Rewriting Preserving Recognizability of Finite Tree Languages

TL;DR

This paper demonstrates that certain classes of term rewriting systems can preserve the recognizability of finite tree languages and that key properties like reachability and confluence are decidable within this class.

Contribution

It introduces EPRF-TRSs, a class of TRSs that effectively preserve recognizability and establishes decidability results for fundamental properties.

Findings

EPRF-TRSs preserve recognizability of finite tree languages.

Reachability, joinability, and local confluence are decidable for EPRF-TRSs.

Left-linear generalized semi-monadic TRSs are effectively recognizability-preserving.

Abstract

We show that left-linear generalized semi-monadic TRSs effectively preserving recognizability of finite tree languages (are EPRF-TRSs). We show that reachability, joinability, and local confluence are decidable for EPRF-TRSs.