An efficient finite-domain constraint solver for circuits

Parthasarathy, G.; Iyer, M.K.; Cheng, Kwang-Ting; Wang, Li C.

doi:10.1145/996566.996628

Cited by 32 publications

(51 citation statements)

References 19 publications

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“…Many of the verification problems arising in such domains can be naturally modeled as satisfiability in Linear Arithmetic Logic (LAL), i.e., the boolean combination of propositional variables and linear constraints over numerical variables. For its practical relevance, LAL has been devoted a lot of interest, and several decision procedures exist that are able to deal with it (e.g., SVC [17], ICS [24,19], CVCLITE [17,10], UCLID [36,33], HDPLL [30]). …”

Section: Motivations and Goalsmentioning

confidence: 99%

“…The second set of experiments was performed on a benchmark suite (called RTLC hereafter) formalizing safety properties for RTL circuits, provided to us by the authors of [30] (see [30] for a more detailed description of the benchmarks).…”

Section: Description Of the Test Casesmentioning

confidence: 99%

“…Finally, we mention [30], which presents HDPLL, a decision procedure for LAL, specialized to the verification of circuits at RTL level. The procedure is based on DPLLlike Boolean search engine integrated with a constraint solver based on Fourier-Motzkin elimination and finite domain constraint propagation.…”

Section: Related Workmentioning

confidence: 99%

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An Incremental and Layered Procedure for the Satisfiability of Linear Arithmetic Logic

Bozzano¹,

Bruttomesso²,

Cimatti³

et al. 2005

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. In this paper we present a new decision procedure for the satisfiability of Linear Arithmetic Logic (LAL), i.e. boolean combinations of propositional variables and linear constraints over numerical variables. Our approach is based on the well known integration of a propositional SAT procedure with theory deciders, enhanced in the following ways.First, our procedure relies on an incremental solver for linear arithmetic, that is able to exploit the fact that it is repeatedly called to analyze sequences of increasingly large sets of constraints. Reasoning in the theory of LA interacts with the boolean top level by means of a stack-based interface, that enables the top level to add constraints, set points of backtracking, and backjump, without restarting the procedure from scratch at every call. Sets of inconsistent constraints are found and used to drive backjumping and learning at the boolean level, and theory atoms that are consequences of the current partial assignment are inferred.Second, the solver is layered: a satisfying assignment is constructed by reasoning at different levels of abstractions (logic of equality, real values, and integer solutions). Cheaper, more abstract solvers are called first, and unsatisfiability at higher levels is used to prune the search. In addition, theory reasoning is partitioned in different clusters, and tightly integrated with boolean reasoning.We demonstrate the effectiveness of our approach by means of a thorough experimental evaluation: our approach is competitive with and often superior to several state-of-the-art decision procedures. Motivations and GoalsMany practical domains require a degree of expressiveness beyond propositional logic. For instance, timed and hybrid systems have a discrete component as well as a dynamic evolution of real variables; proof obligations arising in software verification are often boolean combinations of constraints over integer variables; circuits described at Register Transfer Level, even though expressible via booleanization, might be easier to analyze at a higher level of abstraction (see e.g. [15]). Many of the verification problems arising in such domains can be naturally modeled as satisfiability in Linear Arithmetic Logic (LAL), i.e., the boolean combination of propositional variables and linear constraints over numerical variables. For its practical relevance, LAL has been devoted a lot of interest, and several decision procedures exist that are able to deal with it (e.g., SVC [17], ICS [24,19], CVCLITE [17,10], UCLID [36,33], HDPLL [30]).In this paper, we propose a new decision procedure for the satisfiability of LAL, both for the real-valued and integer-valued case. We start from a well known approach, previously applied in MATHSAT [26,4] and in several other systems [24,19,17,10, 35,3,21]: a propositional SAT procedure, modified to enumerate propositional assignments for the propositional abstraction of the problem, is integrated with dedicated theory deciders, used to check consistency of propositional assignments wit...

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Section: Motivations and Goalsmentioning

confidence: 99%

Section: Description Of the Test Casesmentioning

confidence: 99%

See 1 more Smart Citation

An Incremental and Layered Procedure for the Satisfiability of Linear Arithmetic Logic

Bozzano¹,

Bruttomesso²,

Cimatti³

et al. 2005

Tools and Algorithms for the Construction and Analysis of Systems

View full text Add to dashboard Cite

show abstract

“…Each satisfiable assignment for the Boolean SAT problem has to be validated on the concrete problem using the theory solver. The solver proposed in [17] can be seen as a specialized SMT solver for bit vector logic. Tightly coupling the different solvers, especially to enforce learning due to conflicts resulting from partial assignments and to efficiently carry out implications, is a challenge in this area.…”

Section: Introductionmentioning

confidence: 99%

SWORD: A SAT like Prover Using Word Level Information

Wille

Fey

Große

et al. 2009

VLSI-SoC: Advanced Topics on Systems on a Chip

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Abstract-Solvers for Boolean Satisfiability (SAT) are state-of-the-art to solve verification problems. But when arithmetic operations are considered, the verification performance degrades with increasing data-path width. Therefore, several approaches that handle a higher level of abstraction have been studied in the past. But the resulting solvers are still not robust enough to handle problems that mix word level structures with bit level descriptions.In this paper, we present the satisfiability solver SWORD -a SAT like solver that facilitates word level information. SWORD represents the problem in terms of modules that define operations over bit vectors. Thus, word level information and structural knowledge become available in the search process. The experimental results show that on our benchmarks SWORD is more robust than Boolean SAT, K*BMDs or SMT.

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“…However, [32] only aims at the data-paths, and thus, does not allow a Boolean part within the original formula. This is mended by [33] using a lazy encoding with a modified DPLL search.…”

Section: Introductionmentioning

confidence: 99%

Approximating Predicate Images for Bit-Vector Logic

Kroening

Sharygina

2006

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Predicate abstraction refinement is a successful technique for verifying large ANSI-C programs. However, computing the image of the predicates with respect to the transition relation is computationally expensive. Recent results have shown that predicate images can be computed by transforming a proof of a formula over integers into a Boolean formula that is satisfiable if and only if the original formula is satisfiable. However, the existing algorithms compute the closure of the proof rules that are used to axiomatize the logic, and thus, rely on the fact that the set of axioms is small. They are therefore limited to logics of low complexity, such as difference logic.We describe a proof-based algorithm that computes an over-approximation of the predicate image but in turn allows a rich set of axioms. The algorithm can be used to compute images of predicates using a combination of bit-vector logic, the theory of arrays, and pointer arithmetic. The proof-based approach can also be used to refine the image. We quantify the performance of the algorithm in comparison with a Das/Dill-like greedy incremental refinement of the image and a proof-based incremental refinement.

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An efficient finite-domain constraint solver for circuits

Cited by 32 publications

References 19 publications

An Incremental and Layered Procedure for the Satisfiability of Linear Arithmetic Logic

An Incremental and Layered Procedure for the Satisfiability of Linear Arithmetic Logic

SWORD: A SAT like Prover Using Word Level Information

Approximating Predicate Images for Bit-Vector Logic

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