255 research outputs found
Partially-commutative context-free languages
The paper is about a class of languages that extends context-free languages
(CFL) and is stable under shuffle. Specifically, we investigate the class of
partially-commutative context-free languages (PCCFL), where non-terminal
symbols are commutative according to a binary independence relation, very much
like in trace theory. The class has been recently proposed as a robust class
subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We
identify a natural corresponding automaton model: stateless multi-pushdown
automata. We show stability of the class under natural operations, including
homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to
two other relevant classes: CFL extended with shuffle and trace-closures of
CFL. Among technical contributions of the paper are pumping lemmas, as an
elegant completion of known pumping properties of regular languages, CFL and
commutative CFL.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
Commutative positive varieties of languages
We study the commutative positive varieties of languages closed under various
operations: shuffle, renaming and product over one-letter alphabets
Analytic aspects of the shuffle product
There exist very lucid explanations of the combinatorial origins of rational
and algebraic functions, in particular with respect to regular and context free
languages. In the search to understand how to extend these natural
correspondences, we find that the shuffle product models many key aspects of
D-finite generating functions, a class which contains algebraic. We consider
several different takes on the shuffle product, shuffle closure, and shuffle
grammars, and give explicit generating function consequences. In the process,
we define a grammar class that models D-finite generating functions
Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools
We provide simple equational principles for deriving rely-guarantee-style
inference rules and refinement laws based on idempotent semirings. We link the
algebraic layer with concrete models of programs based on languages and
execution traces. We have implemented the approach in Isabelle/HOL as a
lightweight concurrency verification tool that supports reasoning about the
control and data flow of concurrent programs with shared variables at different
levels of abstraction. This is illustrated on two simple verification examples
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
Regular Combinators for String Transformations
We focus on (partial) functions that map input strings to a monoid such as
the set of integers with addition and the set of output strings with
concatenation. The notion of regularity for such functions has been defined
using two-way finite-state transducers, (one-way) cost register automata, and
MSO-definable graph transformations. In this paper, we give an algebraic and
machine-independent characterization of this class analogous to the definition
of regular languages by regular expressions. When the monoid is commutative, we
prove that every regular function can be constructed from constant functions
using the combinators of choice, split sum, and iterated sum, that are analogs
of union, concatenation, and Kleene-*, respectively, but enforce unique (or
unambiguous) parsing. Our main result is for the general case of
non-commutative monoids, which is of particular interest for capturing regular
string-to-string transformations for document processing. We prove that the
following additional combinators suffice for constructing all regular
functions: (1) the left-additive versions of split sum and iterated sum, which
allow transformations such as string reversal; (2) sum of functions, which
allows transformations such as copying of strings; and (3) function
composition, or alternatively, a new concept of chained sum, which allows
output values from adjacent blocks to mix.Comment: This is the full version, with omitted proofs and constructions, of
the conference paper currently in submissio
Capacity Bounded Grammars and Petri Nets
A capacity bounded grammar is a grammar whose derivations are restricted by
assigning a bound to the number of every nonterminal symbol in the sentential
forms. In the paper the generative power and closure properties of capacity
bounded grammars and their Petri net controlled counterparts are investigated
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