started with 4

diff --git a/.gitignore b/.gitignore
index 6f82654..0dd8aea 100644 (file)
--- a/.gitignore
+++ b/.gitignore
@@ -2,3 +2,5 @@
 *.aux
 *.pdf
 *.dvi
+NuSMV
+nusmv

diff --git a/e3.tex b/e3.tex
index 33bcca5..4c5e97d 100644 (file)
--- a/e3.tex
+++ b/e3.tex
@@ -37,21 +37,24 @@
                Sat(\forall(a\un \forall\ev c))=\{s_0,s_1,s_4\}\\
                \{s_0\}\subseteq \{s_0,s_1,s_4\}\text{ thus }\Phi_2\text{ is satisfied} $
        \item 
+               
        \item
                For formula:
                $$\varphi:=\al(a\ra(\neg b\un(a\wedge b)))$$
                We create an automaton $\neg\varphi$ where
-               $$\begin{array}{rl}
+               $$\begin{array}{rlr}
                        \neg\varphi 
                        & :=\ev\neg(a\ra(\neg b\un(a\wedge b)))\\
                        & :=\ev(a\wedge\neg(\neg b\un(a\wedge b)))\\
-                       & :=\ev(a\wedge(\al\neg b\vee
-                               
-                               
+                       & :=\ev(a\wedge(\al\neg b\vee(\neg b\un(a\wedge b))))\\
+                       & :=\ev(a\wedge\al\neg b)\vee\ev(a\wedge(\neg b\un(a\wedge b)))\\
+                       & :=\ev(a\wedge\neg\ev b) & \ev(a\wedge(\neg b\un(a\wedge b)))\\
                \end{array}$$
-               Elementary sets:
-               $$\begin{array}{lll}
-                       a & b & 
+               Elementary sets for $\varphi=\ev(a\wedge\neg\ev b)$ where
+               $\psi=a\wedge\neg\ev b$:
+               $$\begin{array}{llll}
+                       a & b & \varphi & \ev\psi\\
+                       a & b & \varphi & \ev\psi\\
                \end{array}$$
 \end{enumerate}
 \end{document}

diff --git a/e41.smv b/e41.smv
new file mode 100644 (file)
index 0000000..3cbf9c1
--- /dev/null
+++ b/e41.smv
@@ -0,0 +1,46 @@
+MODULE proc(i, s, yme, yother)
+VAR
+       line: {l2, l3, l4, l7, l8};
+ASSIGN
+       init(line):=l2;
+       next(line):=case
+               line=l2: l3;
+               line=l3: l4;
+               line=l4: case
+                       !(yother=0 | s!=i) : l4;
+                       TRUE: l7;
+               esac;
+               line=l7: l8;
+               line=l8: l2;
+       esac;
+
+MODULE main
+VAR
+       y0: 0..1;
+       y1: 0..1;
+       s: 0..1;
+       proc0: proc(0, s, y0, y1);
+       proc1: proc(1, s, y1, y0);
+ASSIGN
+       next(y0):=case
+               proc0.line=l3: 1;
+               proc0.line=l8: 0;
+               TRUE: y0;
+       esac;
+       next(y1):=case
+               proc1.line=l3: 1;
+               proc1.line=l8: 0;
+               TRUE: y1;
+       esac;
+       next(s):=case
+               proc0.line=l3 & proc1.line=l3: {0,1};
+               proc0.line=l3: 0;
+               proc1.line=l3: 1;
+               TRUE: s;
+       esac;
+
+--Mutual exclusion
+LTLSPEC G(!(proc0.line=l7 & proc1.line=l7))
+
+--Absence of starvation
+LTLSPEC G (F(proc0.line=l7) & F(proc1.line=l7))

diff --git a/e42.smv b/e42.smv
new file mode 100644 (file)
index 0000000..a142f73
--- /dev/null
+++ b/e42.smv
@@ -0,0 +1,76 @@
+MODULE phil(leftfork, rightfork)
+VAR
+       state: {none, left, both};
+ASSIGN
+       init(state) := none;
+       next(state) := case
+               state=none: case
+                       leftfork=inuse: none;
+                       TRUE: left;
+               esac;
+               state=left: case
+                       rightfork=inuse: left;
+                       TRUE: both;
+               esac;
+               TRUE: none;
+       esac;
+
+MODULE main
+VAR
+       f: array 0..6 of {free, inuse};
+       ph0: phil(f[6], f[1]);
+       ph1: phil(f[0], f[2]);
+       ph2: phil(f[1], f[3]);
+       ph3: phil(f[2], f[4]);
+       ph4: phil(f[3], f[5]);
+       ph5: phil(f[4], f[6]);
+       ph6: phil(f[5], f[0]);
+ASSIGN
+       init(f[0]):=free;
+       init(f[1]):=free;
+       init(f[2]):=free;
+       init(f[3]):=free;
+       init(f[4]):=free;
+       init(f[5]):=free;
+       init(f[6]):=free;
+
+       next(f[0]) := case
+               ph6.state=both | ph1.state=left | ph0.state=both: inuse;
+               TRUE: free;
+       esac;
+       next(f[1]) := case
+               ph0.state=both | ph2.state=left | ph2.state=both: inuse;
+               TRUE: free;
+       esac;
+       next(f[2]) := case
+               ph1.state=both | ph3.state=left | ph3.state=both: inuse;
+               TRUE: free;
+       esac;
+       next(f[3]) := case
+               ph2.state=both | ph4.state=left | ph4.state=both: inuse;
+               TRUE: free;
+       esac;
+       next(f[4]) := case
+               ph3.state=both | ph5.state=left | ph5.state=both: inuse;
+               TRUE: free;
+       esac;
+       next(f[5]) := case
+               ph4.state=both | ph6.state=left | ph6.state=both: inuse;
+               TRUE: free;
+       esac;
+       next(f[6]) := case
+               ph5.state=both | ph0.state=left | ph0.state=both: inuse;
+               TRUE: free;
+       esac;
+LTLSPEC F(
+       G(ph0.state=left) | 
+       G(ph1.state=left) | 
+       G(ph2.state=left) | 
+       G(ph3.state=left) | 
+       G(ph4.state=left) | 
+       G(ph5.state=left) | 
+       G(ph6.state=left))
+--LTLSPEC G(
+--     (F (ph0.state=both)) & (F (ph1.state=both)) & (F (ph2.state=both)) &
+--     (F (ph3.state=both)) & (F (ph4.state=both)) & (F (ph5.state=both)) &
+--     (F (ph6.state=both)))