Permutation Groups in Automata Diagrams


  • Gan Yee Siang
  • Fong Wan Heng
  • Nor Haniza Sarmin
  • Sherzod Turaev



Finite automata, Watson-Crick finite automata, Cayley table, Permutation group, Automata diagram,


Automata act as classical models for recognition devices. From the previous researches, the classical models of automata have been used to scan strings and to determine the types of languages a string belongs to. In the study of automata and group theory, it has been found that the properties of a group can be recognized by the automata using the automata diagrams. There are two types of automata used to study the properties of a group, namely modified finite automata and modified Watson-Crick finite automata. Thus, in this paper, automata diagrams are constructed to recognize permutation groups using the data given by the Cayley table. Thus, the properties of permutation group are analyzed using the automaton diagram that has been constructed. Moreover, some theorems for the properties of permutation group in term of automata are also given in this paper.


M. V. Lawson. Finite Automata. A CRC press company, New York. 2003.

M. Maxim, Algorithms, Languages, Automata and Compilers, Jones and Bartlett Publishers, USA, 2010.

C. Martin-Vide, V. Mitrana and Gh. Păun, Formal Languages and Applications, Springer-Verlag, Berlin, 2004.

E. Czeizler, L. Kari and A. Salomaa. Theoretical Computer Science 410 (2009), 3250-3260.

Y. S. Gan, W.H. Fong, N.H. Sarmin and S. Turaev. Malaysian Journal of Fundamental and Applied Sciences, 8(1) (2012), 24-30.

Y. S. Gan, W.H. Fong, N.H. Sarmin and S. Turaev. American Institute of Physics (AIP), 2012. To appear.

P. Linz, An Introduction to Formal Languages and Automata, Jones and Bartlett Publishers, USA, 2006.

J. C. Martin. Introduction to Languages and the Theory of Computation. McGraw-Hill Companies Inc., New York, 2003.

A. T. Sudkamp, Languages and Machines, Addison Wesley Longman, Inc., USA, 1998.

L. Walter and J.W. Alan, Introduction to Group Theory, Addison Wesley Longman, USA, 1996.

C. Predrag. Group Theory, Princeton University Press, USA, 2008.

M. John. Groups, Graphs and Trees: An Introduction to the geometry of Infinite Groups, University Press, Cambridge, 2008. [13] G. Paun, G. Rozenberg, A. Salomaa. DNA Computing. Springer-Verlag Berlin Heidelberg, New York. 1998.