Abstraction Refinement for Large Scale Model Checking by Chao Wang

By Chao Wang

Abstraction Refinement for giant Scale version Checking summarizes contemporary learn on abstraction innovations for version checking huge electronic process. contemplating either the dimensions of trendy electronic structures and the ability of state of the art verification algorithms, abstraction is the one plausible answer for the profitable software of version checking thoughts to industrial-scale designs. This ebook describes fresh examine advancements in automated abstraction refinement thoughts. The suite of algorithms offered during this e-book has validated major development over earlier paintings; a few of them have already been followed by way of the EDA businesses of their commercial/in-house verification instruments.

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The first subformula, denoted by ^ M ? captures all the length k execution traces that are possible in the Kripke structure, all of which start from the initial states. The second subformula, denoted by $ p , captures the constraint for a length k path to violate the given property. The conjunction of the above two subformulae captures all the length k counterexamples with respect to the property. Such a counterexample exists if and only if the Boolean formula has a satisfiable assignment. First, we explain how to create the subformula ^M- We use V to represent the set of state variables (or latches) and U to represent the rest of the signals (primary inputs, outputs, and signals of internal logic gates).

T h e semantics of LTL formulae are defined recursively as follows: TT \= true TT \= ->(/? n [= (p A^/j TT \=X (p n \= (pU^/j TT [= (pRip always holds iS n ^ (p iS TT \=^ cp and n [= ^/j iS 7T^ \= (p i f f 3 i > 0 such that TT'^ \= ^p and for all 0 < j < ^ , n^ \= (p iff for alH > 0, TT^ ^ V^; or 3j > 0 such that TT^ \= (p and for all 0 < i < j , TT'^ \= ip The Kripke structure K satisfies an LTL formula 4> if and only if all paths from the initial states do. This means that all LTL properties are universal properties in the sense that we can add the path quantifier A as a prefix without changing the meaning of the properties.

Early termination, efficient hashing techniques, and partial order reduction can be used to reduce memory usage during the search and the number of interleavings that need to be inspected. The scalability issue in explict-state enumeration makes them unsuitable for hardware designs, although they have been successful in verifying controllers and software. Symbolic state space traversal techniques are another effective way of dealing with the extremely large state transition graphs. Instead of manipulating each individual state separately, symbolic algorithms manipulate sets of states.

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