Principal ideal languages and synchronizing automata
Vladimir V. Gusev, Marina I. Maslennikova, Elena V. Pribavkina
TL;DR
This paper investigates principal ideal languages generated by a single word and introduces methods to construct synchronizing automata and compute their syntactic complexity.
Contribution
It provides an algorithm for constructing strongly connected synchronizing automata and a formula for calculating the syntactic complexity of principal ideal languages.
Findings
Algorithm for constructing synchronizing automata
Compact formula for syntactic complexity
Analysis of ideal languages generated by a single word
Abstract
We study ideal languages generated by a single word. We provide an algorithm to construct a strongly connected synchronizing automaton for which such a language serves as the language of synchronizing words. Also we present a compact formula to calculate the syntactic complexity of this language.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Logic, programming, and type systems