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.

Parallel Communicating Grammar Systems with Incomplete Information Communication

Abstract: We examine the generative power of parallel communicating (PC) grammar systems with context-free or E0L components communicating incomplete information, that is, only subwords of their sentential forms. We prove that these systems in most cases, even with E0L components, generate all recursively enumerable languages.

Recursively enumerable bw-degrees

Abstract: For every nonrecursive recursively enumerable (r.e.) set A are constructed bw-incomparable r.e. sets Bi, i e N, such that Bi

Recursively Enumerable m‐ and tt‐Degrees III: Realizing all Finite Distributive Lattices

Abstract: In [1], Degtev constructed a non-zero r.e. tt-degree containing a single r.e. m-degree, and it is certainly possible to construct an r.e. tt-degree with no greatest m-degree (Downey, [4]) and hence an r.e. tt-degree can also have infinitely many r.e. m-degrees (Fischer [8]). Odifreddi [12, Problem 10, 13], asked if each r.e. tt-degree had to either contain one or infinitely many r.e. m-degrees. The second author in Downey [5] showed that it is possible to construct an r.e. m-degree with exactly 3 r.e. m-degrees. He also claimed that one could use the techniques of [5] to construct an r.e. tt-degrees with exactly 2 − 1 r.e. m-degrees and hence arbitrarily large numbers of r.e. m-degrees.

Computational completeness of complete, star-like, and linear hybrid networks of evolutionary processors with a small number of processors

Abstract: A hybrid network of evolutionary processors (HNEP) is a graph where each node is associated with a special rewriting system called an evolutionary processor, an input filter, and an output filter. Each evolutionary processor is given a finite set of one type of point mutations (insertion, deletion or a substitution of a symbol) which can be applied to certain positions in a string. An HNEP rewrites the strings in the nodes and then re-distributes them according to a filter-based communication protocol; the filters are defined by certain variants of random-context conditions. HNEPs can be considered both as languages generating devices (GHNEPs) and language accepting devices (AHNEPs); most previous approaches treated the accepting and generating cases separately. For both cases, in this paper we show that five nodes are sufficient to accept (AHNEPs) or generate (GHNEPs) any recursively enumerable language by showing the more general result that any partial recursive relation can be computed by an HNEP with (at most) five nodes with the underlying graph structure for the communication between the evolutionary processors being the complete or the linear graph with five nodes, whereas with a star-like communication graph we need six nodes. If the final results are defined by only taking the terminal strings out of the designated output node, then for these extended HNEPs we can prove that only four nodes are needed in all cases--for computing any partial recursive relation as well as for generating and accepting any recursively enumerable language--and the underlying communication structure can be a complete or a linear graph, but now even a star-like graph, too.

Diophantine sets of polynomials over number fields

Abstract: Let R be a recursive subring of a number field. We show that recursively enumerable sets are diophantine for the polynomial ring R[Z].