An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints
For researchers in formal language theory, this work systematically maps the decidability and complexity of key problems for a broad class of relational patterns, filling a gap in the literature.
The paper extends decision problems (equivalence, inclusion, membership) from standard patterns to relational pattern languages under various constraints, providing a comprehensive analysis of their complexity.
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.