Solving Using Approximations

Maxwell Levatich; Nikolaj Bjørner; Ruzica Piskac; Sharon Shoham

doi:10.1007/978-3-030-39322-9_17

Solving Using Approximations

Maxwell Levatich, Nikolaj Bjørner^*, Ruzica Piskac, Sharon Shoham

^*Corresponding author for this work

School of Computer Science

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
Publisher	Springer
Pages	360-378
Number of pages	19
ISBN (Print)	9783030393212
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
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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

Access to Document

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). Springer. 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. Springer, 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, Springer, 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. Springer, 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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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. Springer. 2020. p. 360-378. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-39322-9_17

Solving Using Approximations

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