On Problems Dual to Unification: The String-Rewriting Case
Abstract
In this paper, we investigate problems which are dual to the unification problem, namely the Fixed Point (FP) problem, Common Term (CT) problem and the Common Equation (CE) problem for string rewriting systems. Our main motivation is computing fixed points in systems, such as loop invariants in programming languages. We show that the fixed point (FP) problem is reducible to the common term problem. Our new results are: (i) the fixed point problem is undecidable for finite convergent string rewriting systems whereas it is decidable in polynomial time for finite, convergent and dwindling string rewriting systems, (ii) the common term problem is undecidable for the class of dwindling string rewriting systems, and (iii) for the class of finite, monadic and convergent systems, the common equation problem is decidable in polynomial time but for the class of dwindling string rewriting systems, common equation problem is undecidable.
Cite
@article{arxiv.2103.00386,
title = {On Problems Dual to Unification: The String-Rewriting Case},
author = {Zümrüt Akçam and Kimberly A. Cornell and Daniel S. Hono and Paliath Narendran and Andrew Pulver},
journal= {arXiv preprint arXiv:2103.00386},
year = {2024}
}
Comments
28 pages, 6 figures, will be submitted for LMCS journal. arXiv admin note: substantial text overlap with arXiv:1706.05607