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
Journal of Automata, Languages and Combinatorics
A regularity condition for parallel rewriting systems
ACM SIGACT News
The size of Higman-Haines sets
Theoretical Computer Science
The Complexity of Finding SUBSEQ(A)
Theory of Computing Systems
Hi-index | 0.00 |
A not so well-known result in formal language theory is that the Higman-Haines sets for any language are regular [11, Theorem 4.4]. It is easily seen that these sets cannot be effectively computed in general. The Higman-Haines sets are the languages of all scattered subwords of a given language as well as 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 [8]. Here we focus on language families whose Higman-Haines sets are effectively constructible. In particular, we study the size of descriptions of Higman-Haines sets for the lower classes of the Chomsky hierarchy, namely for the family of regular, linear context-free, and context-free languages. We prove upper and lower bounds on the size of descriptions of these sets for general and unary languages.