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

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

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

Simulation study of magnetic holes at the Earth's collisionless bow shock

Recent observations by the Cluster and Double Star spacecraft at the Earth's bow shock have revealed localized magnetic field and density holes in the solar wind plasma. These structures are characterized by a local depletion of the magnetic field and the plasma density, and by a strong increase of the plasma temperature inside the magnetic and density cavities. Our objective here is to report results of a hybrid-Vlasov simulations of ion-Larmor-radius sized plasma density cavities with parameters that are representative of the high-beta solar wind plasma at the Earth's bow shock. We observe the asymmetric self-steepening and shock-formation of the cavity, and a strong localized temperature increase (by a factor of 5–7) of the plasma due to reflections and shock surfing of the ions against the collisionless shock. Temperature maxima are correlated with density minima, in agreement with Cluster observations. For oblique incidence of the solar wind, we observe efficient acceleration of ions along the magnetic field lines by the shock drift acceleration process

Conjugacy and Equivalence of Weighted Automata and Functional Transducers

International audienceWe show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) ¯eld and that the same holds true for functional tranducers as well

Classifying Non-periodic Sequences by Permutation Transducers

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Minimal Synthesis of String To String Functions From Examples

We study the problem of synthesizing string to string transformations from a set of input/output examples. The transformations we consider are expressed using deterministic finite automata (DFA) that read pairs of letters, one letter from the input and one from the output. The DFA corresponding to these transformations have additional constraints, ensuring that each input string is mapped to exactly one output string. We suggest that, given a set of input/output examples, the smallest DFA consistent with the examples is a good candidate for the transformation the user was expecting. We therefore study the problem of, given a set of examples, finding a minimal DFA consistent with the examples and satisfying the functionality and totality constraints mentioned above. We prove that, in general, this problem (the corresponding decision problem) is NP-complete. This is unlike the standard DFA minimization problem which can be solved in polynomial time. We provide several NP-hardness proofs that show the hardness of multiple (independent) variants of the problem. Finally, we propose an algorithm for finding the minimal DFA consistent with input/output examples, that uses a reduction to SMT solvers. We implemented the algorithm, and used it to evaluate the likelihood that the minimal DFA indeed corresponds to the DFA expected by the user.Comment: SYNT 201

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Modular Descriptions of Regular Functions

We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one may use more human friendly descriptions based on some simple basic transformations (e.g., copy, duplicate, erase, reverse) and various combinators such as function composition or extensions of regular operations.Comment: preliminary version appeared in CAI 2019, LNCS 1154