Complexity and structural heuristics for propositional and quantified satisfiability

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dc.contributor.advisorVardi, Moshe Y.en_US
dc.creatorPan, Guoqiangen_US
dc.date.accessioned2009-06-03T21:08:09Zen_US
dc.date.available2009-06-03T21:08:09Zen_US
dc.date.issued2007en_US
dc.description.abstractDecision procedures for various logics are used as general-purpose solvers in computer science. A particularly popular choice is propositional logic, which is simultaneously powerful enough to model problems in many application domains, including formal verification and planning, while at the same time simple enough to be efficiently solved for many practical cases. Similarly, there are also recent interests in using QBF, an extension of propositional logic, as a modeling language to be used in a similar fashion. The hope is that QBF, being a more powerful language, can compactly encode, and in turn, be used to solve, a larger range of applications. Still, propositional logic and QBF are respectively complete for the complexity classes NP and PSPACE, thus, both can be theoretically considered intractable. A popular hypothesis is that real-world problems contain underlying structure that can be exploited by the decision procedures. In this dissertation, we study the impact of structural constraints (in the form of bounded width) and heuristics on the performance of propositional and QBF decision procedures. The results presented in this dissertation can be seen as a contrast on how bounded-width impacts propositional and quantified problems differently. Starting with a size bound on BDDs under bounded width, we proceed to compare symbolic decision procedures against the standard DPLL search-based approach for propositional logic, as well as compare different width-based heuristics for the symbolic approaches. In general, symbolic approaches for propositional satisfiability are only competitive for a small range of problems, and the theoretical tractability for the bounded-width case rarely applies in practice. However, the picture is very different for quantified satisfiability. To that end, we start with a series of "intractability in tractability" results which shows that although the complexity of QBF with constant width and alternation is tractable, there is an inherent non-elementary blowup in the width and alternation depth such that a width-bound that is slightly above constant leads to intractability. To contrast the theoretical intractability, we apply structural heuristics to a symbolic decision procedure of QBF and show that symbolic approaches complement search-based approaches quite well for QBF.en_US
dc.format.extent131 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS COMP.SCI. 2007 PANen_US
dc.identifier.citationPan, Guoqiang. "Complexity and structural heuristics for propositional and quantified satisfiability." (2007) Diss., Rice University. <a href="https://hdl.handle.net/1911/20686">https://hdl.handle.net/1911/20686</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/20686en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectComputer scienceen_US
dc.titleComplexity and structural heuristics for propositional and quantified satisfiabilityen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputer Scienceen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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