EF+EX Forest Algebras

TL;DR

This paper characterizes the class of unranked forest languages definable with EF and EX temporal operators using algebraic methods, providing decision algorithms and a theoretical framework.

Contribution

It introduces algebraic characterizations for EF and EX-definable forest languages and develops efficient algorithms for their decidability.

Findings

Algebraic characterization of EF+EX definable languages.

Efficient decision algorithms for forest language definability.

Introduction of a general ideal theory for forest algebras.

Abstract

We examine languages of unranked forests definable using the temporal operators EF and EX. We characterize the languages definable in this logic, and various fragments thereof, using the syntactic forest algebras introduced by Bojanczyk and Walukiewicz. Our algebraic characterizations yield efficient algorithms for deciding when a given language of forests is definable in this logic. The proofs are based on understanding the wreath product closures of a few small algebras, for which we introduce a general ideal theory for forest algebras. This combines ideas from the work of Bojanczyk and Walukiewicz for the analogous logics on binary trees and from early work of Stiffler on wreath product of finite semigroups.