Semilinearity and Context-Freeness of Languages Accepted by Valence Automata
نویسندگان
چکیده
Valence automata are a generalization of various models of automata with storage. Here, each edge carries, in addition to an input word, an element of a monoid. A computation is considered valid if multiplying the monoid elements on the visited edges yields the identity element. By choosing suitable monoids, a variety of automata models can be obtained as special valence automata. This work is concerned with the accepting power of valence automata. Specifically, we ask for which monoids valence automata can accept only context-free languages or only languages with semilinear Parikh image, respectively. First, we present a characterization of those graph products (of monoids) for which valence automata accept only context-free languages. Second, we provide a necessary and sufficient condition for a graph product of copies of the bicyclic monoid and the integers to yield only languages with semilinear Parikh image when used as a storage mechanism in valence automata. Third, we show that all languages accepted by valence automata over torsion groups have a semilinear Parikh image.
منابع مشابه
Hyperedge Replacement Languages and Pushdown Automata
In this paper we are studying the relations between generated and accepted hyperedge replacement languages. In context freeness of hyperedge replacement grammars we can transform each grammar into an equivalent one in Greibach Normal Form (HRGNF). In order to create a pushdown automata for hyperedge replacement languages (PDAH) we build an algorithm to transform the planar structure of a hyperg...
متن کاملDecision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages
Let C be a class of automata (in a precise sense to be defined) and C be the class obtained by augmenting each automaton in C with finitely many reversal-bounded counters. We show that if the languages defined by C are effectively semilinear, then so are the languages defined by C , and, hence, their emptiness problem is decidable. We give examples of how this result can be used to show the dec...
متن کاملDegrees of (Non)Monotonicity of RRW-Automata
We introduce and study the notion of j-monotonicity of RRand RRW -automata (special types of restarting automata without working symbols). We show that the j-monotonicity can be considered as a degree of non-context-freeness of languages recognized by RRW -automata and RR-automata. 1-monotonic RRW -automata recognize a subset of the class of context-free languages. For j > 1, the j-monotonic RR...
متن کاملNew Frontiers Beyond Context-Freeness: DI-Grammars And DI-Automata
A new class of formal languages will be defined the Distributed Index Languages (DI-languages). The grammar-formalism generating the new class the DI-grammars cover unbound dependencies in a rather natural way. The place of DI-languages in the Chomsky-hierarchy will be determined: Like Aho's indexed Languages, DI-languages represent a proper subclass of Type 1 (contextsensitive languages) and p...
متن کاملMultipass automata and group word problems
We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean closure of the class of deterministic context-free languages while the class of languages accepted by nondeterministic multipass automata is exactly the clas...
متن کامل