By a News Reporter-Staff News Editor at Information Technology Newsweekly -- A new study on Information Technology is now available. According to news reporting originating from Paris, France, by VerticalNews correspondents, research stated, "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 A(2) is a transitive relation."
Our news editors obtained a quote from the research from National Center for Scientific Research (CNRS), "We also give a sufficient 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 defined as the largest positive variety of languages not containing (ab)*. It is also closed under intersection, union, shuffle, 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."
According to the news editors, the research concluded: "The proofs are nontrivial and combine several advanced techniques, including combinatorial Ramsey type arguments, algebraic properties of the syntactic monoid, finiteness conditions on semigroups and properties of insertion systems."
For more information on this research see: Regular languages and partial commutations. Information and Computation, 2013;230():76-96. Information and Computation can be contacted at: Academic Press Inc Elsevier Science, 525 B St, Ste 1900, San Diego, CA 92101-4495, USA. (Elsevier - www.elsevier.com; Information and Computation - www.elsevier.com/wps/product/cws_home/622844)
The news editors report that additional information may be obtained by contacting A. Cano, CNRS, F-75205 Paris 13, France. Additional authors for this research include G. Guaiana and J.E. Pin.
Keywords for this news article include: Paris, France, Europe, Information Technology
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