Work

Further Tackling Post Correspondence Problem and Proof Generation

Year: 2025

Type: conference-paper

Abstract: Post Correspondence Problem (PCP) is a classic example of an undecidable problem, with various heuristic algorithms proposed to tackle its instances. In this study, we focus on solving a particular subset of instances known as PCP[3,4]. We introduce a novel algorithm that leverages regular lan- guages and automata theory to identify inductive invariants within the transition systems associated with these instances, enabling us to demonstrate the unsolvability of instances. Additionally, we manually found some inductive invariants using an interactive tool developed specifically for this pur- pose. As a result, we successfully solved all instances except for two. To ensure the correctness of our results, we gen- erated proofs for each instance that can be verified using Isabelle/HOL.

Source: ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP)

DOI: 10.1145/3703595.3705886

Authors: Akihiro Omori, Yasuhiko Minamide

Institution: Institute of Science Tokyo

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: Japan Society for the Promotion of Science

Awards: Software Verification Based on the Theory of Transducers, Depeeping Sotfware Verifaction Based on Transducer Theory, G7584280688, Synthesis of High-Level Programs from Temporal and Relational Specifications