Solving Using Approximations

Maxwell Levatich; Nikolaj Bjørner; Ruzica Piskac; Sharon Shoham

doi:https://doi.org/10.1007/978-3-030-39322-9_17

Solving Using Approximations

Maxwell Levatich, Nikolaj Bjørner, Ruzica Piskac, Sharon Shoham

School of Computer Science

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Linear arithmetic with stars,, is an extension of Presburger arithmetic that allows forming indefinite summations over values that satisfy a formula. It has found uses in decision procedures for multi-sets and for vector addition systems. formulas can be translated back into Presburger arithmetic, but with non-trivial space overhead. In this paper we develop a decision procedure for that checks satisfiability of formulas. By refining on-demand under and over-approximations of formulas, it can avoid the space overhead that is integral to previous approaches. We have implemented our procedure in a prototype and report on encouraging results that suggest that formulas can be checked for satisfiability without computing a prohibitively large equivalent Presburger formula.

Original language	English
Title of host publication	Verification, Model Checking, and Abstract Interpretation - 21st International Conference, VMCAI 2020, Proceedings
Editors	Dirk Beyer, Damien Zufferey
Pages	360-378
Number of pages	19
DOIs	https://doi.org/10.1007/978-3-030-39322-9_17
State	Published - 2020
Event	21st International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2020 - New Orleans, United States Duration: 16 Jan 2020 → 21 Jan 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11990 LNCS

Conference

Conference	21st International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2020
Country/Territory	United States
City	New Orleans
Period	16/01/20 → 21/01/20

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

https://doi.org/10.1007/978-3-030-39322-9_17

Cite this

Levatich, M., Bjørner, N., Piskac, R., & Shoham, S. (2020). Solving Using Approximations. In D. Beyer, & D. Zufferey (Eds.), Verification, Model Checking, and Abstract Interpretation - 21st International Conference, VMCAI 2020, Proceedings (pp. 360-378). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11990 LNCS). https://doi.org/10.1007/978-3-030-39322-9_17

Levatich, Maxwell ; Bjørner, Nikolaj ; Piskac, Ruzica et al. / Solving Using Approximations. Verification, Model Checking, and Abstract Interpretation - 21st International Conference, VMCAI 2020, Proceedings. editor / Dirk Beyer ; Damien Zufferey. 2020. pp. 360-378 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Linear arithmetic with stars,, is an extension of Presburger arithmetic that allows forming indefinite summations over values that satisfy a formula. It has found uses in decision procedures for multi-sets and for vector addition systems. formulas can be translated back into Presburger arithmetic, but with non-trivial space overhead. In this paper we develop a decision procedure for that checks satisfiability of formulas. By refining on-demand under and over-approximations of formulas, it can avoid the space overhead that is integral to previous approaches. We have implemented our procedure in a prototype and report on encouraging results that suggest that formulas can be checked for satisfiability without computing a prohibitively large equivalent Presburger formula.",

author = "Maxwell Levatich and Nikolaj Bj{\o}rner and Ruzica Piskac and Sharon Shoham",

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Levatich, M, Bjørner, N, Piskac, R & Shoham, S 2020, Solving Using Approximations. in D Beyer & D Zufferey (eds), Verification, Model Checking, and Abstract Interpretation - 21st International Conference, VMCAI 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11990 LNCS, pp. 360-378, 21st International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2020, New Orleans, United States, 16/01/20. https://doi.org/10.1007/978-3-030-39322-9_17

Solving Using Approximations. / Levatich, Maxwell; Bjørner, Nikolaj; Piskac, Ruzica et al.
Verification, Model Checking, and Abstract Interpretation - 21st International Conference, VMCAI 2020, Proceedings. ed. / Dirk Beyer; Damien Zufferey. 2020. p. 360-378 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11990 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Linear arithmetic with stars,, is an extension of Presburger arithmetic that allows forming indefinite summations over values that satisfy a formula. It has found uses in decision procedures for multi-sets and for vector addition systems. formulas can be translated back into Presburger arithmetic, but with non-trivial space overhead. In this paper we develop a decision procedure for that checks satisfiability of formulas. By refining on-demand under and over-approximations of formulas, it can avoid the space overhead that is integral to previous approaches. We have implemented our procedure in a prototype and report on encouraging results that suggest that formulas can be checked for satisfiability without computing a prohibitively large equivalent Presburger formula.

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Levatich M, Bjørner N, Piskac R, Shoham S. Solving Using Approximations. In Beyer D, Zufferey D, editors, Verification, Model Checking, and Abstract Interpretation - 21st International Conference, VMCAI 2020, Proceedings. 2020. p. 360-378. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: https://doi.org/10.1007/978-3-030-39322-9_17

Solving Using Approximations

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