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Translating pseudoboolean constraints into SAT
 Journal on Satisfiability, Boolean Modeling and Computation
, 2006
"... In this paper, we describe and evaluate three different techniques for translating pseudoboolean constraints (linear constraints over boolean variables) into clauses that can be handled by a standard SATsolver. We show that by applying a proper mix of translation techniques, a SATsolver can perfor ..."
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Cited by 181 (2 self)
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In this paper, we describe and evaluate three different techniques for translating pseudoboolean constraints (linear constraints over boolean variables) into clauses that can be handled by a standard SATsolver. We show that by applying a proper mix of translation techniques, a SATsolver can perform on a par with the best existing native pseudoboolean solvers. This is particularly valuable in those cases where the constraint problem of interest is naturally expressed as a SAT problem, except for a handful of constraints. Translating those constraints to get a pure clausal problem will take full advantage of the latest improvements in SAT research. A particularly interesting result of this work is the efficiency of sorting networks to express pseudoboolean constraints. Although tangential to this presentation, the result gives a suggestion as to how synthesis tools may be modified to produce arithmetic circuits more suitable for SAT based reasoning. Keywords: pseudoBoolean, SATsolver, SAT translation, integer linear programming
Improvements to Combinational Equivalence Checking
 In Proc. Int’l Conf. on ComputerAided Design
, 2006
"... The paper explores several ways to improve the speed and capacity of combinational equivalence checking based on Boolean satisfiability (SAT). Stateoftheart methods use simulation and BDD/SAT sweeping on the input side (i.e. proving equivalence of some internal nodes in a topological order), inte ..."
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Cited by 51 (20 self)
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The paper explores several ways to improve the speed and capacity of combinational equivalence checking based on Boolean satisfiability (SAT). Stateoftheart methods use simulation and BDD/SAT sweeping on the input side (i.e. proving equivalence of some internal nodes in a topological order), interleaved with attempts to run SAT on the output (i.e. proving equivalence of the output to constant 0). This paper improves on this method by (a) using more intelligent simulation, (b) using CNFbased SAT with circuitbased decision heuristics, and (c) interleaving SAT with loweffort logic synthesis. Experimental results on public and industrial benchmarks demonstrate substantial reductions in runtime, compared to the current methods. In several cases, the new solver succeeded in solving previously unsolved problems. 1
Scalable Exploration of Functional Dependency by Interpolation and
 Incremental SAT Solving,” in Proc. Int. Conf. ComputerAided Design
, 2007
"... Functional dependency is concerned with rewriting a Boolean function f as a function h over a set of base functions {g1, …, gn}, i.e. f = h(g1, …, gn). It plays an important role in many aspects of electronic design automation (EDA), ranging from logic synthesis to formal verification. Prior approac ..."
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Cited by 21 (6 self)
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Functional dependency is concerned with rewriting a Boolean function f as a function h over a set of base functions {g1, …, gn}, i.e. f = h(g1, …, gn). It plays an important role in many aspects of electronic design automation (EDA), ranging from logic synthesis to formal verification. Prior approaches to the exploration of functional dependency are based on binary decision diagrams (BDDs), which may not be easily scalable to large designs. This paper proposes a novel reformulation that extensively exploits the capability of modern satisfiability (SAT) solvers. Thereby, functional dependency is detected effectively through incremental SAT solving, and the dependency function h, if it exists, is obtained through Craig interpolation. The main strengths of the proposed approach include: (1) fast detection of functional dependency with modest memory consumption and thus scalable to large designs, (2) a full capacity to handle a large set of base functions and thus discovering dependency whenever exists, and (3) potential application to largescale logic optimization and verification reduction. Experimental results show the proposed method is far superior to prior work and scales well in dealing with the largest ISCAS89 and ITC99 benchmark circuits with up to 200K gates. 1.
SWORD: a SAT like prover using word level information
 in Int’l Conference on Very Large Scale Integration, 2007
"... Abstract — Solvers for Boolean Satisfiability (SAT) are stateoftheart to solve verification problems. But when arithmetic operations are considered, the verification performance degrades with increasing datapath width. Therefore, several approaches that handle a higher level of abstraction have ..."
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Cited by 13 (5 self)
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Abstract — Solvers for Boolean Satisfiability (SAT) are stateoftheart to solve verification problems. But when arithmetic operations are considered, the verification performance degrades with increasing datapath 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. I.
To SAT ot not to SAT: Scalable . . .
, 2010
"... Functional dependency is concerned with rewriting a Boolean function f as a function h over a set of base functions {g1;...;gn}, i.e., f hðg1;...;gnÞ. It plays an important role in many aspects of electronic design automation (EDA). Prior approaches to the exploration of functional dependency are ..."
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Functional dependency is concerned with rewriting a Boolean function f as a function h over a set of base functions {g1;...;gn}, i.e., f hðg1;...;gnÞ. It plays an important role in many aspects of electronic design automation (EDA). Prior approaches to the exploration of functional dependency are based on binary decision diagrams (BDDs), which may not be easily scalable to large designs. This paper formulates both singleoutput and multipleoutput functional dependencies as satisfiability (SAT) solving and exploits extensively the capability of a modern SAT solver. Thereby, functional dependency can be detected effectively through incremental SAT solving, and the dependency function h, if it exists, is obtained through Craig interpolation. The proposed method enables 1) scalable detection of functional dependency, 2) fast enumeration of dependency function under a large set of candidate base functions, and 3) potential application to largescale logic synthesis and formal verification. Experimental results show that the proposed method is far superior to prior work and scales well in dealing with the largest ISCAS and ITC benchmark circuits with up to 200K gates.
Circuit Based Encoding of CNF formula
"... Abstract. In this paper a new circuit sat based encoding of boolean formula is proposed. It makes an original use of the concept of restrictive models introduced by Boufkhad to polynomially translate any formula in conjunctive normal form (CNF) to a circuit sat representation (a conjunction of gates ..."
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Abstract. In this paper a new circuit sat based encoding of boolean formula is proposed. It makes an original use of the concept of restrictive models introduced by Boufkhad to polynomially translate any formula in conjunctive normal form (CNF) to a circuit sat representation (a conjunction of gates and clauses). Our proposed encoding preserves the satisfiability of the original formula. The set of models of the obtained circuit w.r.t. the original set of variables is a subset of the models (with special characteristics) of the original formula. Each gate represents both a subset of clauses from the original CNF formula and a set of new additional clauses which constrains the set of models to those with a special structure. Using two variant of restrictive models, our circuit sat based encoding leads to a conjunction of two subformulas: a set of gates and a horn formula. We also provided a connection between our encoding and the satisfiability of the original formula i.e. when the input formula is satisfiable, our proposed translation delivers a full circuit formula. A new incremental preprocessing process is designed leading to interesting experimental improvements of Minisat a stateoftheart satisfiability solver. Finally, using our circuit encoding, on many SAT instances interesting results are also obtained wrt. the backdoor set computation problem. 1