Random generation of possibly incomplete deterministic automata.

This paper presents an efficient random generator, based on a Boltzmann sampler, for accessible, deterministic and possibly not complete automata.

[1]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

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

[3]  Robert W. Robinson.  Counting strongly connected finite automata , 1985 .

[4]  Jeffrey Shallit,et al.  On the Number of Distinct Languages Accepted by Finite Automata with n States , 2002, DCFS.

[5]  P. Flajolet,et al.  Boltzmann Sampling of Unlabelled Structures , 2006 .

[6]  Michael A. Harrison.  A census finite automata , 1964 .

[7]  Frank Harary,et al.  Enumeration of Finite Automata , 1967, Inf. Control..

[8]  Philippe Flajolet,et al.  Analytic Combinatorics , 2009 .

[9]  Guy Louchard,et al.  Boltzmann Samplers for the Random Generation of Combinatorial Structures , 2004, Combinatorics, Probability and Computing.

[10]  Philippe Flajolet,et al.  A Calculus for the Random Generation of Labelled Combinatorial Structures , 1994, Theor. Comput. Sci..

[11]  V. Liskovets.  The number of connected initial automata , 1969 .

[12]  Valery A. Liskovets,et al.  Exact enumeration of acyclic deterministic automata , 2006, Discret. Appl. Math..

[13]  Frédérique Bassino,et al.  Enumeration and random generation of accessible automata , 2007, Theor. Comput. Sci..

[14]  Jean-Marc Champarnaud,et al.  Random generation of DFAs , 2005, Theor. Comput. Sci..

[15]  Aleksej D. Korshunov.  On the Number of Non-isomorphic Strongly Connected Finite Automata , 1986, J. Inf. Process. Cybern..

[16]  Cyril Nicaud,et al.  Etude du comportement en moyenne des automates finis et des langages rationnels , 2000 .

[17]  J. Sakarovitch.  Eléments de théorie des automates , 2003 .

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

[19]  I. Good.  An Asymptotic Formula for the Differences of the Powers at Zero , 1961 .