A Characterization of Totally Compatible Automata
David Fernando Casas Torres
TL;DR
This paper characterizes totally compatible automata, which are automata where every possible state partition is the kernel of some input word, and provides a polynomial-time recognition algorithm.
Contribution
It offers a new characterization of totally compatible automata and introduces an efficient algorithm to identify them.
Findings
Characterization of totally compatible automata
Polynomial-time recognition algorithm
Applicable to finite automata with any number of states
Abstract
Every function on a finite set defines an equivalence relation and, therefore, a partition called the kernel of the function. Automata such that every possible partition is the kernel of a word are called totally compatible. A characterization of such automata is given together with an algorithm to recognize them in polynomial running time with respect to the number of states.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Logic, programming, and type systems