Automorphism groups and quotients of strongly connected automata and monadic algebras
- 1 October 1966
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- No. 02724847,p. 282-297
- https://doi.org/10.1109/swat.1966.5
Abstract
The class of total automata is characterized. Relationships between the structure of the automorphism group G(A) of a finite automaton A and G(A/H), where A/H is a quotient [9] of A, are exhibited. It is shown that the poset PA of isomorphism classes of quotients of A is an antihomomorphic, image of the poset PG(A) of conjugacy classes of subgroups of G(A). Some results are obtained about natural series of quotient automata. Applications to decomposition theory, in particular to the problem of factoring out identical parallel front components, are given. A generalization of the major parts of the theory to infinite strongly connected monadic algebras is obtained.Keywords
This publication has 12 references indexed in Scilit:
- Methods of the algebraic theory of machinesJournal of Computer and System Sciences, 1967
- Group-Type AutomataJournal of the ACM, 1966
- Algebraic Theory of Machines. I. Prime Decomposition Theorem for Finite Semigroups and MachinesTransactions of the American Mathematical Society, 1965
- The Automorphism Group of the Direct Product of Strongly Related AutomataJournal of the ACM, 1965
- Reversibility in monadic algebras and automataPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1965
- Partially ordered classes of finite automataPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1965
- Isomorphism Groups of AutomataJournal of the ACM, 1962
- The Structure of an Automaton and Its Operation-Preserving Transformation GroupJournal of the ACM, 1962
- On the State Assignment Problem for Sequential Machines. IIEEE Transactions on Electronic Computers, 1961
- On the Structure of Abstract AlgebrasMathematical Proceedings of the Cambridge Philosophical Society, 1935