More on the size of higman-haines sets: effective constructions

Authors:
Hermann Gruber;Markus Holzer;Martin Kutrib
Affiliations:
Institut für Informatik, Ludwig-Maximilians-Universität München, München, Germany;Institut für Informatik, Technische Universität München, Garching bei München, Germany;Institut für Informatik, Universität Giessen, Giessen, Germany
Venue:
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Year:
2007

Citing 7
Cited 0

A shrinking lemma for indexed languages

Theoretical Computer Science
A lower bound technique for the size of nondeterministic finite automata

Information Processing Letters
Growing context-sensitive languages and Church-Rosser languages

Information and Computation
Characterizations of recursively enumerable languages by programmed grammars with unconditional transfer

Journal of Automata, Languages and Combinatorics
Regulated Rewriting in Formal Language Theory

Regulated Rewriting in Formal Language Theory
A regularity condition for parallel rewriting systems

ACM SIGACT News
The size of Higman-Haines sets

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

A not well-known result [9, Theorem 4.4] in formal language theory is that the Higman-Haines sets for any language are regular, but it is easily seen that these sets cannot be effectively computed in general. Here the Higman-Haines sets are the languages of all scattered subwords of a given language and the sets of all words that contain some word of a given language as a scattered subword. Recently, the exact level of unsolvability of Higman-Haines sets was studied in [10]. We focus on language families whose Higman-Haines sets are effectively constructible. In particular, we study the size of Higman-Haines sets for the lower classes of the Chomsky hierarchy, namely for the families of regular, linear contextfree, and context-free languages, and prove upper and lower bounds on the size of these sets.