Pumping and Counting on the Regular Post Embedding Problem

The Regular Post Embedding Problem is a variant of Post's Correspondence Problem where one compares strings with the subword relation and imposes additional regular constraints on admissible solutions. It is known that this problem is decidable, albeit with very high complexity. We consider and solve variant problems where the set of solutions is compared to regular constraint sets and where one counts the number of solutions. Our positive results rely on two non-trivial pumping lemmas for Post-embedding languages and their complements.

[1]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[2]  Tomasz Jurdzinski.  Leftist Grammars Are Non-primitive Recursive , 2008, ICALP.

[3]  M. Lothaire.  Combinatorics on words: Bibliography , 1997 .

[4]  Tomasz Jurdzi.  Leftist Grammars Are Non-primitive Recursive , 2008 .

[5]  Slawomir Lasota,et al.  Alternating timed automata , 2005, TOCL.

[6]  Joël Ouaknine,et al.  On the decidability and complexity of Metric Temporal Logic over finite words , 2007, Log. Methods Comput. Sci..

[7]  Philippe Schnoebelen,et al.  Post Embedding Problem Is Not Primitive Recursive, with Applications to Channel Systems , 2007, FSTTCS.

[8]  W. Marsden.  I and J , 2012 .

[9]  Frank Wolter,et al.  Non-primitive recursive decidability of products of modal logics with expanding domains , 2006, Ann. Pure Appl. Log..

[10]  Philippe Schnoebelen,et al.  Toward a Compositional Theory of Leftist Grammars and Transformations , 2010, FoSSaCS.

[11]  Parosh Aziz Abdulla,et al.  Universality Analysis for One-Clock Timed Automata , 2009, Fundam. Informaticae.

[12]  Joël Ouaknine,et al.  Nets with Tokens which Carry Data , 2008, Fundam. Informaticae.

[13]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

[14]  Philippe Schnoebelen,et al.  Computing Blocker Sets for the Regular Post Embedding Problem , 2010, Developments in Language Theory.

[15]  M. Lothaire.  Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications) , 2005 .

[16]  Philippe Schnoebelen,et al.  The omega-Regular Post Embedding Problem , 2008, FoSSaCS.

[17]  Sanjiva Prasad,et al.  FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science, 27th International Conference, New Delhi, India, December 12-14, 2007, Proceedings , 2007, FSTTCS.

[18]  Elias Tahhan-Bittar,et al.  Ordinal Recursive Bounds for Higman's Theorem , 1998, Theor. Comput. Sci..

[19]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[20]  P. Schnoebelen,et al.  The ω-Regular Post Embedding Problem ⋆ , 2008 .

[21]  M. Lothaire.  Algebraic Combinatorics on Words , 2002 .

[22]  Philippe Schnoebelen,et al.  The Ordinal Recursive Complexity of Lossy Channel Systems , 2008, 2008 23rd Annual IEEE Symposium on Logic in Computer Science.