An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints

TL;DR

This paper investigates decision problems for relational pattern languages, extending classical pattern concepts to include arbitrary relations among variables, and analyzes their computational properties under various constraints.

Contribution

It provides a comprehensive analysis of the main decision problems for relational pattern languages with diverse relations, broadening the theoretical understanding.

Findings

Extended pattern notions to include arbitrary relations among variables.

Analyzed the complexity of equivalence, inclusion, and membership problems.

Established foundational results for relational pattern languages under various constraints.

Abstract

Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for multiple distinct occurrences of some variables to be related by the equality relation, represented by using the same variable multiple times. In an extended notion, called relational patterns and relational pattern languages, variables may be related by arbitrary other relations. We extend the ongoing investigation of the main decision problems for patterns (namely, the equivalence problem, the inclusion problem, and the membership problem) to relational pattern languages under a wide range of relevant individual relations, providing a comprehensive foundation in all three research directions.