Unified Analysis of Collapsible and Ordered Pushdown Automata via Term Rewriting

TL;DR

This paper presents a unified framework for analyzing collapsible and ordered pushdown automata using term rewriting, extending classic saturation techniques to demonstrate recognizability preservation.

Contribution

It introduces a novel encoding of higher-order stacks into trees and proves a unified recognizability preservation result for these systems.

Findings

Unified inverse preservation of recognizability for both automata types

Extension of saturation-based approach to term rewriting systems

Generalization that subsumes previous analyses

Abstract

We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term rewriting systems, which is obtained by extending the classic saturation-based approach. This result subsumes and unifies similar analyses on collapsible and ordered pushdown systems. Despite the rich literature on inverse preservation of recognizability for term rewrite systems, our result does not seem to follow from any previous study.