Regular Separability of Well Structured Transition Systems

We investigate languages recognized by well structured transition systems (WSTS) with upward (resp. downward) compatibility. We show that under mild assumptions every two disjoint WSTS languages are regular separable, i.e., there exists a regular language containing one of them and disjoint from the other. In particular, if a language, as well as its complement, are both recognized by a WSTS, then they are necessarily regular.

[1]  Markus Lohrey,et al.  On Boolean Closed Full Trios and Rational Kripke Frames , 2017, Theory of Computing Systems.

[2]  Slawomir Lasota,et al.  Regular separability of one counter automata , 2017, 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[3]  Lorenzo Clemente,et al.  Regular Separability of Parikh Automata , 2016, ICALP.

[4]  Lorenzo Clemente,et al.  Separability of Reachability Sets of Vector Addition Systems , 2016, STACS.

[5]  Alain Finkel,et al.  Well Behaved Transition Systems , 2016, Log. Methods Comput. Sci..

[6]  Eryk Kopczynski,et al.  Invisible Pushdown Languages , 2015, 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[7]  Sylvain Schmitz,et al.  Demystifying Reachability in Vector Addition Systems , 2015, 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science.

[8]  Fernando Rosa-Velardo,et al.  Dynamic Networks of Timed Petri Nets , 2014, Petri Nets.

[9]  Thomas Place,et al.  Going Higher in the First-Order Quantifier Alternation Hierarchy on Words , 2014, ICALP.

[10]  Thomas Place,et al.  Separating regular languages with first-order logic , 2014, CSL-LICS.

[11]  Thomas Place,et al.  Separating Regular Languages by Locally Testable and Locally Threshold Testable Languages , 2013, FSTTCS.

[12]  Thomas Place,et al.  Separating Regular Languages by Piecewise Testable and Unambiguous Languages , 2013, MFCS.

[13]  Wim Martens,et al.  Efficient Separability of Regular Languages by Subsequences and Suffixes , 2013, ICALP.

[14]  Jean Goubault-Larrecq,et al.  Forward Analysis for WSTS, Part II: Complete WSTS , 2009, ICALP.

[15]  Barbara König,et al.  Applying the Graph Minor Theorem to the Verification of Graph Transformation Systems , 2008, CAV.

[16]  Parosh Aziz Abdulla,et al.  Comparing the Expressive Power of Well-Structured Transition Systems , 2007, CSL.

[17]  Jean-François Raskin,et al.  Well-structured languages , 2007, Acta Informatica.

[18]  Parosh Aziz Abdulla,et al.  Multi-clock timed networks , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[19]  Philippe Schnoebelen,et al.  Well-structured transition systems everywhere! , 2001, Theor. Comput. Sci..

[20]  P. Jančar.  A Note on Well Quasi-Orderings for Powersets , 1999, Inf. Process. Lett..

[21]  Ahmed Bouajjani,et al.  Model Checking Lossy Vector Addition Systems , 1999, STACS.

[22]  Dexter Kozen,et al.  Automata and Computability , 1997, Undergraduate Texts in Computer Science.

[23]  Alberto Marcone,et al.  Foundations of BQO theory , 1994 .

[24]  Alain Finkel,et al.  Reduction and covering of infinite reachability trees , 1990, Inf. Comput..

[25]  Alain Finkel,et al.  A Generalization of the Procedure of Karp and Miller to Well Structured Transition Systems , 1987, ICALP.

[26]  Daniel Brand,et al.  On Communicating Finite-State Machines , 1983, JACM.

[27]  Harry B. Hunt,et al.  On the Decidability of Grammar Problems , 1982, JACM.

[28]  Giorgio Delzanno,et al.  On the coverability and reachability languages of monotonic extensions of Petri nets , 2013, Theor. Comput. Sci..

[29]  W. Gasarch.  A Survey of Recursive Combinatorics , 2007 .

[30]  Thomas G. Szymanski,et al.  Noncanonical Extensions of Bottom-Up Parsing Techniques , 1976, SIAM J. Comput..