Nondeterministic state complexity of star-free languages

We investigate the nondeterministic state complexity of several operations on finite automata accepting star-free and unary star-free languages. It turns out that in most cases exactly the same tight bounds as for general regular languages are reached. This nicely complements the results recently obtained by Brzozowski and Liu (2011) [8] for the operation problem of star-free and unary star-free languages accepted by deterministic finite automata.

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

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

[3]  Carlo Mereghetti,et al.  Two-Way Automata Simulations and Unary Languages , 2000, J. Autom. Lang. Comb..

[4]  Galina Jirásková,et al.  Complexity in Prefix-Free Regular Languages , 2010, DCFS.

[5]  Martin Kutrib,et al.  Determination of finite automata accepting subregular languages , 2009, Theor. Comput. Sci..

[6]  Marek Chrobak,et al.  Errata to: "finite automata and unary languages" , 2003 .

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

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

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

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

[11]  Bo Liu,et al.  Quotient Complexity of Star-Free Languages , 2010, Int. J. Found. Comput. Sci..

[12]  Janusz Brzozowski,et al.  Quotient Complexity of Regular Languages , 2009, J. Autom. Lang. Comb..

[13]  Yo-Sub Han,et al.  Nondeterministic State Complexity for Suffix-Free Regular Languages , 2010, DCFS.

[14]  Martin Kutrib,et al.  The Magic Number Problem for Subregular Language Families , 2010, DCFS.

[15]  Carlo Mereghetti,et al.  Optimal Simulations Between Unary Automata , 1998, STACS.

[16]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[17]  Janusz A. Brzozowski.  Roots of Star Events , 1967, JACM.

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

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

[20]  Tomás Masopust,et al.  Complexity in Union-Free Regular Languages , 2010, Int. J. Found. Comput. Sci..

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

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

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

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

[25]  Janusz A. Brzozowski,et al.  Quotient Complexity of Bifix-, Factor-, and Subword-Free Languages , 2010, ArXiv.

[26]  E. Landau.  Handbuch der Lehre von der Verteilung der Primzahlen , 1974 .

[27]  Martin Kutrib,et al.  Descriptional and computational complexity of finite automata - A survey , 2011, Inf. Comput..

[28]  FRANK R. MOORE,et al.  On the Bounds for State-Set Size in the Proofs of Equivalence Between Deterministic, Nondeterministic, and Two-Way Finite Automata , 1971, IEEE Transactions on Computers.

[29]  Martin Kutrib,et al.  Descriptional Complexity - An Introductory Survey , 2010, Scientific Applications of Language Methods.

[30]  Marcel Paul Schützenberger,et al.  On Finite Monoids Having Only Trivial Subgroups , 1965, Inf. Control..

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

[32]  Janusz A. Brzozowski,et al.  On Decompositions of Regular Events , 1967, JACM.

[33]  Huei-Jan Shyr,et al.  Power-separating regular languages , 2005, Mathematical systems theory.