Complement on Prefix-Free, Suffix-Free, and Non-Returning NFA Languages

We prove that the tight bound on the nondeterministic state complexity of complementation on prefix-free and suffix-free languages is 2 n − 1. To prove tightness, we use a ternary alphabet, and we show that this bound cannot be met by any binary prefix-free language. On non-returning languages, the upper bound is 2 n − 1 + 1, and it is tight already in the binary case. We also study the unary case in all three classes.

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

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

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

[4]  Alexander Okhotin,et al.  Descriptional Complexity of Formal Systems , 2016, Theor. Comput. Sci..

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

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

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

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

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

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

[11]  Galina Jirásková,et al.  State Complexity of Some Operations on Regular Languages , 2003, DCFS.

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

[13]  Alfred V. Aho,et al.  On notions of information transfer in VLSI circuits , 1983, STOC.

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

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

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

[17]  Anthony Widjaja To.  Unary finite automata vs. arithmetic progressions , 2008 .

[18]  Yo-Sub Han,et al.  State Complexity of Basic Operations on Non-returning Regular Languages , 2013, DCFS.