Fixpoint Computation: Leaking Gas Burner
نویسندگان
چکیده
Real-time distributed system speciication and veriication in asynchronous propositional temporal logic. Let A be the integrator system deened in Figure 5. We use the xpoint computation procedure to prove that the formula y 60 ! 20t y is an invariant of A. It follows that the gas burner leaks at most one twentieth of the time in any interval of at least 60 seconds. Let R i = hpc = 1 ^ t = 0 ^ x = 0i be the region of initial states and let R f = hy 60 ^ 20t > yi be the region of \bad" states. Let R i again denote the value of R = pre(R cur) after the i-th iteration of the algorithm. 1 = h(pc = 2 ^ ?19 < 20 t ? y ^ 11 < 20 t + x ? y ^ 2 < t ^ 0 t ^ 0 x) _ (pc = 1 ^ ?19 < 20t ? 19x ? y ^ 2 < t ? x ^ ?1 ?x ^ 0 x)i R 2 = h(pc = 1 ^ ?8 < 20t ? 19x ? y ^ 1 < t ? x ^ ?1 ?x ^ 0 x) _ (pc = 2 ^ ?19 < 20 t ? y ^ 2 < t ^ 11 < 20 t + x ? y ^ 0 x)i R 3 = h(pc = 2 ^ ?8 < 20 t ? y ^ 1 < t ^ 22 < 20 t + x ? y ^ 0 x) _ (pc = 1 ^ ?8 < 20t ? 19x ? y ^ 1 < t ? x ^ ?1 ?x ^ 0 x)i R 4 = h(pc = 1 ^ 0 < t ? x ^ 3 < 20t ? 19x ? y ^ ?1 ?x ^ 0 x) _ (pc = 2 ^ ?8 < 20 t ? y ^ 1 < t ^ 22 < 20 t + x ? y ^ 0 x)i R 5 = h(pc = 2 ^ 0 < t ^ 3 < 20 t ? y ^ 33 < 20 t + x ? y ^ 0 x) _ (pc = 1 ^ 0 < t ? x ^ 3 < 20t ? 19x ? y ^ ?1 ?x ^ 0 x)i R 6 = h(pc = 1 ^ ?1 < t ? x …
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