Abstract
This paper is motivated by the results in [M. Ito, Algebraic structures of automata, Theoretical Computer Science 428 (2012) 164-168.]. Structures and the number of subautomata of a finite automaton are investigated. It is shown that the set of all subautomata of a finite automaton A is upper semilattice. We give conditions which allow us to determine whether for a finite upper semilattice (L;≤) there exists an automaton A such that the set of all subautomata of A under set inclusion is isomorphic to (L;≤). Examples illustrating the results are presented.
Highlights
With the advent of electronic computers in the 1950’s, the study of simple formal models of computers such as automata was given a lot of attention
It is shown that the set of all subautomata of a ...nite automaton A is upper semilattice
The fact that automata without outputs, and the automata without outputs belonging to arbitrary automata, can be treated as algebras whose all fundamental operations are unary, that is as unary algebras
Summary
With the advent of electronic computers in the 1950’s, the study of simple formal models of computers such as automata was given a lot of attention. It is shown that the set of all subautomata of a ...nite automaton A is upper semilattice. The following proposition is a reformulation of [7, Theorem 2] and it gives a more explicit description of subautomaton of an automaton. Let L1, L2 and L be Lower sets of a poset (P; ).
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