408 research outputs found
Automata and rational expressions
This text is an extended version of the chapter 'Automata and rational
expressions' in the AutoMathA Handbook that will appear soon, published by the
European Science Foundation and edited by JeanEricPin
On the Minimal Uncompletable Word Problem
Let S be a finite set of words over an alphabet Sigma. The set S is said to
be complete if every word w over the alphabet Sigma is a factor of some element
of S*, i.e. w belongs to Fact(S*). Otherwise if S is not complete, we are
interested in finding bounds on the minimal length of words in Sigma* which are
not elements of Fact(S*) in terms of the maximal length of words in S.Comment: 5 pages; added references, corrected typo
Foreword
Report of TAC 62 held in Washington, October 18-23, 1993, Alex McCalla presiding. TAC discussed the report of the CGIAR Steering Committee on International Livestock Research. It agreed that the expertise of existing IARCs should not dominate the new center. TAC commissioned a stripe study of plant genetic resources to recommend options to TAC for a change in CGIAR strategy which would recognize its place in a global system of biodiversity. The Committee agreed that the document on CGIAR resource allocation for 1994-1998 submitted to ICW accurately reflected its views. It also endorsed the version of Chapter 13 of the Report on CGIAR Priorities and Strategies as submitted to ICW.Issues on various aspects of the process for external reviews of centers raised in the ICARDA EPMR were discussed by TAC alone, and in a joint session with center directors and board chairs. TAC agreed to experiment with new ideas of strengthen the process. TAC decided to undertake a strategic stripe study of public policy and public management research, but asked for greater definition of the boundaries of the study. It also endorsed a proposal, discussed at TAC 61, to study CGIAR delivery mechanisms, starting in West Africa. TAC further agreed on an inter-center study of CGIAR research on roots and tubers in conjunction with the external reviews of CIP, CIAT and IITA.TAC held a critical discussion of the activities proposed to follow up on UNCED by the CGIAR task force headed by Stein Bie, and made a number of comments for consideration of the Group. The Committee reviewed and revised the criteria for the King Baudouin Award
Graph Spectral Properties of Deterministic Finite Automata
We prove that a minimal automaton has a minimal adjacency matrix rank and a
minimal adjacency matrix nullity using equitable partition (from graph spectra
theory) and Nerode partition (from automata theory). This result naturally
introduces the notion of matrix rank into a regular language L, the minimal
adjacency matrix rank of a deterministic automaton that recognises L. We then
define and focus on rank-one languages: the class of languages for which the
rank of minimal automaton is one. We also define the expanded canonical
automaton of a rank-one language.Comment: This paper has been accepted at the following conference: 18th
International Conference on Developments in Language Theory (DLT 2014),
August 26 - 29, 2014, Ekaterinburg, Russi
Une application de la representation matricielle des transductions
RésuméOn étudie le problème suivant, fréquemment rencontré en théorie des langages: soient n langages L1,…,Ln reconnus par les monoïdes M1,…,Mn respectivement. Etant donné une opération ϕ, on cherche à construire un monoïde M, fonction de M1,…,Mn, qui reconnaisse le langage (L1,…,Ln)ϕ. Nous montrons que la plupart des constructions proposées dans la littérature pour ce type de problème sont en fait des cas particuliers d'une méthode générale que nous exposons ici. Cette méthode s'applique également à certains problèmes moins classiques relatifs par exemple à la réduction du groupe libre ou aux opérations de contrôle sur les T0L-systèmes.AbstractWe study the following classical problem of formal language theory: let L1,…,Ln be n languages recognized by the monoids M1,…,Mn respectively. Given an operation ϕ, we want to build a monoid M, function of M1,…,Mn, which recognizes the language (L1,…,Ln)ϕ. We show that most of the constructions given in the literature for this kind of problem are particular cases of a general method. This method can also be applied to some less classical problems related for example to the Dyck-reduction of the free-group or to control operations on T0L-systems
Series which are both max-plus and min-plus rational are unambiguous
Consider partial maps from the free monoid into the field of real numbers
with a rational domain. We show that two families of such series are actually
the same: the unambiguous rational series on the one hand, and the max-plus and
min-plus rational series on the other hand. The decidability of equality was
known to hold in both families with different proofs, so the above unifies the
picture. We give an effective procedure to build an unambiguous automaton from
a max-plus automaton and a min-plus one that recognize the same series
Quantum finite automata and linear context-free languages: a decidable problem
We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable whether or not they have a nonempty intersection. This extends a result of Blondel et al. which can be interpreted as solving the problem with the free monoid in place of the family of linear context-free languages. © 2013 Springer-Verlag
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