Outfix-Free Regular Languages and Prime Outfix-Free Decomposition

A string x is an outfix of a string y if there is a string w such that x1wx2=y, where x = x1x2 and a set X of strings is outfix-free if no string in X is an outfix of any other string in X. We examine the outfix-free regular languages. Based on the properties of outfix strings, we develop a polynomial-time algorithm that determines the outfix-freeness of regular languages. We consider two cases: A language is given as a set of strings and a language is given by an acyclic deterministic finite-state automaton. Furthermore, we investigate the prime outfix-free decomposition of outfix-free regular languages and design a linear-time prime outfix-free decomposition algorithm for outfix-free regular languages. We demonstrate the uniqueness of prime outfix-free decomposition.

[1]  Jian Ma,et al.  Structure of 3-Infix-Outfix Maximal Codes , 1997, Theor. Comput. Sci..

[2]  Arto Salomaa,et al.  On the decomposition of finite languages , 1999, Developments in Language Theory.

[3]  S. Golomb,et al.  Comma-Free Codes , 1958, Canadian Journal of Mathematics.

[4]  Derick Wood,et al.  Intercode Regular Languages , 2007, Fundam. Informaticae.

[5]  Antonio Restivo,et al.  Computing forbidden words of regular languages , 2003, Fundam. Informaticae.

[6]  Derick Wood,et al.  Simple-Regular Expressions and Languages , 2005, DCFS.

[7]  Derick Wood,et al.  Prefix-Free Regular-Expression Matching , 2005, CPM.

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

[9]  Charles L. A. Clarke,et al.  On the use of regular expressions for searching text , 1997, TOPL.

[10]  Antonio Restivo,et al.  Automata and Forbidden Words , 1998, Inf. Process. Lett..

[11]  Dora Giammarresi,et al.  Deterministic Generalized Automata , 1995, Theor. Comput. Sci..

[12]  Derick Wood,et al.  Data structures, algorithms, and performance , 1992 .

[13]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .

[14]  Lila Kari,et al.  On Language Equations with Invertible Operations , 1994, Theor. Comput. Sci..

[15]  Arto Salomaa,et al.  Factorizations of Languages and Commutativity Conditions , 2002, Acta Cybern..

[16]  YO-SUB HAN,et al.  Infix-free Regular Expressions and Languages , 2006, Int. J. Found. Comput. Sci..

[17]  Derick Wood,et al.  The generalization of generalized automata: expression automata , 2004, Int. J. Found. Comput. Sci..

[18]  J. van Leeuwen,et al.  Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[19]  守屋 悦朗,et al.  J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .

[20]  Helmut Jürgensen,et al.  n-Prefix–suffix languages ∗ , 1989 .

[21]  Masami Ito,et al.  Outfix and Infix Codes and Related Classes of Languages , 1991, J. Comput. Syst. Sci..

[22]  D UllmanJeffrey,et al.  Introduction to automata theory, languages, and computation, 2nd edition , 2001 .

[23]  Wojciech Rytter,et al.  Linear-Time Prime Decomposition Of Regular Prefix Codes , 2003, Int. J. Found. Comput. Sci..

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

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

[26]  David Maier.  Review of "Introduction to automata theory, languages and computation" by John E. Hopcroft and Jeffrey D. Ullman. Addison-Wesley 1979. , 1980, SIGA.