On the Synchronization of Circular Semi-Flower Automata
Shubh N. Singh, Ankit Raj
TL;DR
This paper investigates the synchronization properties of circular semi-flower automata, establishing conditions under which they are guaranteed to be synchronizing, including cases with 1-cycles and odd numbers of states with 2-cycles.
Contribution
It introduces new synchronization results for circular semi-flower automata, extending known conditions to broader classes of these automata.
Findings
Semi-flower automata are one-cluster automata.
Semi-flower automata with a 1-cycle are synchronizing.
Circular semi-flower automata with an odd number of states and a 2-cycle are synchronizing.
Abstract
Pin proved that every circular automaton with a prime number of states containing a non-permutation is synchronizing. In this paper, we investigate the synchronization of circular semi-flower automata. We first prove that every semi-flower automaton is a one-cluster automaton. Subsequently, we prove that every semi-flower automaton containing a 1-cycle is synchronizing. Further, we prove that every circular semi-flower automaton with an odd number of states containing a 2-cycle is synchronizing.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Advanced Algebra and Logic