Complexity in Prefix-Free Regular Languages
Galina Jir\'askov\'a, Monika Krausov\'a
TL;DR
This paper investigates the complexities of various operations on prefix-free regular languages, providing tighter bounds and minimal alphabet witness languages for both deterministic and nondeterministic cases.
Contribution
It offers new tight bounds on state complexities of key operations and constructs minimal alphabet witness languages, advancing understanding of prefix-free language complexities.
Findings
Tight bounds on symmetric difference complexity.
Minimal alphabet witness languages for complexity bounds.
Improved bounds for difference and cyclic shift operations.
Abstract
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next provide the tight bounds on state complexity of symmetric difference, and deterministic and nondeterministic state complexity of difference and cyclic shift of prefix-free languages.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Coding theory and cryptography