & p'==p & x'==x} goto Rescued;
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when (e == 40) sync jump do {e'==e & p'==p & x'==x} goto Rescued;
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loc CntrClkW:
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while 0 <= e <= 40 & 0 <= p <= 40 & x <= 2 wait
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{e'==-5 & -0.5 <= p' <= 6 & x'==1}
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when (p == 0) sync jump do {e'==e & p'==40 & x'==x} goto CntrClkW;
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when (p == 40) sync jump do {e'==e & p'==0 & x'==x} goto CntrClkW;
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when (x >= 2) & (0 < e < 40) & (6*e - 5*p > 40) sync jump do
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{e'==e & p'==p & x'==0} goto ClkW;
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when (x >= 2) & (0 < e < 40) & (6*e - 5*p <= 40) sync jump do
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{e'==e & p'==p & x'==0} goto CntrClkW;
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when (e == 0) sync jump do {e'==e & p'==p & x'==x} goto Rescued;
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when (e == 40) sync jump do {e'==e & p'==p & x'==x} goto Rescued;
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loc Rescued:
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while true wait {e'==0 & p'==0 & x'==0 };
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initially: ClkW & x == 2 & e == 20 & p == 10;
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end
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// Compute the reachable set
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//
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region=evader.reachable;
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//
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// Output to file
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//
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// List regions (pairs of locations names and linear formulas)
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region.print("evader_regions.txt", 0);
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// Sequence of vertices in floating point form.
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// Can be plotted with gnuplot
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// Project on e and p
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region.project_to(e, p);
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region.print("evader.txt", 2);
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// Safety verification
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//
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// definition of bad states
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forbidden = evader.{$ & e == p};
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reach_set = evader.is_reachable(forbidden);
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reach_set.intersection_assign(forbidden);
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echo "The intersection between the reachable set and the bad region is:";
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reach_set.is_empty;
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59
lab3/examples/evader2.pha
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lab3/examples/evader2.pha
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// Constants definition
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//
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// Automaton definition
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//
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automaton evader
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contr_var: e, p, x, p_zero; // e position of the evader
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// p position of the pursuer
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// x timer
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// p_zero "frozen variable" that stores the
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// initial position of the pursuer
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synclabs: jump;
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loc ClkW:
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while 0 <= e <= 40 & 0 <= p <= 40 & x <= 2 wait
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{e'==5 & -0.5 <= p' <= 6 & x'==1 & p_zero'==0}
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when (p == 0) sync jump do {e'==e & p'==40 & x'==x & p_zero'==p_zero} goto ClkW;
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when (p == 40) sync jump do {e'==e & p'==0 & x'==x & p_zero'==p_zero} goto ClkW;
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when (x >= 2) & (0 < e < 40) & (6*e - 5*p > 40) sync jump do
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{e'==e & p'==p & x'==0 & p_zero'==p_zero} goto ClkW;
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when (x >= 2) & (0 < e < 40) & (6*e - 5*p <= 40) sync jump do
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{e'==e & p'==p & x'==0 & p_zero'==p_zero} goto CntrClkW;
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when (e == 0) sync jump do {e'==e & p'==p & x'==x & p_zero'==p_zero} goto Rescued;
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when (e == 40) sync jump do {e'==e & p'==p & x'==x & p_zero'==p_zero} goto Rescued;
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loc CntrClkW:
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while 0 <= e <= 40 & 0 <= p <= 40 & x <= 2 wait
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{e'==-5 & -0.5 <= p' <= 6 & x'==1 & p_zero'==0}
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when (p == 0) sync jump do {e'==e & p'==40 & x'==x & p_zero'==p_zero} goto CntrClkW;
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when (p == 40) sync jump do {e'==e & p'==0 & x'==x & p_zero'==p_zero} goto CntrClkW;
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when (x >= 2) & (0 < e < 40) & (6*e - 5*p > 40) sync jump do
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{e'==e & p'==p & x'==0 & p_zero'==p_zero} goto ClkW;
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when (x >= 2) & (0 < e < 40) & (6*e - 5*p <= 40) sync jump do
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{e'==e & p'==p & x'==0 & p_zero'==p_zero} goto CntrClkW;
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when (e == 0) sync jump do {e'==e & p'==p & x'==x & p_zero'==p_zero} goto Rescued;
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when (e == 40) sync jump do {e'==e & p'==p & x'==x & p_zero'==p_zero} goto Rescued;
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loc Rescued:
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while true wait {e'==0 & p'==0 & x'==0 & p_zero'==0};
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initially: ClkW & x == 2 & e == 20 & p == p_zero & 0 <= p <= 40;
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end
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// Find winning starting points for pursuer
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//
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// Compute the reachable set
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//
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region=evader.reachable;
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// Intersect with states where pursuer wins
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forbidden = evader.{$ & e == p};
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region.intersection_assign(forbidden);
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// Project on p_zero to get the initial position for the pursuer for which the
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// pursuer can win the game
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region.project_to(p_zero);
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// union over all locations
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pursuer_wins = region.loc_union;
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echo "The pursuer can win the game if it starts from:";
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pursuer_wins.print;
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16
lab3/examples/txt/evader.txt
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16
lab3/examples/txt/evader.txt
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20 10
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20 10
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30 9
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30 22
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20 10
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30 22
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30 9
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40 8
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40 34
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30 22
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40 8
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40 34
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4
lab3/examples/txt/evader_regions.txt
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4
lab3/examples/txt/evader_regions.txt
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region = evader.{
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ClkW & (x == 2 & p == 10 & e == 20 | e == 5*x + 20 & 6*e >= 5*p + 70 & e + 10*p >= 120 & e <= 30 | e == 5*x + 30 & e + 10*p >= 120 & 30 <= e <= 40 & 6*e >= 5*p + 70),
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Rescued & x == 2 & e == 40 & 8 <= p <= 34
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};
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BIN
lab3/exercise/ex1.1/lake.pdf
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BIN
lab3/exercise/ex1.1/lake.pdf
Normal file
Binary file not shown.
40
lab3/exercise/ex1.1/lake.pha
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40
lab3/exercise/ex1.1/lake.pha
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r_in := 15;
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r_out := 15.7;
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automaton lake
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contr_var: x, t;
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synclabs: lakelab;
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loc single:
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while x >= 0 wait
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{ 0.7 * r_in - r_out <= x' <= r_in - r_out & t' == 1}
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initially: single & x == 25.7 & t == 0;
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end
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// Compute the reachable set
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//
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region=lake.reachable;
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//
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// Output to file
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region.print("lake_regions.txt", 0);
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region.project_to(t, x);
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region.print("lake.txt", 2);
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// Safety verification
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forbidden = lake.{$ & x < 0};
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reach_set = lake.is_reachable(forbidden);
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reach_set.intersection_assign(forbidden);
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echo "The intersection between the reachable set and the bad region is:";
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reach_set.is_empty;
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
5
lab3/exercise/ex1.1/lake.txt
Normal file
5
lab3/exercise/ex1.1/lake.txt
Normal file
@@ -0,0 +1,5 @@
|
|||||||
|
0 4.94230769230769162447814
|
||||||
|
25.6999999999999992894573 0
|
||||||
|
0 36.714285714285708195348
|
||||||
|
0 4.94230769230769162447814
|
||||||
|
|
||||||
3
lab3/exercise/ex1.1/lake_regions.txt
Normal file
3
lab3/exercise/ex1.1/lake_regions.txt
Normal file
@@ -0,0 +1,3 @@
|
|||||||
|
region = lake.{
|
||||||
|
single & 10*x + 7*t <= 257 & 10*x + 52*t >= 257 & x >= 0
|
||||||
|
};
|
||||||
BIN
lab3/exercise/ex1.2/lake2.pdf
Normal file
BIN
lab3/exercise/ex1.2/lake2.pdf
Normal file
Binary file not shown.
47
lab3/exercise/ex1.2/lake2.pha
Normal file
47
lab3/exercise/ex1.2/lake2.pha
Normal file
@@ -0,0 +1,47 @@
|
|||||||
|
r_in_r := 30;
|
||||||
|
r_in_d := 10;
|
||||||
|
r_out := 15.7;
|
||||||
|
|
||||||
|
automaton lake
|
||||||
|
contr_var: x, t, c;
|
||||||
|
|
||||||
|
synclabs: lakelab;
|
||||||
|
loc dry:
|
||||||
|
while x >= 0 & c <= 0.75 wait
|
||||||
|
{ 0.7 * r_in_d - r_out <= x' <= r_in_d - r_out & t' == 1 & c' == 1}
|
||||||
|
when (c >= 0.75) sync lakelab goto rain;
|
||||||
|
|
||||||
|
loc rain:
|
||||||
|
while x >= 0 & c <= 1 wait
|
||||||
|
{ 0.7 * r_in_r - r_out <= x' <= r_in_r - r_out & t' == 1 & c' == 1}
|
||||||
|
when (c >= 1) sync lakelab do {c' == 0 & t' == t & x' == x} goto dry;
|
||||||
|
|
||||||
|
initially: dry & x == 25.7 & t == 0 & c == 0;
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
// Compute the reachable set
|
||||||
|
//
|
||||||
|
region=lake.reachable;
|
||||||
|
|
||||||
|
//
|
||||||
|
// Output to file
|
||||||
|
|
||||||
|
region.print("lake2_regions.txt", 0);
|
||||||
|
|
||||||
|
region.project_to(t, x);
|
||||||
|
region.print("lake2.txt", 2);
|
||||||
|
|
||||||
|
// Safety verification
|
||||||
|
|
||||||
|
forbidden = lake.{$ & x < 0};
|
||||||
|
reach_set = lake.is_reachable(forbidden);
|
||||||
|
reach_set.intersection_assign(forbidden);
|
||||||
|
|
||||||
|
echo "The intersection between the reachable set and the bad region is:";
|
||||||
|
reach_set.is_empty;
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
404
lab3/exercise/ex1.2/lake2.txt
Normal file
404
lab3/exercise/ex1.2/lake2.txt
Normal file
@@ -0,0 +1,404 @@
|
|||||||
|
0 31.152298850574709376815
|
||||||
|
1.32499999999999995559108 31
|
||||||
|
4 31
|
||||||
|
0 31.7017543859649109094789
|
||||||
|
0 31.152298850574709376815
|
||||||
|
|
||||||
|
0 30.152298850574709376815
|
||||||
|
1.32499999999999995559108 30
|
||||||
|
4.69999999999999928945726 30
|
||||||
|
0.42499999999999998889777 30.75
|
||||||
|
0 30.75
|
||||||
|
0 30.152298850574709376815
|
||||||
|
|
||||||
|
0 29.152298850574709376815
|
||||||
|
1.32499999999999995559108 29
|
||||||
|
5.39999999999999946709295 29
|
||||||
|
1.125 29.75
|
||||||
|
0 29.75
|
||||||
|
0 29.152298850574709376815
|
||||||
|
|
||||||
|
0 28.152298850574709376815
|
||||||
|
1.32499999999999995559108 28
|
||||||
|
6.09999999999999964472863 28
|
||||||
|
1.82499999999999995559108 28.75
|
||||||
|
0 28.75
|
||||||
|
0 28.152298850574709376815
|
||||||
|
|
||||||
|
19.1749999999999971578291 0.75
|
||||||
|
25.6999999999999992894573 0
|
||||||
|
21.4249999999999971578291 0.75
|
||||||
|
19.1749999999999971578291 0.75
|
||||||
|
|
||||||
|
0 27.152298850574709376815
|
||||||
|
1.32499999999999995559108 27
|
||||||
|
6.79999999999999982236432 27
|
||||||
|
2.52499999999999991118216 27.75
|
||||||
|
0 27.75
|
||||||
|
0 27.152298850574709376815
|
||||||
|
|
||||||
|
0 26.152298850574709376815
|
||||||
|
1.32499999999999995559108 26
|
||||||
|
7.5 26
|
||||||
|
3.22499999999999964472863 26.75
|
||||||
|
0 26.75
|
||||||
|
0 26.152298850574709376815
|
||||||
|
|
||||||
|
0 25.152298850574709376815
|
||||||
|
1.32499999999999995559108 25
|
||||||
|
8.19999999999999928945726 25
|
||||||
|
3.92499999999999982236432 25.75
|
||||||
|
0 25.75
|
||||||
|
0 25.152298850574709376815
|
||||||
|
|
||||||
|
0 24.152298850574709376815
|
||||||
|
1.32499999999999995559108 24
|
||||||
|
8.89999999999999857891453 24
|
||||||
|
4.625 24.75
|
||||||
|
0 24.75
|
||||||
|
0 24.152298850574709376815
|
||||||
|
|
||||||
|
0 23.152298850574709376815
|
||||||
|
1.32499999999999995559108 23
|
||||||
|
9.59999999999999964472863 23
|
||||||
|
5.32499999999999928945726 23.75
|
||||||
|
0 23.75
|
||||||
|
0 23.152298850574709376815
|
||||||
|
|
||||||
|
0 22.152298850574709376815
|
||||||
|
1.32499999999999995559108 22
|
||||||
|
10.2999999999999989341859 22
|
||||||
|
6.02499999999999946709295 22.75
|
||||||
|
0 22.75
|
||||||
|
0 22.152298850574709376815
|
||||||
|
|
||||||
|
0 21.152298850574709376815
|
||||||
|
1.32499999999999995559108 21
|
||||||
|
11 21
|
||||||
|
6.72499999999999964472863 21.75
|
||||||
|
0 21.75
|
||||||
|
0 21.152298850574709376815
|
||||||
|
|
||||||
|
13.9749999999999996447286 1.75
|
||||||
|
20.5 1
|
||||||
|
25 1
|
||||||
|
20.7249999999999978683718 1.75
|
||||||
|
13.9749999999999996447286 1.75
|
||||||
|
|
||||||
|
0 20.152298850574709376815
|
||||||
|
1.32499999999999995559108 20
|
||||||
|
11.6999999999999992894573 20
|
||||||
|
7.42499999999999982236432 20.75
|
||||||
|
0 20.75
|
||||||
|
0 20.152298850574709376815
|
||||||
|
|
||||||
|
0 19.152298850574709376815
|
||||||
|
1.32499999999999995559108 19
|
||||||
|
12.3999999999999985789145 19
|
||||||
|
8.125 19.75
|
||||||
|
0 19.75
|
||||||
|
0 19.152298850574709376815
|
||||||
|
|
||||||
|
0 18.152298850574709376815
|
||||||
|
1.32499999999999995559108 18
|
||||||
|
13.0999999999999996447286 18
|
||||||
|
8.82499999999999928945726 18.75
|
||||||
|
0 18.75
|
||||||
|
0 18.152298850574709376815
|
||||||
|
|
||||||
|
0 17.152298850574709376815
|
||||||
|
1.32499999999999995559108 17
|
||||||
|
13.7999999999999989341859 17
|
||||||
|
9.52499999999999857891453 17.75
|
||||||
|
0 17.75
|
||||||
|
0 17.152298850574709376815
|
||||||
|
|
||||||
|
0 16.152298850574709376815
|
||||||
|
1.32499999999999995559108 16
|
||||||
|
14.5 16
|
||||||
|
10.2249999999999996447286 16.75
|
||||||
|
0 16.75
|
||||||
|
0 16.152298850574709376815
|
||||||
|
|
||||||
|
0 15.1522988505747111531718
|
||||||
|
1.32499999999999995559108 15
|
||||||
|
15.1999999999999992894573 15
|
||||||
|
10.9249999999999989341859 15.75
|
||||||
|
0 15.75
|
||||||
|
0 15.1522988505747111531718
|
||||||
|
|
||||||
|
8.77499999999999857891453 2.75
|
||||||
|
15.2999999999999989341859 2
|
||||||
|
24.2999999999999971578291 2
|
||||||
|
20.0249999999999985789145 2.75
|
||||||
|
8.77499999999999857891453 2.75
|
||||||
|
|
||||||
|
0 14.1522988505747111531718
|
||||||
|
1.32499999999999995559108 14
|
||||||
|
15.8999999999999985789145 14
|
||||||
|
11.625 14.75
|
||||||
|
0 14.75
|
||||||
|
0 14.1522988505747111531718
|
||||||
|
|
||||||
|
0 13.1522988505747111531718
|
||||||
|
1.32499999999999995559108 13
|
||||||
|
16.5999999999999978683718 13
|
||||||
|
12.3249999999999992894573 13.75
|
||||||
|
0 13.75
|
||||||
|
0 13.1522988505747111531718
|
||||||
|
|
||||||
|
0 12.1522988505747111531718
|
||||||
|
1.32499999999999995559108 12
|
||||||
|
17.2999999999999971578291 12
|
||||||
|
13.0249999999999985789145 12.75
|
||||||
|
0 12.75
|
||||||
|
0 12.1522988505747111531718
|
||||||
|
|
||||||
|
0 11.1522988505747111531718
|
||||||
|
1.32499999999999995559108 11
|
||||||
|
18 11
|
||||||
|
13.7249999999999996447286 11.75
|
||||||
|
0 11.75
|
||||||
|
0 11.1522988505747111531718
|
||||||
|
|
||||||
|
0 10.1522988505747111531718
|
||||||
|
1.32499999999999995559108 10
|
||||||
|
18.6999999999999992894573 10
|
||||||
|
14.4249999999999989341859 10.75
|
||||||
|
0 10.75
|
||||||
|
0 10.1522988505747111531718
|
||||||
|
|
||||||
|
0 9.15229885057471115317185
|
||||||
|
1.32499999999999995559108 9
|
||||||
|
19.3999999999999985789145 9
|
||||||
|
15.125 9.75
|
||||||
|
0 9.75
|
||||||
|
0 9.15229885057471115317185
|
||||||
|
|
||||||
|
3.57499999999999973354647 3.75
|
||||||
|
10.0999999999999996447286 3
|
||||||
|
23.5999999999999978683718 3
|
||||||
|
19.3249999999999992894573 3.75
|
||||||
|
3.57499999999999973354647 3.75
|
||||||
|
|
||||||
|
0 8.15229885057471115317185
|
||||||
|
1.32499999999999995559108 8
|
||||||
|
20.0999999999999978683718 8
|
||||||
|
15.8249999999999992894573 8.75
|
||||||
|
0 8.75
|
||||||
|
0 8.15229885057471115317185
|
||||||
|
|
||||||
|
0 7.15229885057471204135027
|
||||||
|
1.32499999999999995559108 7
|
||||||
|
20.7999999999999971578291 7
|
||||||
|
16.5249999999999985789145 7.75
|
||||||
|
0 7.75
|
||||||
|
0 7.15229885057471204135027
|
||||||
|
|
||||||
|
0 6.15229885057471204135027
|
||||||
|
1.32499999999999995559108 6
|
||||||
|
21.5 6
|
||||||
|
17.2249999999999978683718 6.75
|
||||||
|
0 6.75
|
||||||
|
0 6.15229885057471204135027
|
||||||
|
|
||||||
|
0 5.15229885057471204135027
|
||||||
|
1.32499999999999995559108 5
|
||||||
|
22.1999999999999992894573 5
|
||||||
|
17.9249999999999971578291 5.75
|
||||||
|
0 5.75
|
||||||
|
0 5.15229885057471204135027
|
||||||
|
|
||||||
|
0 4.56321839080459756843311
|
||||||
|
4.89999999999999946709295 4
|
||||||
|
22.8999999999999985789145 4
|
||||||
|
18.625 4.75
|
||||||
|
0 4.75
|
||||||
|
0 4.56321839080459756843311
|
||||||
|
|
||||||
|
0 30.75
|
||||||
|
0.42499999999999998889777 30.75
|
||||||
|
4 31
|
||||||
|
1.32499999999999995559108 31
|
||||||
|
0 30.75
|
||||||
|
|
||||||
|
0 29.75
|
||||||
|
1.125 29.75
|
||||||
|
4.69999999999999928945726 30
|
||||||
|
1.32499999999999995559108 30
|
||||||
|
0 29.75
|
||||||
|
|
||||||
|
0 28.75
|
||||||
|
1.82499999999999995559108 28.75
|
||||||
|
5.39999999999999946709295 29
|
||||||
|
1.32499999999999995559108 29
|
||||||
|
0 28.75
|
||||||
|
|
||||||
|
20.5 1
|
||||||
|
19.1749999999999971578291 0.75
|
||||||
|
21.4249999999999971578291 0.75
|
||||||
|
25 1
|
||||||
|
20.5 1
|
||||||
|
|
||||||
|
0 27.75
|
||||||
|
2.52499999999999991118216 27.75
|
||||||
|
6.09999999999999964472863 28
|
||||||
|
1.32499999999999995559108 28
|
||||||
|
0 27.75
|
||||||
|
|
||||||
|
0 26.75
|
||||||
|
3.22499999999999964472863 26.75
|
||||||
|
6.79999999999999982236432 27
|
||||||
|
1.32499999999999995559108 27
|
||||||
|
0 26.75
|
||||||
|
|
||||||
|
0 25.75
|
||||||
|
3.92499999999999982236432 25.75
|
||||||
|
7.5 26
|
||||||
|
1.32499999999999995559108 26
|
||||||
|
0 25.75
|
||||||
|
|
||||||
|
0 24.75
|
||||||
|
4.625 24.75
|
||||||
|
8.19999999999999928945726 25
|
||||||
|
1.32499999999999995559108 25
|
||||||
|
0 24.75
|
||||||
|
|
||||||
|
0 23.75
|
||||||
|
5.32499999999999928945726 23.75
|
||||||
|
8.89999999999999857891453 24
|
||||||
|
1.32499999999999995559108 24
|
||||||
|
0 23.75
|
||||||
|
|
||||||
|
0 22.75
|
||||||
|
6.02499999999999946709295 22.75
|
||||||
|
9.59999999999999964472863 23
|
||||||
|
1.32499999999999995559108 23
|
||||||
|
0 22.75
|
||||||
|
|
||||||
|
0 21.75
|
||||||
|
6.72499999999999964472863 21.75
|
||||||
|
10.2999999999999989341859 22
|
||||||
|
1.32499999999999995559108 22
|
||||||
|
0 21.75
|
||||||
|
|
||||||
|
15.2999999999999989341859 2
|
||||||
|
13.9749999999999996447286 1.75
|
||||||
|
20.7249999999999978683718 1.75
|
||||||
|
24.2999999999999971578291 2
|
||||||
|
15.2999999999999989341859 2
|
||||||
|
|
||||||
|
0 20.75
|
||||||
|
7.42499999999999982236432 20.75
|
||||||
|
11 21
|
||||||
|
1.32499999999999995559108 21
|
||||||
|
0 20.75
|
||||||
|
|
||||||
|
0 19.75
|
||||||
|
8.125 19.75
|
||||||
|
11.6999999999999992894573 20
|
||||||
|
1.32499999999999995559108 20
|
||||||
|
0 19.75
|
||||||
|
|
||||||
|
0 18.75
|
||||||
|
8.82499999999999928945726 18.75
|
||||||
|
12.3999999999999985789145 19
|
||||||
|
1.32499999999999995559108 19
|
||||||
|
0 18.75
|
||||||
|
|
||||||
|
0 17.75
|
||||||
|
9.52499999999999857891453 17.75
|
||||||
|
13.0999999999999996447286 18
|
||||||
|
1.32499999999999995559108 18
|
||||||
|
0 17.75
|
||||||
|
|
||||||
|
0 16.75
|
||||||
|
10.2249999999999996447286 16.75
|
||||||
|
13.7999999999999989341859 17
|
||||||
|
1.32499999999999995559108 17
|
||||||
|
0 16.75
|
||||||
|
|
||||||
|
0 15.75
|
||||||
|
10.9249999999999989341859 15.75
|
||||||
|
14.5 16
|
||||||
|
1.32499999999999995559108 16
|
||||||
|
0 15.75
|
||||||
|
|
||||||
|
10.0999999999999996447286 3
|
||||||
|
8.77499999999999857891453 2.75
|
||||||
|
20.0249999999999985789145 2.75
|
||||||
|
23.5999999999999978683718 3
|
||||||
|
10.0999999999999996447286 3
|
||||||
|
|
||||||
|
0 14.75
|
||||||
|
11.625 14.75
|
||||||
|
15.1999999999999992894573 15
|
||||||
|
1.32499999999999995559108 15
|
||||||
|
0 14.75
|
||||||
|
|
||||||
|
0 13.75
|
||||||
|
12.3249999999999992894573 13.75
|
||||||
|
15.8999999999999985789145 14
|
||||||
|
1.32499999999999995559108 14
|
||||||
|
0 13.75
|
||||||
|
|
||||||
|
0 12.75
|
||||||
|
13.0249999999999985789145 12.75
|
||||||
|
16.5999999999999978683718 13
|
||||||
|
1.32499999999999995559108 13
|
||||||
|
0 12.75
|
||||||
|
|
||||||
|
0 11.75
|
||||||
|
13.7249999999999996447286 11.75
|
||||||
|
17.2999999999999971578291 12
|
||||||
|
1.32499999999999995559108 12
|
||||||
|
0 11.75
|
||||||
|
|
||||||
|
0 10.75
|
||||||
|
14.4249999999999989341859 10.75
|
||||||
|
18 11
|
||||||
|
1.32499999999999995559108 11
|
||||||
|
0 10.75
|
||||||
|
|
||||||
|
0 9.75
|
||||||
|
15.125 9.75
|
||||||
|
18.6999999999999992894573 10
|
||||||
|
1.32499999999999995559108 10
|
||||||
|
0 9.75
|
||||||
|
|
||||||
|
4.89999999999999946709295 4
|
||||||
|
3.57499999999999973354647 3.75
|
||||||
|
19.3249999999999992894573 3.75
|
||||||
|
22.8999999999999985789145 4
|
||||||
|
4.89999999999999946709295 4
|
||||||
|
|
||||||
|
0 8.75
|
||||||
|
15.8249999999999992894573 8.75
|
||||||
|
19.3999999999999985789145 9
|
||||||
|
1.32499999999999995559108 9
|
||||||
|
0 8.75
|
||||||
|
|
||||||
|
0 7.75
|
||||||
|
16.5249999999999985789145 7.75
|
||||||
|
20.0999999999999978683718 8
|
||||||
|
1.32499999999999995559108 8
|
||||||
|
0 7.75
|
||||||
|
|
||||||
|
0 6.75
|
||||||
|
17.2249999999999978683718 6.75
|
||||||
|
20.7999999999999971578291 7
|
||||||
|
1.32499999999999995559108 7
|
||||||
|
0 6.75
|
||||||
|
|
||||||
|
0 5.75
|
||||||
|
17.9249999999999971578291 5.75
|
||||||
|
21.5 6
|
||||||
|
1.32499999999999995559108 6
|
||||||
|
0 5.75
|
||||||
|
|
||||||
|
0 4.75
|
||||||
|
18.625 4.75
|
||||||
|
22.1999999999999992894573 5
|
||||||
|
1.32499999999999995559108 5
|
||||||
|
0 4.75
|
||||||
|
|
||||||
4
lab3/exercise/ex1.2/lake2_regions.txt
Normal file
4
lab3/exercise/ex1.2/lake2_regions.txt
Normal file
@@ -0,0 +1,4 @@
|
|||||||
|
region = lake.{
|
||||||
|
dry & (t == c + 31 & 40*x + 348*t >= 10841 & t >= 31 & 10*x + 57*t <= 1807 & x >= 0 | t == c + 30 & 40*x + 348*t >= 10493 & t >= 30 & 10*x + 57*t <= 1757 & x >= 0 & 4*t <= 123 | t == c + 29 & 40*x + 348*t >= 10145 & t >= 29 & 10*x + 57*t <= 1707 & x >= 0 & 4*t <= 119 | t == c + 28 & 40*x + 348*t >= 9797 & t >= 28 & 10*x + 57*t <= 1657 & x >= 0 & 4*t <= 115 | t == c & 10*x + 57*t <= 257 & 10*x + 87*t >= 257 & 4*t <= 3 | t == c + 27 & 40*x + 348*t >= 9449 & t >= 27 & 10*x + 57*t <= 1607 & x >= 0 & 4*t <= 111 | t == c + 26 & 40*x + 348*t >= 9101 & t >= 26 & 10*x + 57*t <= 1557 & x >= 0 & 4*t <= 107 | t == c + 25 & 40*x + 348*t >= 8753 & t >= 25 & 10*x + 57*t <= 1507 & x >= 0 & 4*t <= 103 | t == c + 24 & 40*x + 348*t >= 8405 & t >= 24 & 10*x + 57*t <= 1457 & x >= 0 & 4*t <= 99 | t == c + 23 & 40*x + 348*t >= 8057 & t >= 23 & 10*x + 57*t <= 1407 & x >= 0 & 4*t <= 95 | t == c + 22 & 40*x + 348*t >= 7709 & t >= 22 & 10*x + 57*t <= 1357 & x >= 0 & 4*t <= 91 | t == c + 21 & 40*x + 348*t >= 7361 & t >= 21 & 10*x + 57*t <= 1307 & x >= 0 & 4*t <= 87 | t == c + 1 & 10*x + 87*t >= 292 & t >= 1 & 10*x + 57*t <= 307 & 4*t <= 7 | t == c + 20 & 40*x + 348*t >= 7013 & t >= 20 & 10*x + 57*t <= 1257 & x >= 0 & 4*t <= 83 | t == c + 19 & 40*x + 348*t >= 6665 & t >= 19 & 10*x + 57*t <= 1207 & x >= 0 & 4*t <= 79 | t == c + 18 & 40*x + 348*t >= 6317 & t >= 18 & 10*x + 57*t <= 1157 & x >= 0 & 4*t <= 75 | t == c + 17 & 40*x + 348*t >= 5969 & t >= 17 & 10*x + 57*t <= 1107 & x >= 0 & 4*t <= 71 | t == c + 16 & 40*x + 348*t >= 5621 & t >= 16 & 10*x + 57*t <= 1057 & x >= 0 & 4*t <= 67 | t == c + 15 & 40*x + 348*t >= 5273 & t >= 15 & 10*x + 57*t <= 1007 & x >= 0 & 4*t <= 63 | t == c + 2 & 10*x + 87*t >= 327 & t >= 2 & 10*x + 57*t <= 357 & 4*t <= 11 | t == c + 14 & 40*x + 348*t >= 4925 & t >= 14 & 10*x + 57*t <= 957 & x >= 0 & 4*t <= 59 | t == c + 13 & 40*x + 348*t >= 4577 & t >= 13 & 10*x + 57*t <= 907 & x >= 0 & 4*t <= 55 | t == c + 12 & 40*x + 348*t >= 4229 & t >= 12 & 10*x + 57*t <= 857 & x >= 0 & 4*t <= 51 | t == c + 11 & 40*x + 348*t >= 3881 & t >= 11 & 10*x + 57*t <= 807 & x >= 0 & 4*t <= 47 | t == c + 10 & 40*x + 348*t >= 3533 & t >= 10 & 10*x + 57*t <= 757 & x >= 0 & 4*t <= 43 | t == c + 9 & 40*x + 348*t >= 3185 & t >= 9 & 10*x + 57*t <= 707 & x >= 0 & 4*t <= 39 | t == c + 3 & 10*x + 87*t >= 362 & t >= 3 & 10*x + 57*t <= 407 & 4*t <= 15 | t == c + 8 & 40*x + 348*t >= 2837 & t >= 8 & 10*x + 57*t <= 657 & x >= 0 & 4*t <= 35 | t == c + 7 & 40*x + 348*t >= 2489 & t >= 7 & 10*x + 57*t <= 607 & x >= 0 & 4*t <= 31 | t == c + 6 & 40*x + 348*t >= 2141 & t >= 6 & 10*x + 57*t <= 557 & x >= 0 & 4*t <= 27 | t == c + 5 & 40*x + 348*t >= 1793 & t >= 5 & 10*x + 57*t <= 507 & x >= 0 & 4*t <= 23 | t == c + 4 & 10*x + 87*t >= 397 & t >= 4 & 10*x + 57*t <= 457 & x >= 0 & 4*t <= 19),
|
||||||
|
rain & (t == c + 30 & 40*x >= 212*t - 6519 & 4*t >= 123 & 143*t >= 10*x + 4393 & t <= 31 | t == c + 29 & 40*x >= 212*t - 6307 & 4*t >= 119 & 143*t >= 10*x + 4243 & t <= 30 | t == c + 28 & 40*x >= 212*t - 6095 & 4*t >= 115 & 143*t >= 10*x + 4093 & t <= 29 | t == c & 10*x >= 53*t + 152 & 4*t >= 3 & 143*t >= 10*x - 107 & t <= 1 | t == c + 27 & 40*x >= 212*t - 5883 & 4*t >= 111 & 143*t >= 10*x + 3943 & t <= 28 | t == c + 26 & 40*x >= 212*t - 5671 & 4*t >= 107 & 143*t >= 10*x + 3793 & t <= 27 | t == c + 25 & 40*x >= 212*t - 5459 & 4*t >= 103 & 143*t >= 10*x + 3643 & t <= 26 | t == c + 24 & 40*x >= 212*t - 5247 & 4*t >= 99 & 143*t >= 10*x + 3493 & t <= 25 | t == c + 23 & 40*x >= 212*t - 5035 & 4*t >= 95 & 143*t >= 10*x + 3343 & t <= 24 | t == c + 22 & 40*x >= 212*t - 4823 & 4*t >= 91 & 143*t >= 10*x + 3193 & t <= 23 | t == c + 21 & 40*x >= 212*t - 4611 & 4*t >= 87 & 143*t >= 10*x + 3043 & t <= 22 | t == c + 1 & 10*x >= 53*t + 47 & 4*t >= 7 & 143*t >= 10*x + 43 & t <= 2 | t == c + 20 & 40*x >= 212*t - 4399 & 4*t >= 83 & 143*t >= 10*x + 2893 & t <= 21 | t == c + 19 & 40*x >= 212*t - 4187 & 4*t >= 79 & 143*t >= 10*x + 2743 & t <= 20 | t == c + 18 & 40*x >= 212*t - 3975 & 4*t >= 75 & 143*t >= 10*x + 2593 & t <= 19 | t == c + 17 & 40*x >= 212*t - 3763 & 4*t >= 71 & 143*t >= 10*x + 2443 & t <= 18 | t == c + 16 & 40*x >= 212*t - 3551 & 4*t >= 67 & 143*t >= 10*x + 2293 & t <= 17 | t == c + 15 & 40*x >= 212*t - 3339 & 4*t >= 63 & 143*t >= 10*x + 2143 & t <= 16 | t == c + 2 & 10*x >= 53*t - 58 & 4*t >= 11 & 143*t >= 10*x + 193 & t <= 3 | t == c + 14 & 40*x >= 212*t - 3127 & 4*t >= 59 & 143*t >= 10*x + 1993 & t <= 15 | t == c + 13 & 40*x >= 212*t - 2915 & 4*t >= 55 & 143*t >= 10*x + 1843 & t <= 14 | t == c + 12 & 40*x >= 212*t - 2703 & 4*t >= 51 & 143*t >= 10*x + 1693 & t <= 13 | t == c + 11 & 40*x >= 212*t - 2491 & 4*t >= 47 & 143*t >= 10*x + 1543 & t <= 12 | t == c + 10 & 40*x >= 212*t - 2279 & 4*t >= 43 & 143*t >= 10*x + 1393 & t <= 11 | t == c + 9 & 40*x >= 212*t - 2067 & 4*t >= 39 & 143*t >= 10*x + 1243 & t <= 10 | t == c + 3 & 10*x >= 53*t - 163 & 4*t >= 15 & 143*t >= 10*x + 343 & t <= 4 | t == c + 8 & 40*x >= 212*t - 1855 & 4*t >= 35 & 143*t >= 10*x + 1093 & t <= 9 | t == c + 7 & 40*x >= 212*t - 1643 & 4*t >= 31 & 143*t >= 10*x + 943 & t <= 8 | t == c + 6 & 40*x >= 212*t - 1431 & 4*t >= 27 & 143*t >= 10*x + 793 & t <= 7 | t == c + 5 & 40*x >= 212*t - 1219 & 4*t >= 23 & 143*t >= 10*x + 643 & t <= 6 | t == c + 4 & 40*x >= 212*t - 1007 & 4*t >= 19 & 143*t >= 10*x + 493 & t <= 5)
|
||||||
|
};
|
||||||
BIN
lab3/phaver
Executable file
BIN
lab3/phaver
Executable file
Binary file not shown.
2
lab3/phaverplot.gp
Normal file
2
lab3/phaverplot.gp
Normal file
@@ -0,0 +1,2 @@
|
|||||||
|
set offsets graph 0.1, 0.1, 0.1, 0.1
|
||||||
|
plot ARG1 using 1:2 with filledcurves
|
||||||
Reference in New Issue
Block a user