Characterizing Equivalence of Logically Constrained Terms via Existentially Constrained Terms (Full Version)

TL;DR

This paper introduces existentially constrained terms to characterize the equivalence of constrained terms in logically constrained rewriting, providing sound and complete methods for both practical checking and theoretical analysis.

Contribution

It proposes a novel concept of existentially constrained terms and offers multiple syntactic characterizations for their equivalence, advancing the understanding of constrained term equivalence.

Findings

Two complete characterizations for equivalence checking.

Syntactic criteria for equivalence of existentially constrained terms.

Enhanced methods for analyzing constrained terms in rewriting systems.

Abstract

Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained term rewriting. A fundamental question on constrained terms arising there is how to characterize equivalence between them. However, in the current literature only limited progress has been made on this. In this paper, we provide several sound and complete solutions to tackle this problem. Our key idea is the introduction of a novel concept, namely existentially constrained terms, into which the original form of constrained terms can be embedded. We present several syntactic characterizations of equivalence between existentially constrained terms. In particular, we provide two different kinds of complete characterizations: one is designed to facilitate equivalence checking, while the other is intended for theoretical analysis.