The ksmt Calculus Is a $$\delta $$-complete Decision Procedure for Non-linear Constraints-Reference-Cited by-同舟云学术

The ksmt Calculus Is a $$\delta $$-complete Decision Procedure for Non-linear Constraints

Published:2021 Issue: Volume: Page:113-130
ISSN:0302-9743
Container-title:Automated Deduction – CADE 28
language:
Short-container-title:

Author:

Brauße Franz^ORCID,Korovin Konstantin^ORCID,Korovina Margarita V.^ORCID,Müller Norbert Th.^ORCID

Abstract

Abstract is a CDCL-style calculus for solving non-linear constraints over the real numbers involving polynomials and transcendental functions. In this paper we investigate properties of the calculus and show that it is a

$$\delta $$

δ -complete decision procedure for bounded problems. We also propose an extension with local linearisations, which allow for more efficient treatment of non-linear constraints.

Publisher

Springer International Publishing

Link

https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_7

Reference32 articles.

1. Bard, J., Becker, H., Darulova, E.: Formally verified roundoff errors using SMTbased certificates and subdivisions. In: ter Beek, M.H., McIver, A., Oliveira, J.N. (eds.) Formal Methods - The Next 30 Years - Third World Congress, FM 2019, Proceedings. LNCS, vol. 11800, pp. 38–44. Springer (2019)

2. Benvenuti, L., Bresolin, D., Collins, P., Ferrari, A., Geretti, L., Villa, T.: Assume–guarantee verification of nonlinear hybrid systems with Ariadne. International Journal of Robust and Nonlinear Control 24(4), 699–724 (2014)

3. Bonacina, M.P., Graham-Lengrand, S., Shankar, N.: Conflict-driven satisfiability for theory combination: Transition system and completeness. J. Autom. Reason. 64(3), 579–609 (2020)

4. Brattka, V., Hertling, P.: Topological properties of real number representations. Theor. Comput. Sci. 284(2), 241–257 (2002)

5. Brattka, V., Hertling, P., Weihrauch, K.: A Tutorial on Computable Analysis, pp. 425–491. Springer New York, New York, NY (2008)

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Satisfiability of Non-linear Transcendental Arithmetic as a Certificate Search Problem;Lecture Notes in Computer Science;2023

2. Handling Polynomial and Transcendental Functions in SMT via Unconstrained Optimisation and Topological Degree Test;Automated Technology for Verification and Analysis;2022