Article

An algebraic approach for the unsatisfiability of nonlinear constraints

Author:

Ashish TiwariAuthors Info & Claims

CSL'05: Proceedings of the 19th international conference on Computer Science Logic

Pages 248 - 262

https://doi.org/10.1007/11538363_18

Published: 22 August 2005 Publication History

Abstract

We describe a simple algebraic semi-decision procedure for detecting unsatisfiability of a (quantifier-free) conjunction of nonlinear equalities and inequalities. The procedure consists of Gröbner basis computation plus extension rules that introduce new definitions, and hence it can be described as a critical-pair completion-based logical procedure. This procedure is shown to be sound and refutationally complete. When projected onto the linear case, our procedure reduces to the Simplex method for solving linear constraints. If only finitely many new definitions are introduced, then the procedure is also terminating. Such terminating, but potentially incomplete, procedures are used in “incompleteness-tolerant” applications.

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cover image Guide Proceedings

CSL'05: Proceedings of the 19th international conference on Computer Science Logic

August 2005

567 pages

ISBN:3540282319

Editor:
Luke Ong
Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, United Kingdom

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 22 August 2005

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Cited By

Bjørner NNachmanson L(2024)Arithmetic Solving in Z3Computer Aided Verification10.1007/978-3-031-65627-9_2(26-41)Online publication date: 24-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-65627-9_2
Kincaid ZKoh NZhu S(2023)When Less Is More: Consequence-Finding in a Weak Theory of ArithmeticProceedings of the ACM on Programming Languages10.1145/35712377:POPL(1275-1307)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571237
Tiwari ALincoln P(2016)A search-based procedure for nonlinear real arithmeticFormal Methods in System Design10.1007/s10703-016-0245-848:3(257-273)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1007/s10703-016-0245-8
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