Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

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Principles of Model Checking

Model Checking

Symbolic model checking is a powerful formal specification and verification method that has been applied successfully in several industrial designs. Using symbolic model checking techniques it is possible to verify industrial-size finite state systems. State spaces with up to 1030 states can be exhaustively searched in minutes. Models with more than 10120 states have been verified using special techniques.

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Symbolic Model Checking

A general method that represents the state space symbolically instead of explicitly is described. The generality of the method comes from using a dialect of the mu-calculus as the primary specification language. A model-checking algorithm for mu-calculus formulas which uses R.E. Bryant's (1986) binary decision diagrams to represent relations and formulas symbolically is described. It is then shown how the novel mu-calculus model checking algorithm can be used to derive efficient decision procedures for CTL model checking, satisfiability of linear-time temporal logic formulas, strong and weak observational equivalence of finite transition systems, and language containment of finite omega -automata. This eliminates the need to describe complicated graph-traversal or nested fixed-point computations for each decision procedure. The authors illustrate the practicality of their approach to symbolic model checking by discussing how it can be used to verify a simple synchronous pipeline. >

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Symbolic model checking: 10/sup 20/ states and beyond

Symbolic Model Checking [3, 14] has proven to be a powerful technique for the verification of reactive systems. BDDs [2] have traditionally been used as a symbolic representation of the system. In this paper we show how boolean decision procedures, like Stalmarck's Method [16] or the Davis & Putnam Procedure [7], can replace BDDs. This new technique avoids the space blow up of BDDs, generates counterexamples much faster, and sometimes speeds up the verification. In addition, it produces counterexamples of minimal length. We introduce a bounded model checking procedure for LTL which reduces model checking to propositional satisfiability. We show that bounded LTL model checking can be done without a tableau construction. We have implemented a model checker BMC, based on bounded model checking, and preliminary results are presented.

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Symbolic Model Checking without BDDs

In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach.

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Bryant

Papers

Graph-Based Algorithms for Boolean Function Manipulation