193 research outputs found
Regular languages and partial commutations
[EN] The closure of a regular language under a [partial] commutation I has been extensively
studied. We present new advances on two problems of this area: (1) When is the
closure of a regular language under [partial] commutation still regular? (2) Are there
any robust classes of languages closed under [partial] commutation? We show that the
class Pol(G) of polynomials of group languages is closed under commutation, and under
partial commutation when the complement of I in A2 is a transitive relation. We also
give a su¿cient graph theoretic condition on I to ensure that the closure of a language
of Pol(G) under I-commutation is regular. We exhibit a very robust class of languages W
which is closed under commutation. This class contains Pol(G), is decidable and can be
de¿ned as the largest positive variety of languages not containing (ab)¿. It is also closed
under intersection, union, shu¿e, concatenation, quotients, length-decreasing morphisms
and inverses of morphisms. If I is transitive, we show that the closure of a language of W
under I-commutation is regular. The proofs are nontrivial and combine several advanced
techniques, including combinatorial Ramsey type arguments, algebraic properties of the
syntactic monoid, ¿niteness conditions on semigroups and properties of insertion systems.
© 2013 Elsevier Inc. All rights reserved[ES] El cierre de un lenguaje regular bajo una conmutación [parcial]
se ha estudiado extensivamente. Presentamos nuevos avances sobre los dos problemas
de esta zona: (1) cuando es el cierre de un lenguaje regular bajo
¿conmutación [parcial] todavía regular? (2) Hay alguna clase robusta
¿de idiomas cerraron bajo conmutación [parcial]? Demostramos que la
clase \PolG de polinomios de grupo idiomas está cerrada bajo
conmutación y bajo conmutación parcial cuando el complemento de I
en es una relación transitiva. También damos un gráfico suficiente
condición teórica en I para asegurarse de que el cierre de un lenguaje de
\PolG bajo -conmutación es regular. Exhibimos un muy robusto
clase de idiomas \cW que es cerrado bajo conmutación. Esta clase
contiene \PolG, es decidible y puede definirse como el más grande
positiva variedad de idiomas que no contengan . También es
cerrado bajo intersección, Unión, shuffle, concatenación, cocientes,
longitud decreciente morfismos e inversas de morfismos. Si I es
transitivo, demostramos que el cierre de un lenguaje de \cW bajo
-conmutación es regular. Las pruebas son no triviales y se combinan
varias técnicas avanzadas, incluyendo el tipo de Ramsey combinatoria
argumentos, propiedades algebraicas de la monoid sintáctica, finito
condiciones sobre semigrupos y propiedades de los sistemas de inserción.The first author was supported by the project Automatas en dispositivos moviles: interfaces de usuario y realidad aumentada (PAID 2019-06-11) supported by Universidad Politecnica de Valencia. The third author was supported by the project ANR 2010 BLAN 0202 02 FREC.Cano Gómez, A.; Guaiana, G.; Pin, J. (2013). Regular languages and partial commutations. Information and Computation. 230:76-96. https://doi.org/10.1016/j.ic.2013.07.003S769623
Contextual partial commutations
We consider the monoid T with the presentation which is "close" to trace monoids. We prove two different types of results. First, we give a combinatorial description of the lexicographically minimum and maximum representatives of their congruence classes in the free monoid {a; b}* and solve the classical equations, such as commutation and conjugacy in T. Then we study the closure properties of the two subfamilies of the rational subsets of T whose lexicographically minimum and maximum cross-sections respectively, are rational in {a; b}*. © 2010 Discrete Mathematics and Theoretical Computer Science
Computing Semicommutation Closures: a Machine Learning Approach
Semicommutation relations are simple rewriting relation on finite words using rules of the form ab → ba. In this paper we present how to use Angluin style machine learning algorithms to compute the image of regular language by the transitive closure of a semicommutation relation
Markovian dynamics of concurrent systems
Monoid actions of trace monoids over finite sets are powerful models of
concurrent systems---for instance they encompass the class of 1-safe Petri
nets. We characterise Markov measures attached to concurrent systems by
finitely many parameters with suitable normalisation conditions. These
conditions involve polynomials related to the combinatorics of the monoid and
of the monoid action. These parameters generalise to concurrent systems the
coefficients of the transition matrix of a Markov chain.
A natural problem is the existence of the uniform measure for every
concurrent system. We prove this existence under an irreducibility condition.
The uniform measure of a concurrent system is characterised by a real number,
the characteristic root of the action, and a function of pairs of states, the
Parry cocyle. A new combinatorial inversion formula allows to identify a
polynomial of which the characteristic root is the smallest positive root.
Examples based on simple combinatorial tilings are studied.Comment: 35 pages, 6 figures, 33 reference
A Model of Cooperative Threads
We develop a model of concurrent imperative programming with threads. We
focus on a small imperative language with cooperative threads which execute
without interruption until they terminate or explicitly yield control. We
define and study a trace-based denotational semantics for this language; this
semantics is fully abstract but mathematically elementary. We also give an
equational theory for the computational effects that underlie the language,
including thread spawning. We then analyze threads in terms of the free algebra
monad for this theory.Comment: 39 pages, 5 figure
Formal Relationships Between Geometrical and Classical Models for Concurrency
A wide variety of models for concurrent programs has been proposed during the
past decades, each one focusing on various aspects of computations: trace
equivalence, causality between events, conflicts and schedules due to resource
accesses, etc. More recently, models with a geometrical flavor have been
introduced, based on the notion of cubical set. These models are very rich and
expressive since they can represent commutation between any bunch of events,
thus generalizing the principle of true concurrency. While they seem to be very
promising - because they make possible the use of techniques from algebraic
topology in order to study concurrent computations - they have not yet been
precisely related to the previous models, and the purpose of this paper is to
fill this gap. In particular, we describe an adjunction between Petri nets and
cubical sets which extends the previously known adjunction between Petri nets
and asynchronous transition systems by Nielsen and Winskel
Direct and dual laws for automata with multiplicities
We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities in several noncommutative variables). We show that classical formulas are ``almost every time'' optimal, characterize the dual laws preserving rationality and also relators that are compatible with these laws
An introduction to Differential Linear Logic: proof-nets, models and antiderivatives
Differential Linear Logic enriches Linear Logic with additional logical rules
for the exponential connectives, dual to the usual rules of dereliction,
weakening and contraction. We present a proof-net syntax for Differential
Linear Logic and a categorical axiomatization of its denotational models. We
also introduce a simple categorical condition on these models under which a
general antiderivative operation becomes available. Last we briefly describe
the model of sets and relations and give a more detailed account of the model
of finiteness spaces and linear and continuous functions
From Differential Linear Logic to Coherent Differentiation
In this survey, we present in a unified way the categorical and syntactical
settings of coherent differentiation introduced recently, which shows that the
basic ideas of differential linear logic and of the differential
lambda-calculus are compatible with determinism. Indeed, due to the Leibniz
rule of the differential calculus, differential linear logic and the
differential lambda-calculus feature an operation of addition of proofs or
terms operationally interpreted as a strong form of nondeterminism. The main
idea of coherent differentiation is that these sums can be controlled and kept
in the realm of determinism by means of a notion of summability, upon enforcing
summability restrictions on the derivatives which can be written in the models
and in the syntax
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