State complexity of concatenation and complementation

We investigate the state complexity of concatenation and the nondeterministic state complexity of complementation of regular languages. We show that the upper bounds on the state complexity of concatenation are also tight in the case that the first automaton has more than one accepting state. In the case of nondeterministic state complexity of complementation, we show that the entire range of complexities, up to the known upper bound can be produced.

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

[2]  Juraj Hromkovic,et al.  Communication Complexity and Parallel Computing , 1997, Texts in Theoretical Computer Science An EATCS Series.

[3]  Sheng Yu,et al.  On the State Complexity of k-Entry Deterministic Finite Automata , 2001, J. Autom. Lang. Comb..

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

[5]  Hartmut Klauck,et al.  Communication Complexity Method for Measuring Nondeterminism in Finite Automata , 2002, Inf. Comput..

[6]  Jean-Camille Birget,et al.  Partial Orders on Words, Minimal Elements of Regular Languages and State Complexity , 1993, Theor. Comput. Sci..

[7]  William J. Sakoda,et al.  Nondeterminism and the size of two way finite automata , 1978, STOC.

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

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

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

[11]  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.

[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.  State Complexity of Finite and Infinite Regular Languages , 2002, Bull. EATCS.

[14]  Ernst L. Leiss.  Succinct Representation of Regular Languages by Boolean Automata II , 1985, Theor. Comput. Sci..

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

[16]  Galina Jirásková.  Note on Minimal Automata and Uniform Communication Protocols , 2003, Grammars and Automata for String Processing.

[17]  Michael Sipser,et al.  Introduction to the Theory of Computation , 1996, SIGA.

[18]  Giovanni Pighizzini.  Unary Language Concatenation and Its State Complexity , 2000, CIAA.

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

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

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

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

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

[24]  Michael Domaratzki,et al.  State Complexity and Proportional Removals , 2001, DCFS.

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

[26]  Juraj Hromkovic,et al.  Descriptional Complexity of Finite Automata: Concepts and Open Problems , 2002, J. Autom. Lang. Comb..

[27]  Martin Kutrib,et al.  State complexity of basic operations on nondeterministic finite automata , 2002, CIAA'02.