Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Church-Rosser Thue systems and formal languages
Journal of the ACM (JACM)
A shrinking lemma for indexed languages
Theoretical Computer Science
Handbook of formal languages, vol. 1
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
Information and Computation
More on the Size of Higman-Haines Sets: Effective Constructions
Fundamenta Informaticae - Machines, Computations and Universality, Part I
More on the size of higman-haines sets: effective constructions
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
On the State Complexity of Scattered Substrings and Superstrings
Fundamenta Informaticae
More on the Size of Higman-Haines Sets: Effective Constructions
Fundamenta Informaticae - Machines, Computations and Universality, Part I
On inverse operations and their descriptional complexity
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Quotient Complexity of Closed Languages
Theory of Computing Systems
Hi-index | 5.23 |
We show that for the family of Church-Rosser languages the Higman-Haines sets, which are the sets 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, cannot be effectively constructed, although both these sets are regular for any language. This nicely contrasts the result on the effectiveness of the Higman-Haines sets for the family of context-free languages. The non-effectiveness is based on a non-recursive trade-off result between the language description mechanism of Church-Rosser languages and the corresponding Higman-Haines sets, which in turn is also valid for all supersets of the language family under consideration, and in particular for the family of recursively enumerable languages. Finally for the family of regular languages we prove an upper and a matching lower bound on the size of the Higman-Haines sets in terms of nondeterministic finite automata.