Abstract
Much scientific work today is directed towards understanding complexity — the complexity of numerical algorithms, of the English syntax, of living organisms or ecological systems, to cite only a few examples. The aim of this chapter is to introduce the reader to the theory of discrete information processing systems (automata) and to develop an algebraic framework within which we can talk about their complexity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zadeh, L. A., Polak, E.; System Theory, McGraw-Hill Inc., New York, 1968.
Pichler, F.; Mathematische Systemtheorie, Walter de Gryter, Berlin, 1975.
Arbib, M. A.; Theories of Abstract Automata, Prentice Hall, Englewood Cliffs, 1969.
Arbib, M. A., Manes, E. G.; A Category-theoretic approach to systems in a fuzzy world, in Systems: Approaches, Theories, Applications, W. E. Harnett (ed.), D. Reidel Pub. Comp., Dordrecht, 1, 26, 1975.
Eilenberg, S.; Automata, Languages, and Machines, Vol. A, B, Academic Press, New York, 1974/75.
Salomaa, A.; Formal Languages, Academic Press, New York, 1973.
Wells, C.; Some applications of the wreath product construction, Am. Math. Month. 83, 317–338, 1976.
Dal Cin, M., Dilger, E.; On effective structures of automata, Group Theoretical Methods in Physics, P. Kramer and A. Rieckers (eds.), Springer Lecture Notes in Physics, 79, 467–469, Springer Verlag Berlin-Heidelberg-New York, 1978.
Dilger, E.; On permutation reset automata, Information and Control, Vol. 30, 86–95, 1976.
Nozaki, A.; Practical decomposition of automata, Information and Control 36, 275–291, 1978.
Hartmanis, J., Stearns, R. E.; Algebraic Strucutre Theory of Sequential Machines, Prentice-Hall, Englewood Cliffs, 1968.
Jürgensen, H.; Some Applications of the Theory of Semigroups to Automata; in Group Theoretical Methods in Physics, P. Kramer and A. Rieckers eds., Springer Lecture Notes in Physics, 79, 307–322, Springer Verlag, Berlin-Heidelberg-New York, 1978.
Zalcstein, Y.; On the semigroup of linear sequential machines, Int. Journ. of Computer and Information Sciences Vol. 2, 25–28, 1973.
Hotzel, E.; Zur schleifenfreien Zerlegung von Mealy-Automaten, Mitteilungen der Ges. f. Mathem. u. Datenverarb. Nr. 29, Bonn, 1974.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Dal Cin, M. (1980). The Algebraic Theory of Automata. In: Kramer, P., Dal Cin, M. (eds) Groups, Systems and Many-Body Physics. Vieweg Tracts in Pure and Applied Physics, vol 4. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06825-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-663-06825-9_8
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08444-8
Online ISBN: 978-3-663-06825-9
eBook Packages: Springer Book Archive