Slowly synchronizing automata with zero and incomplete sets
E. V. Pribavkina
TL;DR
This paper constructs a series of automata with zero, demonstrating that their shortest synchronizing words have quadratic length, by leveraging combinatorial properties of incomplete sets in free monoids.
Contribution
It introduces a novel construction of automata with zero based on incomplete sets, establishing new bounds on synchronizing word lengths.
Findings
Shortest synchronizing word length is quadratic in the number of states
Uses combinatorial properties of incomplete sets in free monoids
Provides explicit automata constructions with these properties
Abstract
Using combinatorial properties of incomplete sets in a free monoid we construct a series of n-state deterministic automata with zero whose shortest synchronizing word has length n^2/4+n/2-1.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Computability, Logic, AI Algorithms