Transition Complexity of Incomplete DFAs

We consider the transition complexity of regular languages based on the incomplete deterministic finite automata. We establish tight bounds for the transition complexity of Boolean operations, in the case of union the upper and lower bounds differ by a multiplicative constant two. We show that the transition complexity results for union and complementation are very different from the state complexity results for the same operations. However, for intersection, the transition complexity bounds turn out to be similar to the corresponding bounds for state complexity.

[1]  Andrei Paun,et al.  State and Transition Complexity of Watson-Crick Finite Automata , 1999, FCT.

[2]  Lauri Karttunen,et al.  Finite State Morphology , 2003, CSLI Studies in Computational Linguistics.

[3]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[4]  Martin Kutrib,et al.  NONDETERMINISTIC FINITE AUTOMATA — RECENT RESULTS ON THE DESCRIPTIONAL AND COMPUTATIONAL COMPLEXITY , 2009 .

[5]  Derick Wood,et al.  Theory of computation , 1986 .

[6]  Michael Domaratzki,et al.  Transition complexity of language operations , 2007, Theor. Comput. Sci..

[7]  Sheng Yu,et al.  The State Complexities of Some Basic Operations on Regular Languages , 1994, Theor. Comput. Sci..

[8]  Arto Salomaa,et al.  State complexity of combined operations , 2007, Theor. Comput. Sci..

[9]  Karen Rudie.  A Summary of Some Discrete-Event System Control Problems , 2010, CIAA.

[10]  Marek Chrobak,et al.  Finite Automata and Unary Languages , 1986, Theor. Comput. Sci..

[11]  Sheng Yu,et al.  State Complexity of Regular Languages , 2001, J. Autom. Lang. Comb..

[12]  Derrick Wood,et al.  Theory of Computation: A Primer , 1987 .

[13]  Markus Holzer,et al.  On the average state and transition complexity of finite languages , 2007, Theor. Comput. Sci..

[14]  Galina Jirásková,et al.  State complexity of some operations on binary regular languages , 2005, Theor. Comput. Sci..

[15]  Jeffrey Shallit,et al.  A Second Course in Formal Languages and Automata Theory , 2008 .

[16]  Michael Domaratzki,et al.  Lower bounds for the transition complexity of NFAs , 2008, J. Comput. Syst. Sci..

[17]  Yuan Gao,et al.  State Complexity of Catenation Combined with Union and Intersection , 2010, CIAA.

[18]  Jeffrey Shallit,et al.  Unary Language Operations, State Complexity and Jacobsthal's Function , 2002, Int. J. Found. Comput. Sci..

[19]  Michael Domaratzki,et al.  State complexity of power , 2009, Theor. Comput. Sci..