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Suppose I have following structure M = (S, R, L) where S = {s0, s1, s2} is the set of possible states, R is a transition relation such that: s0 -> s1, s0 -> s2, s1 -> s0, s1 -> s2, and s2 -> s2, and L is the labeling function for each state defined by: L(s0) = {p, q}, L(s1) = {q, r}, and L(s2) = {r}. I am using notations describe in Logic in Computer Science textbook by Huth and Ryan.

Clearly, from such model, we have X r is satisfied in s0 (the initial state), since r is satisfied in s1 and s2. My NuSMV code for the Kripke structure is as follows (as described here).

MODULE main
VAR
    p : boolean;
    q : boolean;
    r : boolean;
    state : {s0, s1, s2};

ASSIGN
    init(state) := s0;
    next(state) := 
    case
        state = s0          : {s1, s2};
        state = s1          : {s2};
        state = s2          : {s2};
        TRUE                : state;
    esac;

   init(p) := TRUE; 
   init(q) := TRUE;
   init(r) := FALSE;

   next(p) :=
    case
        state = s1 | state = s2     : FALSE;
    esac;
    next(q) :=
    case
        state = s1                  : TRUE;
        state = s2                  : FALSE;
        TRUE                        : q;
    esac;
   next(r) :=
    case
        state = s1                  : FALSE;
        state = s2                  : TRUE;
        TRUE                        : r;
    esac;

LTLSPEC
    X r

But NuSMV returns that specification X r is false and yields a counterexample.

4

1 回答 1

2

你的模型不正确。最初，state是s0和r是FALSE。

next(r)计算时，state仍为s0。因此，只有最后一种情况为真，其中r还有FALSE。结果，X r不成立。

您可以按如下方式修改模型，其中DEFINE用于定义标记功能：

MODULE main
VAR
  state : {s0, s1, s2};

ASSIGN
  init(state) := s0;
  next(state) :=
  case
    state = s0          : {s1, s2};
    state = s1          : {s0, s2};
    state = s2          : {s2};
  esac;

DEFINE
  p := state = s0;
  q := state = s0 | state = s1;
  r := state = s1 | state = s2;

LTLSPEC
  X r
于 2015-12-01T17:46:08.743 回答