We investigate the problem of finding monoids that recognize languages of the form L1\JoinTL2 where T is an arbitrary set of routes. We present a uniform method based on routes to find such monoids. Many classical operations from the theory of formal languages, such as catenation, bi-catenation, simple splicing, shuffle, literal shuffle, and insertion are shown to be just particular instances of the operation T.
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In this paper we discuss some relationships between cooperating distributed (CD) grammar systems and the basic process algebra (BPA) calculus. We associate different types of process graphs from this calculus to CD grammar systems which describe the behavior of the components of the system under cooperation. We prove that these process graphs form a subalgebra of the graph model of BPA. It is also shown that for certain restricted variants of CD grammar systems and for certain types of these process graphs the bisimilarity of two process graphs is decidable.
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In this paper we investigate the injectivity of the Parikh matrix mapping. This research is done mainly on the binary alphabet. We identify a family of binary words, refered to as ``palindromic amiable'', such that two such words are palindromic amiable if and only if they have the same image by the Parikh matrix mapping. Some other related problems are discussed, too.
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We consider operations between languages, based on splitting the underlying alphabet into two disjoint sets, one of them having some priority. Such operations are generalizations of the classical catenation or shuffle operation, with which rational, linear and algebraic languages can be defined similar to the classical case. The basic properties of the corresponding language families are investigated too.
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