Learning regular omega languages

We provide an algorithm for learning an unknown regular set of infinite words, using membership and equivalence queries. Three variations of the algorithm learn three different canonical representations of omega regular languages, using the notion of families of dfas. One is of size similar to L $, a dfa representation recently learned using L* [7]. The second is based on the syntactic forc, introduced in [14]. The third is introduced herein.We show that the second can be exponentially smaller than the first, and the third is at most as large as the first two, with up to a quadratic saving with respect to the second.

[1]  Pavol Cerný,et al.  Synthesis of interface specifications for Java classes , 2005, POPL '05.

[2]  Dana Fisman,et al.  Learning Regular Omega Languages , 2014, ALT.

[3]  Ludwig Staiger,et al.  Eine Bemerkung über nichtkonstantenfreie sequentielle Operatoren , 1974, J. Inf. Process. Cybern..

[4]  Ludwig Staiger,et al.  Finite-State omega-Languages , 1983, J. Comput. Syst. Sci..

[5]  Andreas Podelski,et al.  Ultimately Periodic Words of Rational w-Languages , 1993, MFPS.

[6]  Amir Pnueli,et al.  On the learnability of infinitary regular sets , 1991, COLT '91.

[7]  Yih-Kuen Tsay,et al.  Extending Automated Compositional Verification to the Full Class of Omega-Regular Languages , 2008, TACAS.

[8]  Martin Leucker,et al.  Learning Meets Verification , 2006, FMCO.

[9]  Helmut Jürgensen,et al.  Onω-Languages whose syntactic monoid is trivial , 2005, International Journal of Computer & Information Sciences.

[10]  Robert McNaughton,et al.  Testing and Generating Infinite Sequences by a Finite Automaton , 1966, Inf. Control..

[11]  Nils Klarlund.  A Homomorphism Concept for omega-Regularity , 1994 .

[12]  Nils Klarlund.  A Homomorphism Concepts for omega-Regularity , 1994, CSL.

[13]  Ludwig Staiger,et al.  On Syntactic Congruences for Omega-Languages , 1997, Theor. Comput. Sci..

[14]  Colin de la Higuera,et al.  Inference of [omega]-languages from prefixes , 2004, Theor. Comput. Sci..

[15]  Dana Angluin,et al.  Learning Regular Sets from Queries and Counterexamples , 1987, Inf. Comput..

[16]  Ludwig Staiger,et al.  On Syntactic Congruences for Omega-Languages , 1993, Theor. Comput. Sci..

[17]  Corina S. Pasareanu,et al.  Learning Assumptions for Compositional Verification , 2003, TACAS.

[18]  André Arnold,et al.  A Syntactic Congruence for Rational omega-Language , 1985, Theor. Comput. Sci..

[19]  Ahmed Saoudi,et al.  Learning local and recognizable Ω-languages and monadic logic programs , 1994, EuroCOLT.

[20]  Charles P. Pfleeger,et al.  State Reduction in Incompletely Specified Finite-State Machines , 1973, IEEE Transactions on Computers.

[21]  Colin de la Higuera,et al.  Inference of omega-Languages from Prefixes , 2001, ALT.

[22]  Rajeev Alur,et al.  Automatic symbolic compositional verification by learning assumptions , 2008, Formal Methods Syst. Des..

[23]  D. Gnanaraj Thomas,et al.  Learning of Bi-ω Languages from Factors , 2012, ICGI.