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Improving Bit-Blasting for Nonlinear Integer Constraints

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Jian ZhangAuthors Info & Claims

ISSTA 2023: Proceedings of the 32nd ACM SIGSOFT International Symposium on Software Testing and Analysis

Pages 14 - 25

https://doi.org/10.1145/3597926.3598034

Published: 13 July 2023 Publication History

Abstract

Nonlinear integer constraints are common and difficult in the verification and analysis of software/hardware. SMT(QF_NIA) generalizes such constraints, which is a boolean combination of nonlinear integer arithmetic constraints. A classical method to solve SMT(QF_NIA) is bit-blasting, which reduces them to boolean satisfiability problems. Currently, the existing pure bit-blasting based solvers are noncompetitive with other state-of-the-art SMT solvers. The bit-blasting based methods have some problems: First, the bit-blasting method is hampered by nonlinear multiplication operations; second, it sometimes does not search in a proper search space; and third, it contains some redundancy.

In this paper, we focus on improving the efficiency of bit-blasting based method. To decide on a proper search space, we proposed an adaptive function for hard nonlinear multiplications, and heuristic strategies to analyze specific constraints. We also found that different orders in successive additions will result in bit vectors with different bit-widths. We proposed an optimal order decision algorithm to save redundancy in successive additions. We implement a solver with the proposed methods named BLAN. Experiments demonstrate that BLAN outperforms other state-of-the-art SMT solvers (APROVE, CVC5, MATHSAT, YICES2, Z3) on the satisfiable SMT(QF_NIA) instances in SMT-LIB. We provide an outlook of BLAN on solving unsatisfiable instances via combining with other solvers. Sensitivity analysis also demonstrates the effectiveness of the proposed methods.

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Cited By

Jia FHan RMa XCui BLiu MHuang PMa FZhang J(2023)PSMT: Satisfiability Modulo Theories Meets Probability Distribution2023 38th IEEE/ACM International Conference on Automated Software Engineering (ASE)10.1109/ASE56229.2023.00183(1756-1760)Online publication date: 11-Sep-2023
https://doi.org/10.1109/ASE56229.2023.00183
Liu MLv KHuang PHan RJia FZhang YMa FZhang J(2023)NRAgo: Solving SMT(NRA) Formulas with Gradient-Based Optimization2023 38th IEEE/ACM International Conference on Automated Software Engineering (ASE)10.1109/ASE56229.2023.00013(2046-2049)Online publication date: 11-Sep-2023
https://doi.org/10.1109/ASE56229.2023.00013

Index Terms

Improving Bit-Blasting for Nonlinear Integer Constraints

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cover image ACM Conferences

ISSTA 2023: Proceedings of the 32nd ACM SIGSOFT International Symposium on Software Testing and Analysis

July 2023

1554 pages

ISBN:9798400702211

DOI:10.1145/3597926

General Chair:
René Just
University of Washington, USA
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Gordon Fraser
University of Passau, Germany

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Published: 13 July 2023

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Cited By

Jia FHan RMa XCui BLiu MHuang PMa FZhang J(2023)PSMT: Satisfiability Modulo Theories Meets Probability Distribution2023 38th IEEE/ACM International Conference on Automated Software Engineering (ASE)10.1109/ASE56229.2023.00183(1756-1760)Online publication date: 11-Sep-2023
https://doi.org/10.1109/ASE56229.2023.00183
Liu MLv KHuang PHan RJia FZhang YMa FZhang J(2023)NRAgo: Solving SMT(NRA) Formulas with Gradient-Based Optimization2023 38th IEEE/ACM International Conference on Automated Software Engineering (ASE)10.1109/ASE56229.2023.00013(2046-2049)Online publication date: 11-Sep-2023
https://doi.org/10.1109/ASE56229.2023.00013

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