Bispecial factors in circular non-pushy D0L languages

We study bispecial factors in fixed points of morphisms. In particular, we propose a simple method of how to find all bispecial words of non-pushy circular D0L-systems. This method can be formulated as an algorithm. Moreover, we prove that non-pushy circular D0L-systems are exactly those with finite critical exponent.Comment: 18 pages, 5 figure

Systems of equations over a free monoid and Ehrenfeucht's conjecture

AbstractEhrenfeucht's conjecture states that every language L has a finite subset F such that, for any pair (g, h) of morphisms, g and h agree on every word of L if and only if they agree on every word of F. We show that it holds if and only if every infinite system of equations (with a finite number of unknowns) over a free monoid has an equivalent finite subsystem. It is shown that this holds true for rational (regular) systems of equations.The equivalence and inclusion problems for finite and rational systems of equations are shown to be decidable and, consequently, the validity of Ehrenfeucht's conjecture implies the decidability of the HDOL and DTOL sequence equivalence problems. The simplicity degree of a language is introduced and used to argue in support of Ehrenfeucht's conjecture

The separation problem for regular languages by piecewise testable languages

Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem for regular languages. We then give a direct polynomial time algorithm to check whether two given regular languages are separable by a piecewise testable language, that is, whether a $B{\Sigma}1(<)$ sentence can witness that the languages are indeed disjoint. The proof is a reformulation and a refinement of an algebraic argument already given by Almeida and the second author

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Quantum Systems as results of Geometric Evolutions

In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is introduced. It is based on a geometric evolution from Finsler to Riemann structures defined in ${\bf TM}$. Quantum states are generated and interpreted as equivalence classes, composed by the configurations that evolve through an internal dynamics, to the same final state. The existence of an hermitian scalar product in an associated linear space is discussed and related with the quantum pre-Hilbert space. This hermitian product emerges from geometric and statistical considerations. Our scheme recovers the main ingredients of the usual Quantum Mechanics. Several testable consequences of our scheme are discussed and compared with usual Quantum Mechanics. A tentative solution of the cosmological constant problem is proposed, as well as a mechanism for the absence of quantum interferences at classical scales.Comment: paper withdraw