A simplex-based extension of Fourier-Motzkin for solving linear integer arithmetic. (English) Zbl 1358.68249
Gramlich, Bernhard (ed.) et al., Automated reasoning. 6th international joint conference, IJCAR 2012, Manchester, UK, June 26–29, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-31364-6/pbk). Lecture Notes in Computer Science 7364. Lecture Notes in Artificial Intelligence, 67-81 (2012).
Summary: This paper describes a novel decision procedure for quantifier-free linear integer arithmetic. Standard techniques usually relax the initial problem to the rational domain and then proceed either by projection (e.g. Omega-Test) or by branching/cutting methods (branch-and-bound, branch-and-cut, Gomory cuts). Our approach tries to bridge the gap between the two techniques: it interleaves an exhaustive search for a model with bounds inference. These bounds are computed provided an oracle capable of finding constant positive linear combinations of affine forms. We also show how to design an efficient oracle based on the Simplex procedure. Our algorithm is proved sound, complete, and terminating and is implemented in the alt-ergo theorem prover. Experimental results are promising and show that our approach is competitive with state-of-the-art SMT solvers.
For the entire collection see [Zbl 1245.68010].
For the entire collection see [Zbl 1245.68010].
MSC:
68T15 | Theorem proving (deduction, resolution, etc.) (MSC2010) |
90C49 | Extreme-point and pivoting methods |
90C57 | Polyhedral combinatorics, branch-and-bound, branch-and-cut |