By Chao Wang

This ebook summarizes contemporary study on abstraction thoughts for version checking huge electronic procedure. contemplating the dimensions of ultra-modern electronic structures and the capability of cutting-edge verification algorithms, abstraction is the one potential answer for the profitable program of version checking concepts to industrial-scale designs. The suite of algorithms awarded the following represents major development over past artwork; a few have already been followed via the EDA businesses of their commercial/in-house verification tools.

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**Extra info for Abstraction Refinement for Large Scale Model Checking (Integrated Circuits and Systems)**

**Example text**

When we evaluate the above formula through fixpoint computation, the initial value of the auxiliary iteration variable Z can be set to the entire universe. For our running example, Fo 70 Z^ = {aO, W, cO} _ = {aO, 60, cO, al, 61, cl, a2, 62, c2, a3, 63, c3} EXEZ^U(ZOAFO) = EX E{aO, 60, cO, al, 61, cl, a2,62, c2, a3, 63, c3} U {aO, 60, cO} - EX{al,60} = {al} Z2 ^ EXEZ^U{Z^ A Fo) = EXE{al}U{ } -EX{} -{} Symbolic Model Checking 25 Since no state in the composed system satisfies EGfairtrue, the language is empty.

We can always rewrite an LTL formula into normal form by pushing negation inside temporal operators. The following rules can be apphed during the rewriting: Xp - ^X^p Qp •= - 1 F - i p p\}q = -"(-i^R-ip) Fp == true Up Since an LTL formula (/> is a universal property and is equivalent to A 0, the negation of (j) should be the existential property E -^cj). The two path quantifiers are an integral part of Computational Tree Logic (CTL), and are used exphcitly to specify properties related to execution traces in the computation tree structure.

However, there are also properties that can be expressed in one but not the other. The difference between an LTL formula and a CTL formula can be very subtle. 3, but the CTL formula AF AG ]? fails. ) The reason is that the LTL property is related to the individual paths, and on any infinite path of the given Kripke structure we can reach the state c from which p will holds forever. , on the other hand, requires that on all paths from the state a we can reach a state satisfying AG p. Note that the only state satisfying AGp is the state c; however, the Kripke structure does not satisfy AF{c}—as shown in the right-hand side of the figure, the left most path of the computation tree is a counterexample.