Synchronized Shuffle and Regular Languages
نویسندگان
چکیده
New representation results for three families of regular languages are stated, using a special kind of shuffle operation, namely the synchronized shuffle. First, it is proved that the family of regular star languages is the smallest family containing the language (a+ bc)∗ and closed under synchronized shuffle and length preserving morphism. The second representation result states that the family of εfree regular languages is the smallest family containing the language (a+ bc)∗d and closed under synchronized shuffle, union and length preserving morphism. At last, it is proved that Reg is the smallest family containing the two languages (a+bb)∗ and a+(ab), closed under synchronized shuffle, union and length preserving morphism.
منابع مشابه
Synchronized shuffles
Weextend the basic shuffle onwords and languages, awell-known operation in theoretical computer science, by introducing three synchronized shuffles. These synchronized shuffles have some relevance to molecular biology since they may be viewed as the formal representations of various forms of gene linkage during genome shuffling. More precisely, each synchronized shuffle preserves the genetic ba...
متن کاملPairs of Languages Closed under Shuffle Projection
Shuffle projection is motivated by the verification of safety properties of special parameterized systems. Basic definitions and properties, especially related to alphabetic homomorphisms, are presented. The relation between iterated shuffle products and shuffle projections is shown. A special class of multi-counter automata is introduced, to formulate shuffle projection in terms of computation...
متن کاملValid Identity Problem for Shuffle Regular Expressions
We show that the following problem is decidable: given are expressions E1 and E2 constructed from variables by the regular operations and shuffle. Is the identity E1 = E2 true for all instantiations of its variables by formal languages?
متن کاملOn the Shuffle of Regular Timed Languages
We show that the class of regular timed languages is not closed under shuffle. This gives an answer to a question which was raised by E. Asarin in [2].
متن کاملOn the Learnability of Shuffle Ideals
PAC learning of unrestricted regular languages is long known to be a difficult problem. The class of shuffle ideals is a very restricted subclass of regular languages, where the shuffle ideal generated by a string u is the collection of all strings containing u as a subsequence. This fundamental language family is of theoretical interest in its own right and provides the building blocks for oth...
متن کامل