From 09fec192320c6c9f55235b7aeb7ad6b32be0f2cc Mon Sep 17 00:00:00 2001 From: Mariano Sciacco <34033090+Maxelweb@users.noreply.github.com> Date: Wed, 22 Dec 2021 16:19:50 +0100 Subject: [PATCH] add lab3 exercises --- lab3/README.md | 18 ++ lab3/examples/bouncing.pha | 57 ++++ lab3/examples/bouncing_timed.pha | 81 ++++++ lab3/examples/evader.pha | 63 ++++ lab3/examples/evader2.pha | 59 ++++ lab3/examples/txt/evader.txt | 16 + lab3/examples/txt/evader_regions.txt | 4 + lab3/exercise/ex1.1/lake.pdf | Bin 0 -> 9439 bytes lab3/exercise/ex1.1/lake.pha | 40 +++ lab3/exercise/ex1.1/lake.txt | 5 + lab3/exercise/ex1.1/lake_regions.txt | 3 + lab3/exercise/ex1.2/lake2.pdf | Bin 0 -> 11822 bytes lab3/exercise/ex1.2/lake2.pha | 47 +++ lab3/exercise/ex1.2/lake2.txt | 404 ++++++++++++++++++++++++++ lab3/exercise/ex1.2/lake2_regions.txt | 4 + lab3/phaver | Bin 0 -> 4259448 bytes lab3/phaverplot.gp | 2 + 17 files changed, 803 insertions(+) create mode 100644 lab3/README.md create mode 100644 lab3/examples/bouncing.pha create mode 100644 lab3/examples/bouncing_timed.pha create mode 100644 lab3/examples/evader.pha create mode 100644 lab3/examples/evader2.pha create mode 100644 lab3/examples/txt/evader.txt create mode 100644 lab3/examples/txt/evader_regions.txt create mode 100644 lab3/exercise/ex1.1/lake.pdf create mode 100644 lab3/exercise/ex1.1/lake.pha create mode 100644 lab3/exercise/ex1.1/lake.txt create mode 100644 lab3/exercise/ex1.1/lake_regions.txt create mode 100644 lab3/exercise/ex1.2/lake2.pdf create mode 100644 lab3/exercise/ex1.2/lake2.pha create mode 100644 lab3/exercise/ex1.2/lake2.txt create mode 100644 lab3/exercise/ex1.2/lake2_regions.txt create mode 100755 lab3/phaver create mode 100644 lab3/phaverplot.gp diff --git a/lab3/README.md b/lab3/README.md new file mode 100644 index 0000000..a0cfc63 --- /dev/null +++ b/lab3/README.md @@ -0,0 +1,18 @@ +# CPS Lab 3 Exercise (2021-12-22) + +- Mariano Sciacco +- Federico Carboni +- Giuseppe Rossano +- Alessandro Benetti + +## Notes + +> Note 1: requires `gnuplot` and `phaverlite` (see https://www.cs.unipr.it/~zaffanella/PPLite/PHAVerLite) + +> Note 2: all credits to `phaver` executable in this folder goes to Enea Zaffanella + +> Note 3: execute `./phaver ` to compile the `.pha` file + +> Note 4: execute `gnuplot --persist -c phaverplot.gp filename.txt` to generate the graph + +> Note 5: results of the plot are inside the respective folders as pdf files. diff --git a/lab3/examples/bouncing.pha b/lab3/examples/bouncing.pha new file mode 100644 index 0000000..d41b27e --- /dev/null +++ b/lab3/examples/bouncing.pha @@ -0,0 +1,57 @@ +// ---------------------------------------------------------- +// Hybrid System Example: Bouncing Ball +// ---------------------------------------------------------- + +// ---------------------------------------------------------- +// Constants +// ---------------------------------------------------------- +g:=1; // constant for gravity + +// ---------------------------------------------------------- +// System Description +// ---------------------------------------------------------- +automaton bouncing_ball +contr_var: v, x; +synclabs: jump; +loc state: while x>=0 & x<=10 & v<=10 & v>=-10 wait {x'==v & v'==-g} + when x==0 & v<0 sync jump do {v'==-v*0.5 & x'==x} goto state; +initially: state & x==2 & v==0; +end + +// ---------------------------------------------------------- +// Define Partitioning +// ---------------------------------------------------------- +// Add a new label for the transitions that are introduced +// between partitions +bouncing_ball.add_label(tau); + +// Define the directions of the partitions +// here: in both axes with a min. threshold of partition size 0.2 +bouncing_ball.set_refine_constraints((x, 0.2),(v,0.2),tau); + +// With this partitioning we can use convex hull overapproximations, +// resulting in fewer polyhedra (one per partition) +//REACH_USE_CONVEX_HULL=true; + +// ---------------------------------------------------------- +// Define Partitioning (alternative) +// ---------------------------------------------------------- +// We can also just partition in the v-direction, but then we must turn off +// the convex hull (try it...) +// bouncing_ball.set_refine_constraints((v,0.2),tau); +// REACH_USE_CONVEX_HULL=false; + +// ---------------------------------------------------------- +// Analysis Commands +// ---------------------------------------------------------- +reg=bouncing_ball.reachable; + +// ---------------------------------------------------------- +// Saving Data for Graphical Output +// ---------------------------------------------------------- +reg.print("out_reach",2); // output as a list of vertices + +// for display with graph use, e.g.: +// graph -T X -C -B -q0.5 out_reach +// for display with matlab use, e.g.: +// plot_2d_vertices('out_m_reach') diff --git a/lab3/examples/bouncing_timed.pha b/lab3/examples/bouncing_timed.pha new file mode 100644 index 0000000..138e5b0 --- /dev/null +++ b/lab3/examples/bouncing_timed.pha @@ -0,0 +1,81 @@ +// ---------------------------------------------------------- +// Hybrid System Example: Bouncing Ball +// ---------------------------------------------------------- +// This version produces a plot of position over time. +// A clock is added to the system to model time explicitly. +// This gives us a another choice of partitioning: along +// the time-axis. It's fast, but doesn't work with convex +// hull. +// +// The complexity of this example requires us to put limits +// on the bits used in polyhedral computations. +// Otherwise, it may take very long or not terminate at all. +REACH_CONSTRAINT_LIMIT = 48; +REACH_CONSTRAINT_TRIGGER = 96; +CONSTRAINT_BITSIZE = 24; +REACH_BITSIZE_TRIGGER = 200; +// ---------------------------------------------------------- +// Constants +// ---------------------------------------------------------- +g:=1; // constant for gravity + +// ---------------------------------------------------------- +// System Description +// ---------------------------------------------------------- +automaton bouncing_ball +contr_var: t, x, v; +synclabs: jump; +loc state: while x>=0 & x<=10 & v<=10 & v>=-10 & t<=5 & t>=0 wait {x'==v & v'==-g & t'==1} + when x==0 & v<0 sync jump do {v'==-v*0.5 & x'==x & t'==t} goto state; +initially: state & x==2 & v==0 & t==0; +end + +// ---------------------------------------------------------- +// Define Partitioning +// ---------------------------------------------------------- +// Add a new label for the transitions that are introduced +// between partitions +bouncing_ball.add_label(tau); + +// Define the directions of the partitions +// here: in both axes with a min. threshold of partition size 0.2 +bouncing_ball.set_refine_constraints((x, 0.2),(v,0.2),tau); + +// With this partitioning we can use convex hull overapproximations, +// resulting in fewer polyhedra (one per partition) +//REACH_USE_CONVEX_HULL=true; + +// ---------------------------------------------------------- +// Define Partitioning (alternative 1) +// ---------------------------------------------------------- +// We can also just partition in the v-direction, but then +// we must turn off convex hull (try it...) +// bouncing_ball.set_refine_constraints((v,0.2),tau); +// REACH_USE_CONVEX_HULL=false; + +// ---------------------------------------------------------- +// Define Partitioning (alternative 2) +// ---------------------------------------------------------- +// We can also just partition in the t-direction, but then +// we must turn off convex hull +// and refine the time-elapse operator at least twice +// at every step (try it...) +//TIME_POST_ITER=2; +//bouncing_ball.set_refine_constraints((t, 0.1),tau); +//REACH_USE_CONVEX_HULL=false; + +// ---------------------------------------------------------- +// Analysis Commands +// ---------------------------------------------------------- +reg=bouncing_ball.reachable; + +// ---------------------------------------------------------- +// Saving Data for Graphical Output +// ---------------------------------------------------------- +reg.project_to(t, x); // remove v to get a 2-dim output +reg.print("out_reach",2); // output as a list of vertices + +// for display with graph use, e.g.: +// graph -T X -C -B -q0.5 out_reach +// for display with matlab use, e.g.: +// plot_2d_vertices('out_m_reach') diff --git a/lab3/examples/evader.pha b/lab3/examples/evader.pha new file mode 100644 index 0000000..78cebca --- /dev/null +++ b/lab3/examples/evader.pha @@ -0,0 +1,63 @@ +// Constants definition +// + +// Automaton definition +// +automaton evader +contr_var: e, p, x; // e position of the evader + // p position of the pursuer + // x timer +synclabs: jump; +loc ClkW: + while 0 <= e <= 40 & 0 <= p <= 40 & x <= 2 wait + {e'==5 & -0.5 <= p' <= 6 & x'==1} + when (p == 0) sync jump do {e'==e & p'==40 & x'==x} goto ClkW; + when (p == 40) sync jump do {e'==e & p'==0 & x'==x} goto ClkW; + when (x >= 2) & (0 < e < 40) & (6*e - 5*p > 40) sync jump do + {e'==e & p'==p & x'==0} goto ClkW; + when (x >= 2) & (0 < e < 40) & (6*e - 5*p <= 40) sync jump do + {e'==e & p'==p & x'==0} goto CntrClkW; + when (e == 0) sync jump do {e'==e & p'==p & x'==x} goto Rescued; + when (e == 40) sync jump do {e'==e & p'==p & x'==x} goto Rescued; +loc CntrClkW: + while 0 <= e <= 40 & 0 <= p <= 40 & x <= 2 wait + {e'==-5 & -0.5 <= p' <= 6 & x'==1} + when (p == 0) sync jump do {e'==e & p'==40 & x'==x} goto CntrClkW; + when (p == 40) sync jump do {e'==e & p'==0 & x'==x} goto CntrClkW; + when (x >= 2) & (0 < e < 40) & (6*e - 5*p > 40) sync jump do + {e'==e & p'==p & x'==0} goto ClkW; + when (x >= 2) & (0 < e < 40) & (6*e - 5*p <= 40) sync jump do + {e'==e & p'==p & x'==0} goto CntrClkW; + when (e == 0) sync jump do {e'==e & p'==p & x'==x} goto Rescued; + when (e == 40) sync jump do {e'==e & p'==p & x'==x} goto Rescued; +loc Rescued: + while true wait {e'==0 & p'==0 & x'==0 }; + +initially: ClkW & x == 2 & e == 20 & p == 10; +end + +// Compute the reachable set +// +region=evader.reachable; +// +// Output to file +// +// List regions (pairs of locations names and linear formulas) +region.print("evader_regions.txt", 0); +// Sequence of vertices in floating point form. +// Can be plotted with gnuplot +// Project on e and p +region.project_to(e, p); +region.print("evader.txt", 2); + +// Safety verification +// +// definition of bad states +forbidden = evader.{$ & e == p}; +reach_set = evader.is_reachable(forbidden); +reach_set.intersection_assign(forbidden); + +echo "The intersection between the reachable set and the bad region is:"; +reach_set.is_empty; + + \ No newline at end of file diff --git a/lab3/examples/evader2.pha b/lab3/examples/evader2.pha new file mode 100644 index 0000000..bb2a5a0 --- /dev/null +++ b/lab3/examples/evader2.pha @@ -0,0 +1,59 @@ +// Constants definition +// + +// Automaton definition +// +automaton evader +contr_var: e, p, x, p_zero; // e position of the evader + // p position of the pursuer + // x timer + // p_zero "frozen variable" that stores the + // initial position of the pursuer +synclabs: jump; +loc ClkW: + while 0 <= e <= 40 & 0 <= p <= 40 & x <= 2 wait + {e'==5 & -0.5 <= p' <= 6 & x'==1 & p_zero'==0} + when (p == 0) sync jump do {e'==e & p'==40 & x'==x & p_zero'==p_zero} goto ClkW; + when (p == 40) sync jump do {e'==e & p'==0 & x'==x & p_zero'==p_zero} goto ClkW; + when (x >= 2) & (0 < e < 40) & (6*e - 5*p > 40) sync jump do + {e'==e & p'==p & x'==0 & p_zero'==p_zero} goto ClkW; + when (x >= 2) & (0 < e < 40) & (6*e - 5*p <= 40) sync jump do + {e'==e & p'==p & x'==0 & p_zero'==p_zero} goto CntrClkW; + when (e == 0) sync jump do {e'==e & p'==p & x'==x & p_zero'==p_zero} goto Rescued; + when (e == 40) sync jump do {e'==e & p'==p & x'==x & p_zero'==p_zero} goto Rescued; +loc CntrClkW: + while 0 <= e <= 40 & 0 <= p <= 40 & x <= 2 wait + {e'==-5 & -0.5 <= p' <= 6 & x'==1 & p_zero'==0} + when (p == 0) sync jump do {e'==e & p'==40 & x'==x & p_zero'==p_zero} goto CntrClkW; + when (p == 40) sync jump do {e'==e & p'==0 & x'==x & p_zero'==p_zero} goto CntrClkW; + when (x >= 2) & (0 < e < 40) & (6*e - 5*p > 40) sync jump do + {e'==e & p'==p & x'==0 & p_zero'==p_zero} goto ClkW; + when (x >= 2) & (0 < e < 40) & (6*e - 5*p <= 40) sync jump do + {e'==e & p'==p & x'==0 & p_zero'==p_zero} goto CntrClkW; + when (e == 0) sync jump do {e'==e & p'==p & x'==x & p_zero'==p_zero} goto Rescued; + when (e == 40) sync jump do {e'==e & p'==p & x'==x & p_zero'==p_zero} goto Rescued; +loc Rescued: + while true wait {e'==0 & p'==0 & x'==0 & p_zero'==0}; + +initially: ClkW & x == 2 & e == 20 & p == p_zero & 0 <= p <= 40; +end + +// Find winning starting points for pursuer +// +// Compute the reachable set +// +region=evader.reachable; +// Intersect with states where pursuer wins +forbidden = evader.{$ & e == p}; +region.intersection_assign(forbidden); +// Project on p_zero to get the initial position for the pursuer for which the +// pursuer can win the game +region.project_to(p_zero); +// union over all locations +pursuer_wins = region.loc_union; + +echo "The pursuer can win the game if it starts from:"; +pursuer_wins.print; + + + \ No newline at end of file diff --git a/lab3/examples/txt/evader.txt b/lab3/examples/txt/evader.txt new file mode 100644 index 0000000..dee27fb --- /dev/null +++ b/lab3/examples/txt/evader.txt @@ -0,0 +1,16 @@ +20 10 + +20 10 +30 9 +30 22 +20 10 + +30 22 +30 9 +40 8 +40 34 +30 22 + +40 8 +40 34 + diff --git a/lab3/examples/txt/evader_regions.txt b/lab3/examples/txt/evader_regions.txt new file mode 100644 index 0000000..5a1dd67 --- /dev/null +++ b/lab3/examples/txt/evader_regions.txt @@ -0,0 +1,4 @@ +region = evader.{ +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), +Rescued & x == 2 & e == 40 & 8 <= p <= 34 +}; \ No newline at end of file diff --git a/lab3/exercise/ex1.1/lake.pdf b/lab3/exercise/ex1.1/lake.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2808a4d72ee1fbad8575330afe944442c13ed4fd GIT binary patch literal 9439 zcmb7q1yqz@&^IB1AV>*<3M)v*vg8ti$kHi|bS$_u?9$S$ND4?ww{%Ddh=fQtl7b3I zgOud^Ea<=dzVn{3>}APhbXP7KKTKlg8DgqtTFYdZ^k zu!^w-90}q97*zi;fcK99lCCIeH54!*K3Gj0gmQF3zbJyZIJvm-!KTI_2qza{h4@7) zE~^GIH?~He^B5zoKwu?1TlnAl@ck063rvqf!5wWuU>MvPVG383exUzbY5qTSK6a}&U-aHO4+qbXn$gzJJLZfk1?^h3~&SH%Y_!p#uI5A0k) zy6Ap>UciF$2gD2g{i^>DPn=8ny2HUg z8;90X7xb6^&<^>nxB}eP0`(Xqc%iEl!WwWo2rOj{tS1a^YG(#V%R-`nO=yGfn*1$M z-fj{~+_7;?E<&jtw1KNaK5jONb&nj+IxV=3hT=Oxpc?Pwd#@7)mdQlpykh+bwh<>{ z`O^ps87r@hJdzTF;?o7%#_htS5lXL`>6xOJgf_9wSbqu#o;h-u}{8D23(sZZogJo*8t;oUKD`jN zhf|?f*y|ppmJk?pAO}&qMj=_t61>YCuzu_Z0rwt9e<>opBQ+S%cPj>qPVFJYf81MKusQPtN5@@k01ui=sGLGK8% zes!3rPfVtsO-bGS)+z#q6+iOZoRGCnfQJqCx@=*&`%`XXxbo5PB6#>~tnk`nzO^P3 zl;}u-IZSCw9@=gB(GY`I#bfwyKku)5k|tri@N%)O3v9KcYT*3$U>HJ8c1gtZj->I- zOXM71*HX6n87J`)he3fi<+y8qmZBgND(yDHJlxHop`~03Y`0gB2Tl`ky>rb+>x+0y z^-I_`|0A*`m6w7GdagY@?zN%@_wA&?V;zNCpt_|uj={>$S^)c=Y3YqF1r{vGNLLlG zfaVnaGFsTw)@=q^FQ-OCUVhdy< zw7e*DW-^D;0ZW?HQ#=dS14do;9HtcR*Cd1(QdFk~q-cq2uT(ke-88OzEtxSy{B!1| zbjiY+0IJWgOTtK}D>kjs*F7IT%#vE%@r2ewPTFDbS!jO5JC|3C{2NENck&<52FB&& z*Pb+1i4?c%Ysr%e{k#zgcV7_nd@y6}smJX^xc~TP=A(vwVZZ&j#mUDJM|&o$iP80q zo$pXGvy9#m6CEOdpY>7toW0LZKFB5NuGwrQ;gpLhQSPOrBylQL$_Y`< z!G44icUXHt#Zg`>h01 z5uG0$c22yBk~TlrVm~ThTh$f_SUH`GA-on27gG{!A5#uzDuh*-R^oYl>o9N|ubbXy z%{pum3i%i z>Or~V6zv=}d26wKDtDl{WSgUDc5<|_?{zZk6%`7@OOR}oZ3uvUVbiTCzM+FDy#L=WP{YeDkECS6Sw^|4P@8j+G1hcC5wcI)Y*k z9(UEo&ynQaW#DDixZrK$haqMBI`)MvedxtMzxN_tc z2zFR-u+u21n(7wd+FQ8mZt+uuX4X4$s#BozK-T?d_&3p(-VJ4(>*e94F-%sJk53gAadGtMw$mHWbLFJ+o<%OI*)R5Yx;&BVxl*n@m2WuNSZ(w0eMS(DQ`Pe- z`FM7HY)YGF6Jyn2ow}^r{Nn2M*|(I>X&W8eV%bDb*Chr|Puga!XQOV-RGW4bTc|y~ z%aU(lI-nSuNGAPsHif59X#zQ0;_WeZPxVA^uVOTaAp2&q*ueqeSYJ}pjjSeIsF?N- zk^~7(>_Uw1KU0Gw*P08wI5%xD59 zu3!IoKnCKNMrtXZ`F1=jp)~YZb&z#GhJ0tuU)#bCj<^k;(QVitcaRnGQlO4$52wYp znPqIPA*{>}s1z6-E7FR3)6 z&*!WK<+JL}HtpNWF0b!$ns2LYMYP*SW#R0~8(6>HG(mi6$K9B?5uJMK-qEvAHRhA+ z<*IX{htNKHXA>$;gTx>I%2JvZtcSrZ_k5=MusX13w`cdcRYR3zgu0%Zh{JsBR+1%! z_hIq=uJYt*gRAz$7F|a&0ac`w!qbl5mZ(LW7QcK>}T0A*QCF85; 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+ +echo "The intersection between the reachable set and the bad region is:"; +reach_set.is_empty; + + + + \ No newline at end of file diff --git a/lab3/exercise/ex1.1/lake.txt b/lab3/exercise/ex1.1/lake.txt new file mode 100644 index 0000000..93bf7a5 --- /dev/null +++ b/lab3/exercise/ex1.1/lake.txt @@ -0,0 +1,5 @@ +0 4.94230769230769162447814 +25.6999999999999992894573 0 +0 36.714285714285708195348 +0 4.94230769230769162447814 + diff --git a/lab3/exercise/ex1.1/lake_regions.txt b/lab3/exercise/ex1.1/lake_regions.txt new file mode 100644 index 0000000..257ea88 --- /dev/null +++ b/lab3/exercise/ex1.1/lake_regions.txt @@ -0,0 +1,3 @@ +region = lake.{ +single & 10*x + 7*t <= 257 & 10*x + 52*t >= 257 & x >= 0 +}; \ No newline at end of file diff --git a/lab3/exercise/ex1.2/lake2.pdf b/lab3/exercise/ex1.2/lake2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f67a0675e17d44f51df046d4e8686da8cd63f894 GIT binary patch literal 11822 zcmb7q1yodB7d9z4G)PGeASE%(07G|ocS#I5NI7&$DIg*x0+N!_-5m-jN{1lQUD6Hz zfNy>8_x|J9S`3h?v0V%ySl;rKQ6 zn4{|-A%moy99@x*E3O;E998K+`lD~j*d>q_u!kvYXLy2Fl)Gll#?gW z_~t#77de943&<<*=dI~KGI8tW&-s#evUfsgJ6l-6fH%{pA+7BUycrA9?al4qgSdUR z{Zk;1u<*KZ3HmFEx90NN7QmZC-zNUAOduWKsLCP7b*m-E59I$#$w1xG4rX=x0;%+O zLT?9m6Qwcmul(I4HE5gbo1D zl%*8qD4JTL=f}tT2a^&;s$}UBgg~uL6hjQc2fzqmgv4tS3YSP$v&EgzO)SF)8$T4% z-tHV4yx_|k9=7H)G+jJ>!Bcv5vb{4b{w&3;+3R>`t@CR4YvUJ)Pow>_+>03}qxKNk znRBymikR6?v!A)GQBkM!hr}E?QR*A=wtKe9r-|2B<4YiORq-NzhwH*51*{xZ6Q7N% zB=5;g&*SBOa=uFst>N^c>lyWDms1ec88g;CANx4)(`%9E7O%3!O@ErE2sy%coRx6A zTe9#Z@=#pyW{(&ji+2-}=Y3ry6ZS~}y&^coaoAs2>Pg-D;(zh0b7}OgZo>EusI+A_ zZfN*?XDFmNyvonBwfgL8YONL?GP;v{JY(M1BxgzPE?cVK;-5aevA>^e%_QOsOdIq+p;ahftltCE)=?NiDPBSg~toR&nI# z({GCuwSCM2r5#=*{wvT{d*bOF;2b!i4zY!p4Pc*=`%0x9)u`xgDufP5R!`Io^B*m4nGS_)HJ@@2(deC>d_6jMU%D z)_m7o{YjLZR75Qqgc(u*nR6iK^Ny3*REm>P5eJ38$r04@U+7Q%)eYaz3D9V!0Egdi zR%CF`QDn$XPmr0+k*nQtN`cNr4KFLBz8CTo46pmitl2!otU21R%%F6BR`#_API4vS za0QU~VBU3Lci>*DQ(D!SQ;=R~4ESR2dj;(Y7fud^?=J;wSShNM$~g^1n8K$mkmew& z(IPTc+ifq}ysrraQk;U|W@O(WWZxiU-)8=rmE&XS^;F&|P;)Wtk1W|}3Luq&j?=aH zt2FrG>Pk)ra;i2k-$UBH(bi5dVz=*BrK{75v2Ug9Rf5&nh2ifMsV;r>uC%8vHW%I^ zimAq(O06W3e&SU z6SMmtV7Bq+Wq2FoW^y&d?F7+RbmpHUu77k~yloYz#KXxs>}~MeQg+skJgCRP(!FER3 zXEvY3-$`G75}w;gmk?fvD}?2zma*vL2y5i`hBYAEvfD@)QV-cNbn{yAly);-k-9Az zmc3YOa>*F?f1XkGHh4a?Ha3pjO*cxM9VWRVF@7eeff2-T6w=T%QCz|xoU|;lB9Uh- zNf{dq*}Us!VC`qo?mZwlAV^3NR3V4|xq@Xx^NY~VgMe>=j$b1)QsRRVn|I+cZtly5 z-?4?T8Y)dSbSOby{;RF`PIcrb;<$ZU+wz)*j5Jh~}bD)riTittT5 zxxv>jLb5Cy?=aax*&4O{WCmM{n0otje9DAw1%-JvA6zmTsc?#p_RtDN2?|<>Bh^R? z>{v>-HI9+0G>e!ur%!pMl}36;g_f2^Y1ZfTGUdG@hhv;(1Jznu&LqvgWYC84m2io4 z9m@-iqyyYIh&a#lHA<4t07TDF7mvD$-pkSw8BP3pHz}2+{m2{y$~I^%UyqB`_nU`J zm(722vl$9&e3|Q)J!5dF_@z*6x5BY0;V@_2$V{Q!-)fX4mV9EFB~boSM#XlT5&tk|Nl0JU zz62PAdEiIiT^56|NQJ?q*)rYgrFerh05w7teCz2VP<7lO`Yy;GP0K@cUbIvE zSxM}iSJa`UEhvE!uhHuWq?j2?=biv0XrjkaT7n09dSDZifzfvsApr|O49FgNjU3Q5 z@C0X`58Lfk%JcL$m|KLlXnfSG7wB1%WbwzIc0*jD2(J_{g;?hg|N!qYfqt)!U>B4rUhwqg;6I;OJk!xCG1iqL{JQ(DGP)E2zMlWG2TCa z@AB17SPCud2@pSsu;T?l#@zWi867?9B4hLp#oXPMdu?ZoorobS35UPN00FiCU+>}#D;Ps*iP4n^p57v z2cX^rc-gxW-di58!auvzf?EXk^;t`>ZHuU&V3$fhVn2DkUneRN4<;

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b/lab3/exercise/ex1.2/lake2.pha @@ -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; + + + + \ No 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<= 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) +}; \ No newline at end of file diff --git a/lab3/phaver b/lab3/phaver new file 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