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51
Symbolic Model Checking Using SAT Procedures instead of BDDs
, 1999
"... In this paper, we study the application of propositional decision procedures in hardware verification. In particular, we apply bounded model checking, as introduced in [1], to equivalence and invariant checking. We present several optimizations that reduce the size of generated propositional formula ..."
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Cited by 263 (23 self)
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In this paper, we study the application of propositional decision procedures in hardware verification. In particular, we apply bounded model checking, as introduced in [1], to equivalence and invariant checking. We present several optimizations that reduce the size of generated propositional formulas. In many instances, our SATbased approach can significantly outperform BDDbased approaches. We observe that SATbased techniques are particularly efficient in detecting errors in both combinational and sequential designs. 1
Effective Use of Boolean Satisfiability Procedures in the Formal Verification of Superscalar and VLIW Microprocessors
 Journal of Symbolic Computation
, 2001
"... We compare SATcheckers and decision diagrams on the evaluation of Boolean formulas produced in the formal verification of both correct and buggy versions of superscalar and VLIW microprocessors. We identify one SATchecker that significantly outperforms the rest. We evaluate ways to enhance its per ..."
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Cited by 87 (12 self)
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We compare SATcheckers and decision diagrams on the evaluation of Boolean formulas produced in the formal verification of both correct and buggy versions of superscalar and VLIW microprocessors. We identify one SATchecker that significantly outperforms the rest. We evaluate ways to enhance its performance by variations in the generation of the Boolean correctness formulas. We reassess optimizations previously used to speed up the formal verification and probe future challenges.
Theorem Proving with the Real Numbers
, 1996
"... This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of fl ..."
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Cited by 84 (10 self)
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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the `Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally,...
PBS: A backtrack search pseudo Boolean solver
 In Symposium on the theory and applications of satisfiability testing (SAT
, 2002
"... in areas such as hardware and software verification, FPGA routing, planning in AI, etc. Further uses are complicated by the need to express “counting constraints ” in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those cons ..."
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Cited by 82 (1 self)
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in areas such as hardware and software verification, FPGA routing, planning in AI, etc. Further uses are complicated by the need to express “counting constraints ” in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those constraints can be handled by Integer Linear Programming (ILP), but offtheshelf ILP solvers tend to ignore the Boolean nature of 01 variables. This work attempts to generalize recent highly successful SAT techniques to new applications. First, we extend the basic DavisPutnam framework to handle counting constraints and apply it to solve routing problems. Our implementation outperforms previously reported solvers for the satisfiability with “pseudoBoolean ” constraints and shows significant speedup over best SAT solvers when such constraints are translated into CNF,. Additionally, we solve instances of the MaxONEs optimization problem which seeks to maximize the number of “true ” values over all satisfying assignments. This, and the related MinONEs problem are important due to reductions from MaxClique and Min Vertex Cover. Our experimental results for various benchmarks are superior to all approaches reported earlier. 1
Symbolic Reachability Analysis based on SATSolvers
, 2000
"... The introduction of symbolic model checking using Binary Decision Diagrams (BDDs) has led to a substantial extension of the class of systems that can be algorithmically verified. Although BDDs have played a crucial role in this success, they have some wellknown drawbacks, such as requiring an e ..."
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Cited by 77 (3 self)
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The introduction of symbolic model checking using Binary Decision Diagrams (BDDs) has led to a substantial extension of the class of systems that can be algorithmically verified. Although BDDs have played a crucial role in this success, they have some wellknown drawbacks, such as requiring an externally supplied variable ordering and causing space blowups in certain applications. In a parallel development, SATsolving procedures, such as Stalmarck's method or the DavisPutnam procedure, have been used successfully in verifying very large industrial systems. These efforts have recently attracted the attention of the model checking community resulting in the notion of bounded model checking. In this paper, we show how to adapt standard algorithms for symbolic reachability analysis to work with SATsolvers. The key element of our contribution is the combination of an algorithm that removes quantifiers over propositional variables and a simple representation that allows reuse of subformulas. The result will in principle allow many existing BDDbased algorithms to work with SATsolvers. We show that even with our relatively simple techniques it is possible to verify systems that are known to be hard for BDDbased model checkers.
Satire: A new incremental satisfiability engine
 In Design Automation Conference, 2001. Proceedings
, 2001
"... We introduce SATIRE, a new satisfiability solver that is particularly suited to verification and optimization problems in electronic design automation. SATIRE builds on the most recent advances in satisfiability research, and includes two new features to achieve even higher performance: a facility f ..."
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Cited by 74 (9 self)
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We introduce SATIRE, a new satisfiability solver that is particularly suited to verification and optimization problems in electronic design automation. SATIRE builds on the most recent advances in satisfiability research, and includes two new features to achieve even higher performance: a facility for incrementally solving sets of related problems, and the ability to handle nonCNF constraints. We provide experimental evidence showing the effectiveness of these additions to classical satisfiability solvers. 1.
HOL Light: A tutorial introduction
 Proceedings of the First International Conference on Formal Methods in ComputerAided Design (FMCAD’96), volume 1166 of Lecture Notes in Computer Science
, 1996
"... HOL Light is a new version of the HOL theorem prover. While retaining the reliability and programmability of earlier versions, it is more elegant, lightweight, powerful and automatic; it will be the basis for the Cambridge component of the HOL2000 initiative to develop the next generation of HOL th ..."
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Cited by 70 (9 self)
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HOL Light is a new version of the HOL theorem prover. While retaining the reliability and programmability of earlier versions, it is more elegant, lightweight, powerful and automatic; it will be the basis for the Cambridge component of the HOL2000 initiative to develop the next generation of HOL theorem provers. HOL Light is written in CAML Light, and so will run well even on small machines, e.g. PCs and Macintoshes with a few megabytes of RAM. This is in stark contrast to the resourcehungry systems which are the norm in this field, other versions of HOL included. Among the new features of this version are a powerful simplifier, effective first order automation, simple higherorder matching and very general support for inductive and recursive definitions.
SATbased Verification without State Space Traversal
 In Formal Methods in ComputerAided Design
, 2000
"... . Binary Decision Diagrams (BDDs) have dominated the area of symbolic model checking for the past decade. Recently, the use of satisfiability (SAT) solvers has emerged as an interesting complement to BDDs. SATbased methods are capable of coping with some of the systems that BDDs are unable to h ..."
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Cited by 66 (3 self)
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. Binary Decision Diagrams (BDDs) have dominated the area of symbolic model checking for the past decade. Recently, the use of satisfiability (SAT) solvers has emerged as an interesting complement to BDDs. SATbased methods are capable of coping with some of the systems that BDDs are unable to handle. The most challenging problem that has to be solved in order to adapt standard symbolic model checking to SATsolvers is the boolean quantification necessary for traversing the state space. A possible approach to extending the applicability of SATbased model checkers is therefore to reduce the amount of traversal. In this paper, we investigate a BDDbased verification algorithm due to van Eijk. Van Eijk's algorithm tries to compute information that is sufficient to prove a given safety property directly. When this is not possible, the computed information can be used to reduce the amount of traversal needed by standard model checking algorithms. We convert van Eijk's algori...
A tutorial on Stålmarck's proof procedure for propositional logic
 Formal Methods in System Design
, 1998
"... We explain Stalmarck's proof procedure for classical propositional logic. The method is implemented in a commercial tool that has been used successfully in real industrial verification projects. Here, we present the proof system underlying the method, and motivate the various design decisions th ..."
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Cited by 64 (1 self)
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We explain Stalmarck's proof procedure for classical propositional logic. The method is implemented in a commercial tool that has been used successfully in real industrial verification projects. Here, we present the proof system underlying the method, and motivate the various design decisions that have resulted in a system that copes well with the large formulas encountered in industrialscale verification. 1
Programming Constraint Inference Engines
 Proceedings of the Third International Conference on Principles and Practice of Constraint Programming
, 1997
"... Existing constraint programming systems offer a fixed set of inference engines implementing search strategies such as single, all, and best solution search. This is unfortunate, since new engines cannot be integrated by the user. ..."
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Cited by 49 (6 self)
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Existing constraint programming systems offer a fixed set of inference engines implementing search strategies such as single, all, and best solution search. This is unfortunate, since new engines cannot be integrated by the user.