Automates réversibles: combinatoire, algèbre et topologie

Leçons de mathématiques d'aujourd'hui, édité par E.Charpentier, à paraitre chez Cassini.A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be accepted by a reversible automaton. The first characterization gives a description of the subsets of the free group accepted by a reversible automaton that is somewhat reminiscent of Kleene's theorem. The second characterization is more combinatorial in nature. The decidability follows from the third -- algebraic -- characterization. The last and somewhat unexpected characterization is a topological description of our languages that solves an open problem about the finite-group topology of the free monoid

Shuffle on positive varieties of languages

We show there is a unique maximal positive variety of languages which does not contain the language (ab)*. This variety is the unique maximal positive variety satisfying the two following conditions: it is strictly included in the class of rational languages and is closed under the shuffle operation. It is also the unique maximal proper positive variety closed under length preserving morphims. The ordered monoids of the corresponding variety of ordered monoids are characterized as follows: for every pair (a, b) of mutually inverse elements, and for every element z of the minimal ideal of the submonoid generated by a and b, (abzab)^ω ≤ ab. In particular this variety is decidable

Semigroups whose idempotents form a subsemigroup

We prove that every semigroup S in which the idempotents form a subsemigroup has an E-unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover can be chosen with the same property. Then we describe the structure of E-unitary dense semigroups. Our results generalize Fountain's results on semigroups in which the idempotents commute, and are analogous to those of Birget, Margolis and Rhodes, and of Jones and Szendrei on finite E-semigroups. ––– Nous montrons que tout semigroupe S dont les idempotents forment un sous-semigroupe admet un revêtement E-unitaire avec la même propriété. De plus, si S est E-dense ou orthodoxe, alors son revêtement peut être choisi de même. Enfin, nous décrivons la structure des semigroupes E-unitaires denses. Nos résultats généralisent ceux de Fountain sur les semigroupes dont les idempotents commutent, et sont analogues à ceux de Birget, Margolis et Rhodes et de Jones et Szendrei sur les E-semigroupes finis. ––– Prova-se que todo o semigrupo S cujos idempotentes formam um subsemigrupo admite uma cobertura E-unitária com a mesma propriedade. Além disso, se S é E-denso ou regular, então a sua cobertura pode ser escolhida como sendo do mesmo tipo. Enfim, descreve-se a estrutura dos semigrupos finitos E-unitários densos. Estes resultados estendem os de Fountain sobre semigrupos cujos idempotentes comutam, e os de Birget, Margolis e Rhodes, e Jones e Szendrei sobre E-semigrupos finitos

Operations preserving recognizable languages

Given a strictly increasing sequence s of non-negative integers, filtering a word a_0a_1 ... a_n by s consists in deleting the letters ai such that i is not in the set {s_0, s_1, ...}. By a natural generalization, denote by L[s], where L is a language, the set of all words of L filtered by s. The filtering problem is to characterize the filters s such that, for every regular language L, L[s] is regular. In this paper, the filtering problem is solved, and a unified approach is provided to solve similar questions, including the removal problem considered by Seiferas and McNaughton. Our approach relies on a detailed study of various residual notions, notably residually ultimately periodic sequences and residually rational transductions

Ash's type II theorem, profinite topology and Malcev products

This paper is concerned with the many deep and far reaching consequences of Ash's positive solution of the type II conjecture for finite monoids. After rewieving the statement and history of the problem, we show how it can be used to decide if a finite monoid is in the variety generated by the Malcev product of a given variety and the variety of groups. Many interesting varieties of finite monoids have such a description including the variety generated by inverse monoids, orthodox monoids and solid monoids. A fascinating case is that of block groups. A block group is a monoid such that every element has at most one semigroup inverse. As a consequence of the cover conjecture - also verified by Ash - it follows that block groups are precisely the divisors of power monoids of finite groups. The proof of this last fact uses earlier results of the authors and the deepest tools and results from global semigroup theory. We next give connections with the profinite group topologies on finitely generated free monoids and free groups. In particular, we show that the type II conjecture is equivalent with two other conjectures on the structure of closed sets (one conjecture for the free monoid and another one for the free group). Now Ash's theorem implies that the two topological conjectures are true and independently, a direct proof of the topological conjecture for the free group has been recently obtained by Ribes and Zalesskii. An important consequence is that a rational subset of a finitely generated free group G is closed in the profinite topology if and only if it is a finite union of sets of the form gH1H2... Hn, where each Hi is a finitely generated subgroup of G. This significantly extends classical results by M. Hall. Finally we return to the roots of this problem and give connections with the complexity theory of finite semigroups. We show that the largest local complexity function in the sense of Rhodes and Tilson is computable

10501 Abstracts Collection -- Advances and Applications of Automata on Words and Trees

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 ``Advances and Applications of Automata on Words and Trees\u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Group III metabotropic glutamate receptors inhibit hyperalgesia in animal models of inflammation and neuropathic pain

International audienceGlutamate plays a key role in modulation of nociceptive processing. This excitatory amino acid exerts its action through two distinct types of receptors, ionotropic and metabotropic glutamate receptors (mGluRs). Eight mGluRs have been identified and divided in three groups based on their sequence similarity, pharmacology and G-protein coupling. While the role of group I and II mGluRs is now well established, little is known about the part played by group III mGluRs in pain. In this work, we studied comparatively the involvement of spinal group III mGluR in modulation of acute, inflammatory and neuropathic pain. While intrathecal injection of ACPT-I, a selective group III mGluR agonist, failed to induce any change in vocalization thresholds of healthy animals submitted to mechanical or thermal stimuli, it dose-dependently inhibited the nociceptive behavior of rats submitted to the formalin test and the mechanical hyperalgesia associated with different animal models of inflammatory (carrageenan-treated and monoarthritic rats) or neuropathic pain (mononeuropathic and vincristine-treated rats). Similar effects were also observed following intrathecal injection of PHCCC, a positive allosteric modulator of mGlu4. Antihyperalgesia induced by ACPT-I was blocked either by LY341495, a nonselective antagonist of mGluR, by MAP4, a selective group III antagonist. This study provide new evidences supporting the role of spinal group III mGluRs in the modulation of pain perception in different pathological pain states of various etiologies but not in normal conditions. It more particularly highlights the specific involvement of mGlu4 in this process and may be a useful therapeutic approach to chronic pain treatment

On fixed points of the lower set operator

Lower subsets of an ordered semigroup form in a natural way an ordered semigroup. This lower set operator gives an analogue of the power operator already studied in semigroup theory. We present a complete description of the lower set operator applied to varieties of ordered semigroups. We also obtain large families of fixed points for this operator applied to pseudovarieties of ordered semigroups, including all examples found in the literature. This is achieved by constructing six types of inequalities that are preserved by the lower set operator. These types of inequalities are shown to be independent in a certain sense. Several applications are also presented, including the preservation of the period for a pseudovariety of ordered semigroups whose image under the lower set operator is proper

BRET and Time-resolved FRET strategy to study GPCR oligomerization: from cell lines toward native tissues

The concept of oligomerization of G protein-coupled receptor (GPCR) opens new perspectives regarding physiological function regulation. The capacity of one GPCR to modify its binding and coupling properties by interacting with a second one can be at the origin of regulations unsuspected two decades ago. Although the concept is interesting, its validation at a physiological level is challenging and probably explains why receptor oligomerization is still controversial. Demonstrating direct interactions between two proteins is not trivial since few techniques present a spatial resolution allowing this precision. Resonance energy transfer (RET) strategies are actually the most convenient ones. During the last two decades, bioluminescent resonance energy transfer and time-resolved fluorescence resonance energy transfer (TR-FRET) have been widely used since they exhibit high signal-to-noise ratio. Most of the experiments based on GPCR labeling have been performed in cell lines and it has been shown that all GPCRs have the propensity to form homo- or hetero-oligomers. However, whether these data can be extrapolated to GPCRs expressed in native tissues and explain receptor functioning in real life, remains an open question. Native tissues impose different constraints since GPCR sequences cannot be modified. Recently, a fluorescent ligand-based GPCR labeling strategy combined to a TR-FRET approach has been successfully used to prove the existence of GPCR oligomerization in native tissues. Although the RET-based strategies are generally quite simple to implement, precautions have to be taken before concluding to the absence or the existence of specific interactions between receptors. For example, one should exclude the possibility of collision of receptors diffusing throughout the membrane leading to a specific FRET signal. The advantages and the limits of different approaches will be reviewed and the consequent perspectives discussed

Investigation of Prolactin Receptor Activation and Blockade Using Time-Resolved Fluorescence Resonance Energy Transfer

The prolactin receptor (PRLR) is emerging as a therapeutic target in oncology. Knowledge-based drug design led to the development of a pure PRLR antagonist (Del1-9-G129R-hPRL) that was recently shown to prevent PRL-induced mouse prostate tumorogenesis. In humans, the first gain-of-function mutation of the PRLR (PRLRI146L) was recently identified in breast tumor patients. At the molecular level, the actual mechanism of action of these two novel players in the PRL system remains elusive. In this study, we addressed whether constitutive PRLR activation (PRLRI146L) or PRLR blockade (antagonist) involved alteration of receptor oligomerization and/or of inter-chain distances compared to unstimulated and PRL-stimulated PRLR. Using a combination of various biochemical and spectroscopic approaches (co-IP, blue native electrophoresis, BRET1), we demonstrated that preformed PRLR homodimers are altered neither by PRL- or I146L-induced receptor triggering, nor by antagonist-mediated blockade. These findings were confirmed using a novel time-resolved fluorescence resonance energy transfer (TR-FRET) technology that allows monitoring distance changes between cell surface tagged receptors. This technology revealed that PRLR blockade or activation did not involve detectable distance changes between extracellular domains of receptor chains within the dimer. This study merges with our previous structural investigations suggesting that the mechanism of PRLR activation solely involves intermolecular contact adaptations leading to subtle intramolecular rearrangements