Publication detail

Algebraic Reasoning Meets Automata in Solving Linear Integer Arithmetic

HAVLENA, V. HEČKO, M. HOLÍK, L. LENGÁL, O. HABERMEHL, P.

Original Title

Algebraic Reasoning Meets Automata in Solving Linear Integer Arithmetic

Type

article in a collection out of WoS and Scopus

Language

English

Original Abstract

We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work directly with numbers. This combination is enabled by a fine-grained version of the duality between automata and arithmetic formulae. In particular, we employ a construction where states of automaton are obtained as derivatives of arithmetic formulae: then every state corresponds to a formula. Optimizations based on techniques and ideas transferred from the world of algebraic methods are used on thousands of automata states, which dramatically amplifies their effect. The merit of this combination of automata with algebraic methods is demonstrated by our prototype implementation being competitive to and even superior to state-of-the-art SMT solvers.

Keywords

Presburger arithmetic, linear integer arithmetic, SMT solver, automata-logic connection

Authors

HAVLENA, V.; HEČKO, M.; HOLÍK, L.; LENGÁL, O.; HABERMEHL, P.

Released

24. 7. 2024

Publisher

Springer Verlag

Location

Montreal

ISBN

0302-9743

Periodical

Lecture Notes in Computer Science

Number

14681

State

Federal Republic of Germany

Pages from

42

Pages to

67

Pages count

26

BibTex

@inproceedings{BUT188628,
  author="Vojtěch {Havlena} and Michal {Hečko} and Lukáš {Holík} and Ondřej {Lengál} and Peter {Habermehl}",
  title="Algebraic Reasoning Meets Automata in Solving Linear Integer Arithmetic",
  booktitle="Proceedings of CAV'24",
  year="2024",
  journal="Lecture Notes in Computer Science",
  number="14681",
  pages="42--67",
  publisher="Springer Verlag",
  address="Montreal",
  doi="10.1007/978-3-031-65627-9\{_}3",
  issn="0302-9743"
}