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Automated complexity analysis based on ordered resolution

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44075

Basin,  David
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44474

Ganzinger,  Harald
Programming Logics, MPI for Informatics, Max Planck Society;

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MPI-I-95-2-006.pdf
(Any fulltext), 50MB

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Citation

Basin, D., & Ganzinger, H.(1995). Automated complexity analysis based on ordered resolution (MPI-I-95-2-006). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-A1C3-7
Abstract
We define \emph{order locality} to be a property of clauses relative to a term ordering. This property is a generalization of the subformula property for proofs where terms arising in proofs are bounded, under the given ordering, by terms appearing in the goal clause. We show that when a clause set is order local, then the complexity of its ground entailment problem is a function of its structure (e.g., full versus Horn clauses), and the ordering used. We prove that, in many cases, order locality is equivalent to a clause set being saturated under ordered resolution. This provides a means of using standard resolution theorem provers for testing order locality and transforming non-local clause sets into local ones. We have used the Saturate system to automatically establish complexity bounds for a number of nontrivial entailment problems relative to complexity classes which include Polynomial and Exponential Time and co-NP.