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Benjamin Kiesl

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5 papers

2 author rows

SAT Conference 2022 Conference Paper

Migrating Solver State

Armin Biere
Md. Solimul Chowdhury
Marijn J. H. Heule
Benjamin Kiesl
Michael W. Whalen

We present approaches to store and restore the state of a SAT solver, allowing us to migrate the state between different compute resources, or even between different solvers. This can be used in many ways, e. g. , to improve the fault tolerance of solvers, to schedule SAT problems on a restricted number of cores, or to use dedicated preprocessing tools for inprocessing. We identify a minimum viable subset of the solver state to migrate such that the loss of performance is small. We then present and implement two different approaches to state migration: one approach stores the state at the end of a solver run whereas the other approach stores the state continuously as part of the proof trace. We show that our approaches enable the generation of correct models and valid unsatisfiability proofs. Experimental results confirm that the overhead is reasonable and that in several cases solver performance actually improves.

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SAT Conference 2019 Conference Paper

QRAT Polynomially Simulates ∀ \text -Exp+Res

Benjamin Kiesl
Martina Seidl

Abstract The proof system \(\forall \text {-Exp+Res}\) formally captures expansion-based solving of quantified Boolean formulas (QBFs) whereas the \(\mathsf {QRAT}\) proof system captures QBF preprocessing. From previous work it is known that certain families of formulas have short proofs in \(\mathsf {QRAT}\) but not in \(\forall \text {-Exp+Res}\). However, it was not known if the two proof systems were incomparable (i. e. , if there also existed QBFs with short \(\forall \text {-Exp+Res}\) proofs but without short \(\mathsf {QRAT}\) proofs), or if \(\mathsf {QRAT}\) polynomially simulates \(\forall \text {-Exp+Res}\). We close this gap of the QBF-proof-complexity landscape by presenting a polynomial simulation of \(\forall \text {-Exp+Res}\) in \(\mathsf {QRAT}\). Our simulation shows how definition introduction combined with extended-universal reduction can mimic the concept of universal expansion.

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SAT Conference 2017 Conference Paper

A Little Blocked Literal Goes a Long Way

Benjamin Kiesl
Marijn J. H. Heule
Martina Seidl

Abstract Q-resolution is a generalization of propositional resolution that provides the theoretical foundation for search-based solvers of quantified Boolean formulas (QBFs). Recently, it has been shown that an extension of Q-resolution, called long-distance resolution, is remarkably powerful both in theory and in practice. However, it was unknown how long-distance resolution is related to \(\mathsf {QRAT}\), a proof system introduced for certifying the correctness of QBF-preprocessing techniques. We show that \(\mathsf {QRAT}\) polynomially simulates long-distance resolution. Two simple rules of \(\mathsf {QRAT}\) are crucial for our simulation— blocked-literal addition and blocked-literal elimination. Based on the simulation, we implemented a tool that transforms long-distance-resolution proofs into \(\mathsf {QRAT}\) proofs. In a case study, we compare long-distance-resolution proofs of the well-known Kleine Büning formulas with corresponding \(\mathsf {QRAT}\) proofs.

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LPAR Conference 2017 Conference Paper

Blocked Clauses in First-Order Logic

Benjamin Kiesl
Martin Suda 0001
Martina Seidl
Hans Tompits
Armin Biere

Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper, we lift the notion of blocked clauses to first-order logic. We introduce two types of blocked clauses, one for first-order logic with equality and the other for first-order logic without equality, and prove their redundancy. In addition, we give a polynomial algorithm for checking whether a clause is blocked. Based on our new notions of blocking, we implemented a novel first-order preprocessing tool. Our experiments showed that many first-order problems in the TPTP library contain a large number of blocked clauses whose elimination can improve the performance of modern theorem provers, especially on satisfiable problem instances.

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IJCAI Conference 2017 Conference Paper

Blockedness in Propositional Logic: Are You Satisfied With Your Neighborhood?

Benjamin Kiesl
Martina Seidl
Hans Tompits
Armin Biere

Clause-elimination techniques that simplify formulas by removing redundant clauses play an important role in modern SAT solving. Among the types of redundant clauses, blocked clauses are particularly popular. For checking whether a clause C is blocked in a formula F, one only needs to consider the so-called resolution neighborhood of C, i. e. , the set of clauses that can be resolved with C. Because of this, blocked clauses are referred to as being locally redundant. In this paper, we discuss powerful generalizations of blocked clauses that are still locally redundant, viz. set-blocked clauses and super-blocked clauses. We furthermore present complexity results for deciding whether a clause is set-blocked or super-blocked.

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