Abstract
This paper proposes a state space approach for analyzing the finite automata. A Ψ-representation transforms a set of words into a formal power series for establishing the state equation of a finite automaton. We investigate the structure of the automaton via its corresponding state equation. It is shown that the solution of the state equation always exists and is unique. Furthermore, we prove that the solution field is a separable algebraic extension of the coefficient field. Finally, the concept of the substitution property of a partition is shown to be equivalent to that of invariant subspaces of the associated state space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Artin,Algebraic Numbers and Algebraic Functions, New York University, New York (1951).
G. Bachman and L. Narici,Functional Analysis, Academic Press, New York (1966).
P. R. Halmos,Fnite-Dimensional Vector Space, 2nd ed., D. VanNostrand, Princeton, New Jersey (1958).
J. Hartmanis and R. E. Stearns,Algebraic Structure Theory of Sequential Machines, Prentice-Hall, Englewood Cliffs, New Jersey (1966).
G. Lallement,Semigroups and Combinatorial Applications, John Wiley & Sons, New York (1979).
S. Lang,Algebra, Addison-Wesley, Reading Massachusetts (1965).
T. T. Lee, Order-preserving representations of the partitions on the finite set,J. Combinatorial Theory SE-A31(2):136–145 (1981).
P. J. McCarthy,Algebraic Extensions of Fields, Chelsea Publishing Company, Chelsea, New York, (1976).
M. O. Rabin and D. Scott,Finite automata and their decision problems, IBM J. Res. Dev. 3:114–125 (1959).
H. L. Royden,Real Analysis, Macmillan, New York (1963).
R. M. Smullyan,Theory of Formal Systems, Princeton University Press, Princeton, New Jersey (1961).
O. Zariski and P. Samuel,Commutative Algebra, Vol. 1, D. VanNostrand, Princeton, New Jersey (1958).
Author information
Authors and Affiliations
Additional information
This work was performed in Polytechnic Institute of New York.
Rights and permissions
About this article
Cite this article
Lee, T.T. A state space approach to the finite automata. International Journal of Computer and Information Sciences 12, 317–335 (1983). https://doi.org/10.1007/BF01008044
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01008044