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Satisfiability Solvers
, 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
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Cited by 48 (0 self)
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The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,
Short proofs may be spacious: An optimal separation of space and length in resolution
, 2008
"... A number of works have looked at the relationship between length and space of resolution proofs. A notorious question has been whether the existence of a short proof implies the existence of a proof that can be verified using limited space. In this paper we resolve the question by answering it negat ..."
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A number of works have looked at the relationship between length and space of resolution proofs. A notorious question has been whether the existence of a short proof implies the existence of a proof that can be verified using limited space. In this paper we resolve the question by answering it negatively in the strongest possible way. We show that there are families of 6CNF formulas of size n, for arbitrarily large n, that have resolution proofs of length O(n) but for which any proof requires space Ω(n / log n). This is the strongest asymptotic separation possible since any proof of length O(n) can always be transformed into a proof in space O(n / log n). Our result follows by reducing the space complexity of so called pebbling formulas over a directed acyclic graph to the blackwhite pebbling price of the graph. The proof is somewhat simpler than previous results (in particular, those reported in [Nordström 2006, Nordström and H˚astad 2008]) as it uses a slightly different flavor of pebbling formulas which allows for a rather straightforward reduction of proof space to standard blackwhite pebbling price.
SymChaff: Exploiting Symmetry in a StructureAware Satisfiability Solver PRELIMINARY VERSION – UNDER REVIEW
, 2006
"... We propose a new lowoverhead framework for representing and utilizing problem symmetry in propositional satisfiability algorithms. While many previous approaches have focused on symmetry extraction as a key component, the novelty in our strategy lies in using high level problem description to pass ..."
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We propose a new lowoverhead framework for representing and utilizing problem symmetry in propositional satisfiability algorithms. While many previous approaches have focused on symmetry extraction as a key component, the novelty in our strategy lies in using high level problem description to pass on symmetry information to the SAT solver in a simple and concise form, in addition to the usual CNF formula. This information, comprising of the socalled symmetry sets and variable classes, captures variable semantics relevant to symmetry and is utilized dynamically to prune the search space. This allows us to address many limitations of alternative approaches like symmetry breaking predicates, implicit pseudoBoolean representations, general grouptheoretic methods, ZBDDs, etc. We demonstrate the efficacy of our technique through a solver called SymChaff, which achieves exponential speedup over DPLLbased SAT solvers on problems from both theory and practice, often by simply using natural tags or annotation in the problem specification. 1
Short Proofs May Be Spacious: Understanding Space in Resolution
"... till offentlig granskning för avläggande av teknologie doktorsexamen i datalogi ..."
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till offentlig granskning för avläggande av teknologie doktorsexamen i datalogi