English

Input-based Three-valued Abstraction Refinement

Logic in Computer Science 2025-11-13 v5

Abstract

Unlike Counterexample-Guided Abstraction Refinement (CEGAR), Three-Valued Abstraction Refinement (TVAR) is able to verify all properties of the mu-calculus. We present a novel algorithmic framework for TVAR that employs a simulator-like approach to build and refine the abstract state space with input-based splitting. This leads to a state space formalism that is much simpler than in previous TVAR frameworks, which use modal transitions. We implemented the framework in our open-source tool machine-check and verified properties of machine-code systems for the AVR architecture, showing the ability to verify systems and mu-calculus properties not verifiable by naive model checking or CEGAR, respectively. This is the first practical use of TVAR for machine-code verification.

Cite

@article{arxiv.2408.12668,
  title  = {Input-based Three-valued Abstraction Refinement},
  author = {Jan Onderka and Stefan Ratschan},
  journal= {arXiv preprint arXiv:2408.12668},
  year   = {2025}
}

Comments

20 pages, 4 figures, 1 algorithm, 2 tables, 5 appendix pages