The Quest for Efficient Boolean Satisfiability Solvers

Zhang, Lintao; Malik, Sharad

doi:10.1007/3-540-45620-1_26

Cited by 128 publications

(162 citation statements)

References 43 publications

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“…This SAT instance proved to be unsatisfiable. Upon deeper examination using the Zcore program (distributed with the latest Zchaff [25]), we discovered an unsatisfiable core of 9 clauses. By analyzing these clauses, it was discovered that the error we detected resulted from us forgetting to initialize the memory state prior to the test.…”

Section: Resultsmentioning

confidence: 99%

QB or Not QB: An Efficient Execution Verification Tool for Memory Orderings

Gopalakrishnan

Yang

Sivaraj

2004

Computer Aided Verification

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Abstract. We study the problem of formally verifying shared memory multiprocessor executions against memory consistency models-an important step during post-silicon verification of multiprocessor machines. We employ our previously reported style of writing formal specifications for shared memory models in higher order logic (HOL), obtaining intuitive as well as modular specifications. Our specification consists of a conjunction of rules that constrain the global visibility order. Given an execution to be checked, our algorithm generates Boolean constraints that capture the conditions under which the execution is legal under the visibility order. We initially took the approach of specializing the memory model HOL axioms into equivalent (for the execution to be checked) quantified boolean formulae (QBF). As this technique proved inefficient, we took the alternative approach of converting the HOL axioms into a program that generates a SAT instance when run on an execution. In effect, the quantifications in our memory model specification were realized as iterations in the program. The generated Boolean constraints are satisfiable if and only if the given execution is legal under the memory model. We evaluate two different approaches to encode the Boolean constraints, and also incremental techniques to generate and solve Boolean constraints. Key results include a demonstration that we can handle executions of realistic lengths for the modern Intel Itanium memory model. Further research into proper selection of Boolean encodings, incremental SAT checking, efficient handling of transitivity, and the generation of unsatisfiable cores for locating errors are expected to make our technique practical.

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Section: Resultsmentioning

confidence: 99%

QB or Not QB: An Efficient Execution Verification Tool for Memory Orderings

Gopalakrishnan

Yang

Sivaraj

2004

Computer Aided Verification

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“…Hence, if a solver then decides to assign value F alse to each variable, every clause will be satisfied and a solution will be found. As unit propagation takes linear time [13,20,24], the result follows.…”

Section: Max-closed Constraintsmentioning

confidence: 99%

“…SAT solvers are now considered to be efficient and practical tools for many kinds of problems [24]. In order to use them to solve constraint satisfaction problems (CSPs), various encodings from CSP to SAT have been developed [3,20,23].…”

Section: Introductionmentioning

confidence: 99%

The Order Encoding: From Tractable CSP to Tractable SAT

Petke

Jeavons

2011

Theory and Applications of Satisfiability Testing - SAT 2011

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Many mathematical and practical problems can be expressed as constraint satisfaction problems (CSPs). One way to solve a CSP instance is to encode it into SAT and use a SAT-solver. However, important information about the problem can get lost during the translation stage. For example, although the general constraint satisfaction problem is known to be NP-complete, there are some classes of CSP instances that have been shown to be tractable. These include the classes of CSP instances that contain only max-closed or connected-row-convex constraints. In this paper we show that translating such instances using some common standard encodings results in SAT instances which do not fall into known tractable classes. However, translating such instances using the order encoding results in SAT instances that do fall into known tractable classes. Moreover, modern clause learning SAT-solvers can then solve them efficiently. Hence, we give a theory-based argument to prefer the order encoding for certain families of constraint satisfaction problems.

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“…Most state-of-the-art SAT procedures are evolutions of the Davis-Putnam-Longeman-Loveland (DPLL) procedure [11,10] and they are based on the con ict-driven paradigm [28,33]. A high-level schema of a modern con ict-driven DPLL engine, adapted from the one presented in [34], is reported in Figure 1. The propositional formula ϕ is in CNF; the assignment µ is initially empty, and it is updated in a stack-based manner.…”

Section: Basics On Con Ict-driven Sat Solvingmentioning

confidence: 99%

Axiom Pinpointing in Lightweight Description Logics via Horn-SAT Encoding and Conflict Analysis

Sebastiani

Vescovi

2009

Automated Deduction – CADE-22

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Abstract. The recent quest for tractable logic-based languages arising from the eld of bio-medical ontologies has raised a lot of attention on lightweight (i.e. less expressive but tractable) description logics, like EL and its family. To this extent, automated reasoning techniques in these logics have been developed for computing not only concept subsumptions, but also to pinpoint the set of axioms causing each subsumption. In this paper we build on previous work from the literature and we propose and investigate a simple and novel approach for axiom pinpointing for the logic EL + . The idea is to encode the classi cation of an ontology into a Horn propositional formula, and to exploit the power of Boolean Constraint Propagation and Con ict Analysis from modern SAT solvers to compute concept subsumptions and to perform axiom pinpointing. A preliminary empirical evaluation com rms the potential of the approach.Note: a short version of this paper is currently under submission at CADE-22. Motivations and goalsIn contrast to the trend of the last two decades [3], in which the research in description logic has focused on investigating increasingly expressive logics, the recent quest for tractable logic-based languages arising from the eld of biomedical ontologies has raised a lot of attention on lightweight (i.e. less expressive but tractable) description logics, like EL and its family [1,4,6,16,20,2]. In particular, the logic EL + [4,6,7] extends EL and is of particular relevance due to its algorithmic properties and due to its capability of expressing several important and widely-used bio-medical ontologies, such as Snomed-CT [31,30,32], NCI [29], GeneOntology [9] and the majority of Galen [21]. In fact in EL + not only standard logic problems such as concept subsumption (e.g., is Amputation-of-Finger a subconcept of Amputation-of-Arm in the ontology Snomed-CT? [7]), but also more sophisticated logic problems such as axiom pinpointing (e.g., which minimal sets of axioms in Snomed-CT of the fact that Amputation-of-Finger is a subconcept of Amputation-of-Arm? [7]) are tractable. Importantly, the problem of axiom pinpointing in EL + is of great interest for debugging complex bio-medical ontologies (see, e.g., [7]). To this extent, the problems of concept subsumption and axiom pinpointing in EL + have been thoroughly investigated, and e cient algorithm for these two functionalities have been implemented and tested with success on large ontologies, including Snomed-CT (see e.g. [4,6,7]).The description logic community have spent a considerable e ort in the attempt of extending EL as much as possible, de ning a maximal subset of logical constructors expressive enough to cover the needs of the practical applications above mentioned, but whose standard and even non-standard inference problems remain tractable. Beside the logic EL + [4], on which we focus in this work, many other extension of EL have been studied [1,2].In this paper we build on previous work from the literature of EL + reasoning [4,6,7] and of SAT/SMT [1...

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The Quest for Efficient Boolean Satisfiability Solvers

Cited by 128 publications

References 43 publications

QB or Not QB: An Efficient Execution Verification Tool for Memory Orderings

QB or Not QB: An Efficient Execution Verification Tool for Memory Orderings

The Order Encoding: From Tractable CSP to Tractable SAT

Axiom Pinpointing in Lightweight Description Logics via Horn-SAT Encoding and Conflict Analysis

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