Nondeterministic State Complexity for Suffix-Free Regular Languages

We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case for a minimal nondeterministic finite-state automaton that accepts the language obtained from the operation. We consider basic operations (catenation, union, intersection, Kleene star, reversal and complementation) and establish matching upper and lower bounds for each operation. In the case of complementation the upper and lower bounds differ by an additive constant of two.

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

[2]  Michael Domaratzki,et al.  State Complexity of Proportional Removals , 2002, J. Autom. Lang. Comb..

[3]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[4]  J. Berstel,et al.  Theory of codes , 1985 .

[5]  Tao Jiang,et al.  Minimal NFA Problems are Hard , 1991, SIAM J. Comput..

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

[7]  Yo-Sub Han,et al.  State Complexity of Union and Intersection of Finite Languages , 2008, Int. J. Found. Comput. Sci..

[8]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[9]  Yo-Sub Han,et al.  State complexity of basic operations on suffix-free regular languages , 2009, Theor. Comput. Sci..

[10]  Jozef Jirásek,et al.  State complexity of concatenation and complementation , 2005, Int. J. Found. Comput. Sci..

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

[12]  Sheng Yu,et al.  Tight Lower Bound for the State Complexity of Shuffle of Regular Languages , 2002, J. Autom. Lang. Comb..

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

[14]  Karel Culik,et al.  State Complexity of Basic Operations on Finite Languages , 1999, WIA.

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

[16]  Sheng Yu,et al.  NFA to DFA Transformation for Finite Languages over Arbitrary Alphabets , 1998, J. Autom. Lang. Comb..

[17]  Jeffrey Shallit,et al.  A Lower Bound Technique for the Size of Nondeterministic Finite Automata , 1996, Inf. Process. Lett..

[18]  Derick Wood,et al.  On the state complexity of reversals of regular languages , 2004, Theor. Comput. Sci..

[19]  A. R. Meyer,et al.  Economy of Description by Automata, Grammars, and Formal Systems , 1971, SWAT.

[20]  Martin Kutrib,et al.  Unary Language Operations and Their Nondeterministic State Complexity , 2002, Developments in Language Theory.

[21]  Martin Kutrib,et al.  Nondeterministic Descriptional Complexity Of Regular Languages , 2003, Int. J. Found. Comput. Sci..

[22]  Galina Jirásková,et al.  State Complexity of Intersection and Union of Suffix-Free Languages and Descriptional Complexity , 2009, NCMA.

[23]  Derick Wood,et al.  Operational State Complexity of Prefix-Free Regular Languages , 2009, Automata, Formal Languages, and Related Topics.

[24]  Jean-Camille Birget,et al.  Intersection and Union of Regular Languages and State Complexity , 1992, Inf. Process. Lett..

[25]  Derick Wood,et al.  Nondeterministic State Complexity of Basic Operations for Prefix-Free Regular Languages , 2009, Fundam. Informaticae.

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