Decidability Of Problem Research Articles

Connection between context-free groups and groups with decidable problems of automata equivalence

Connection between context-free groups and groups with decidable problems of automata equivalence

Computation sequence sets

A class of automata based upon generalized Petri nets is introduced and defined. The language which a Petri net generates during an execution is called a computation sequence set (CSS). The class of CSS languages is shown to be closed under union, intersection, concatenation, and concurrency. All regular languages and all bounded context-free languages are CSS, while all CSS are context-sensitive. Not all CSS languages are context-free, nor are all context-free languages CSS. Decidability problems for CSS hinge on the emptiness problem for CSS. This problem is equivalent to the reachability problem for vector addition systems, and is open.

PARALLEL GRAPH GENERATING AND GRAPH RECURRENCE SYSTEMS FOR MULTICELLULAR DEVELOPMENT†

Abstract As an extension of parallel rewriting systems on strings of symbols (L-systems), graph generating systems (graph L-systems) and graph recurrence systems are defined, by which the development of multicellular organisms can be modelled. Organisms are represented by directed graphs with labelled nodes and labeled edges. The nodes stand for cells, their labels for cellular states; the edges for connections between neighbors, their labels and directions for geometric relationships. In generating systems, a new graph is produced by simultaneous substitution of graphs for nodes according to a finite set of production, and by connecting their nodes by adding new edges according to a finite set of connection rules (using “stencils”). In graph recurrence systems larger and larger graphs are defined by recursive formulas on graphs and stencils. Results are given on the hierarchy of graph language families, as well as on some decidability problems concerning them.

Decidability problems for graph-schemes with permutation operators. I

Decidability problems for graph-schemes with permutation operators. I

A. V. Kuznecov. Undecidability of the general problems of completeness, decidability and equivalence for propositional calculi. English translation of XXXVII 772 by E. Mendelson. American Mathematical Society translations, ser. 2 vol. 59 (1966), pp. 56–72.

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Stochastic grammars and languages

This paper summarizes some recent results concerned with the extension of formal languages to their corresponding stochastic versions. Weighted grammars and languages are first defined, and stochastic grammars and languages are defined as a special case of weighted grammars and languages. Fuzzy grammars and languages, which have some properties similar to weighted grammars and languages, are also discussed. Stochastic automata are defined from the language recognition viewpoint. Languages accepted by stochastic finite-state and pushdown automata, with and without a cutpoint, are studied. Weighted and stochastic programmed and indexed grammars, and stochastic nested stack automata are defined. Finally, some decidability problems of stochastic (weighted, fuzzy) languages are discussed, and problems for further research are suggested.

Robert L. Vaught. Applications of the Löwenheim-Skolem-Tarski theorem to problems of completeness and decidability. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, series A, vol. 57 (1954), pp. 467–472; also Indagationes mathematicae, vol. 16 (1954), pp. 467–472.

Robert L. Vaught. Applications of the Löwenheim-Skolem-Tarski theorem to problems of completeness and decidability. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, series A, vol. 57 (1954), pp. 467–472; also <i>Indagationes mathematicae</i>, vol. 16 (1954), pp. 467–472.

Applications of the Lowenheim-Skolem-Tarski Theorem to Problems of Completeness and Decidability.

Applications of the Lowenheim-Skolem-Tarski Theorem to Problems of Completeness and Decidability.

Applications of the Löwenheim–Skolem–Tarski Theorem to Problems of Completeness and Decidability

Applications of the Löwenheim–Skolem–Tarski Theorem to Problems of Completeness and Decidability