FMplex: Exploring a Bridge between Fourier-Motzkin and Simplex

In this paper we present a quantifier elimination method for conjunctions of linear real arithmetic constraints. Our algorithm is based on the Fourier-Motzkin variable elimination procedure, but by case splitting we are able to reduce the worst-case complexity from doubly to singly exponential. The...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 21, Issue 2
Main Authors:	Promies, Valentin, Nalbach, Jasper, Ábrahám, Erika, Kobialka, Paul
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science e.V 01.01.2025
Subjects:	computer science - symbolic computation
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	In this paper we present a quantifier elimination method for conjunctions of linear real arithmetic constraints. Our algorithm is based on the Fourier-Motzkin variable elimination procedure, but by case splitting we are able to reduce the worst-case complexity from doubly to singly exponential. The adaption of the procedure for SMT solving has strong correspondence to the simplex algorithm, therefore we name it FMplex. Besides the theoretical foundations, we provide an experimental evaluation in the context of SMT solving. This is an extended version of the authors' work previously published at the fourteenth International Symposium on Games, Automata, Logics, and Formal Verification (GandALF 2023).
ISSN:	1860-5974 1860-5974
DOI:	10.46298/lmcs-21(2:6)2025