Problem
Research questions and friction points this paper is trying to address.
Relational Pattern Languages
Decision Problems
Equivalence Problem
Inclusion Problem
Membership Problem
An Analysis of Decision Problems for Relational Pattern Languages under Various Constraints
🤖 AI Summary
This study addresses the limitation of traditional pattern definitions, which are confined to equality relations and thus struggle to handle complex constraints involving arbitrary independence among variables, hindering research on decision problems for pattern languages. To overcome this, we generalize pattern languages from purely equational constraints to those supporting arbitrary relational constraints. By integrating formal language theory, automata, and regular expression techniques, this work systematically investigates equivalence, inclusion, and membership decision problems under various constraints. The primary contribution is a unified theoretical framework encompassing these three core decision problems across multiple classes of relational constraints, along with precisely characterized decidability conditions. This framework establishes a solid theoretical foundation for both the analysis and application of pattern languages subject to complex relational 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, achieved by using regular patterns and relating individual variables independently from the patterns structure separately. 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Relational Pattern Languages
Decision Problems
Equivalence Problem
Inclusion Problem
Membership Problem
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