On the structure and syntactic complexity of generalized definite languages

TL;DR

This paper characterizes generalized definite languages using forbidden patterns, analyzes the complexity of related decision problems, and compares their syntactic complexity to that of definite languages, providing bounds and computational insights.

Contribution

It introduces a forbidden pattern characterization for generalized definite languages and analyzes their syntactic complexity and computational properties.

Findings

The problem is NL-complete and solvable in quadratic time.

Syntactic complexity matches that of definite languages.

Upper bound of n! for syntactic complexity.

Abstract

We give a forbidden pattern characterization for the class of generalized definite languages, show that the corresponding problem is NL-complete and can be solved in quadratic time. We also show that their syntactic complexity coincides with that of the definite languages and give an upper bound of n! for this measure.