VIRAS: Conflict-Driven Quantifier Elimination for Integer-Real Arithmetic

18 pages•Published: May 26, 2024

Johannes Schoisswohl, Laura Kovács and Konstantin Korovin

Abstract

We introduce Virtual Integer-Real Arithmetic Substitution (Viras), a quantifier elim- ination procedure for deciding quantified linear mixed integer-real arithmetic problems. Viras combines the framework of virtual substitutions with conflict-driven proof search and linear integer arithmetic reasoning based on Cooper’s method. We demonstrate that Viras gives an exponential speedup over state-of-the-art methods in quantified arithmetic reasoning, proving problems that SMT-based techniques fail to solve.

Keyphrases: arithmetic, decision procedure, lira, quantifier elimination, smt, virtual substitution

In: Nikolaj Bjørner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 147-164.

Links:	https://easychair.org/publications/paper/r6XtS
	https://doi.org/10.29007/kg4v

BibTeX entry

@inproceedings{LPAR2024:VIRAS_Conflict_Driven_Quantifier,
  author    = {Johannes Schoisswohl and Laura Kovács and Konstantin Korovin},
  title     = {VIRAS: Conflict-Driven Quantifier Elimination for Integer-Real Arithmetic},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bjørner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/r6XtS},
  doi       = {10.29007/kg4v},
  pages     = {147-164},
  year      = {2024}}

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