57 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
Differential interaction nets
AbstractWe introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the of course and the why not modalities of linear logic, which is completely similar to the symmetry between the tensor and par connectives of linear logic. We use algebraic intuitions for introducing these nets and their reduction rules, and then we develop two correctness criteria (weak typability and acyclicity) and show that they guarantee strong normalization. Finally, we outline the correspondence between this interaction nets formalism and the resource lambda-calculus
Geometric lifting of the canonical basis and semitoric degenerations of Richardson varieties
In the sl\_n case, A. Berenstein and A. Zelevinsky studied the
Sch\"{u}tzenberger involution in terms of Lusztig's canonical basis, [3]. We
generalize their construction and formulas for any semisimple Lie algebra. We
use for this the geometric lifting of the canonical basis, on which an analogue
of the Sch\"{u}tzenberger involution can be given. As an application, we
construct semitoric degenerations of Richardson varieties, following a method
of P. Caldero, [6]Comment: 22 pages, 3 figure
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