Recursively enumerable language

About: Recursively enumerable language is a research topic. Over the lifetime, 1508 publications have been published within this topic receiving 32382 citations.

Using pseudo-stochastic rational languages in probabilistic grammatical inference

Abstract: In probabilistic grammatical inference, a usual goal is to infer a good approximation of an unknown distribution P called a stochastic language. The estimate of P stands in some class of probabilistic models such as probabilistic automata (PA). In this paper, we focus on probabilistic models based on multiplicity automata (MA). The stochastic languages generated by MA are called rational stochastic languages; they strictly include stochastic languages generated by PA and admit a very concise canonical representation. Despite the fact that this class is not recursively enumerable, it is efficiently identifiable in the limit by using the algorithm DEES, introduced by the authors in a previous paper. However, the identification is not proper and before the convergence of the algorithm, DEES can produce MA that do not define stochastic languages. Nevertheless, it is possible to use these MA to define stochastic languages. We show that they belong to a broader class of rational series, that we call pseudo-stochastic rational languages. The aim of this paper is twofold. First we provide a theoretical study of pseudo-stochastic rational languages, the languages output by DEES, showing for example that this class is decidable within polynomial time. Second, we have carried out experiments to compare DEES to classical inference algorithms (ALERGIA and MDI). They show that DEES outperforms them in most cases.

Bounded Number of Parallel Productions in Scattered Context Grammars with Three Nonterminals

Abstract: Scattered context grammars with three nonterminals are known to be computationally complete. So far, however, it was an open problem whether the number of parallel productions can be bounded along with three nonterminals. In this paper, we prove that every recursively enumerable language is generated by a scattered context grammar with three nonterminals and five parallel productions, each of which simultaneously rewrites no more than nine nonterminals.

Particular Results for Variants of P Systems with One Catalyst in One Membrane

Abstract: Purely catalytic P systems can generate all recursively enumerable sets of natural numbers with only three catalysts in one membrane, whereas we know that one catalyst in one membrane is not enough. On the other hand, P systems also allowing (non-catalytic) non-cooperative evolution rules with only two catalysts in one membrane are already computationally complete, too. We here investigate special variants of P systems with only one catalyst in one membrane that are not computationally complete, i.e., variants of P systems with only one catalyst in one membrane that cannot generate all recursively enumerable sets of natural numbers.

Computing with Shapes

Abstract: Visual languages represent a response to the communicational challenges posed by end-user computing, but lack established computability frameworks for evaluating their computational power. In this paper, we introduce a computability model?called shape completion system?for the restricted, but important, case in which the visual representation of the concepts to be communicated is built as a puzzle. Shape completion systems are based on adjoining polyominoes, shapes from a basic set. A description in the form of a string on some alphabet can be associated with each basic shape. A computation in a shape completion system is correct when: (1) it starts by using a specified polyomino; (2) it ends when a rectangle is obtained (without holes); (3) at any step the current picture is connected; and (4) a sequencing mapping is given, so that at every step (except the first one) we use a polyomino depending on the previously used polyomino, as specified by this mapping (such a condition is essential for interactive visual languages, as formalized in 1, 2). We also establish how symbols associated with the polyominoes are concatenated to form strings in a string language associated with the computation. Surprisingly enough, in these circumstances we can characterize the recursively enumerable languages (hence the power of Turing machines). If we preserve only conditions (1), (2) and (3) above, then we cannot generate all linear languages but we can generate all regular languages and strictly more: also some one-letter non-regular languages can be obtained. In particular, we can obtain as correct computations squares only, which is often a difficult task in picture languages (see, e.g. 3).

On the Power of Accepting Networks of Evolutionary Processors with Special Topologies and Random Context Filters

Abstract: In this paper, we approach the problem of accepting all recursively enumerable languages by accepting networks of evolutionary processors (ANEPs, for short) with a fixed architecture. More precisely, we show that every recursively enumerable language can be accepted by an ANEP with an underlying graph in the form of a star with 13 nodes or by an ANEP with an underlying grid with 13 × 4 = 52 nodes as well as by ANEPs having underlying graphs in the form of a chain, a ring, or a wheel with 29 nodes each. In all these cases, the size and form as well as the general working strategy of the constructed networks do not depend on the accepted language; only the rewriting rules and the filters associated to each node of the networks depend on this language. Noteworthy is also the fact that the filtering process is implemented using random context conditions only. Our results answer problems which were left open in a paper published by J. Dassow and F. Manea at the conference on Descriptional Complexity of Formal Systems (DCFS) 2010 and improve a result published by B. Truthe at the conference on Non-Classical Models of Automata and Applications (NCMA) 2013.