Topic
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.
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TL;DR: It is proved that the proposed model, Accepting Network of Genetic Processors, is computationally complete (it is equivalent to the Turing machine) and can accept any recursively enumerable language.
13 citations
TL;DR: It is proved that recursively enumerable languages can be characterized as projections of inverse-morphic images of languages generated by such sequential SN P systems that are used as language generators.
Abstract: Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In this work, we consider SN P systems with the following restriction: at each step the active neuron with the maximum (or minimum) number of spikes among the neurons that can spike will fire [if there is a tie for the maximum (or minimum) number of spikes stored in the active neurons, only one of the neurons containing the maximum (or minimum) is chosen non-deterministically]. We investigate the computational power of such sequential SN P systems that are used as language generators. We prove that recursively enumerable languages can be characterized as projections of inverse-morphic images of languages generated by such sequential SN P systems. The relationships of the languages generated by these sequential SN P systems with finite and regular languages are also investigated.
13 citations
28 Aug 2006
TL;DR: The notion of limit sets of cellular automata associated with probability measures (μ-limit sets) was introduced by P. Kůrka and A. Maass in this article.
Abstract: We study the notion of limit sets of cellular automata associated with probability measures (μ-limit sets). This notion was introduced by P. Kůrka and A. Maass in [1]. It is a refinement of the classical notion of ω-limit sets dealing with the typical long term behavior of cellular automata. It focuses on the words whose probability of appearance does not tend to 0 as time tends to infinity (the persistent words). In this paper, we give a characterization of the persistent language for non sensitive cellular automata associated with Bernoulli measures. We also study the computational complexity of these languages. We show that the persistent language can be non-recursive. But our main result is that the set of quasi-nilpotent cellular automata (those with a single configuration in their μ-limit set) is neither recursively enumerable nor co-recursively enumerable.
13 citations
01 Jan 1996
TL;DR: For trees arising from Trakhtenbrot's Theorem with parameters m, n, the optimal value is k = n − m + 1 as discussed by the authors, where m is the size of the tree.
Abstract: One topic arising in recent research on “Bounded Query Classes” is to consider quantitative aspects of recursion theory, and in particular various notions of parameterized recursive approximations of sets. An important question is, for which values of the parameters - depending on the type of approximation - the approximated set is necessarily recursive. Beigel's Nonspeedup Theorem, Rummer's Cardinality Theorem and Trakhtenbrot's Theorem provide answers using nonuniform constructions. This paper investigates to which extend these constructions can be made uniform. Beigel's Nonspeedup Theorem is equivalent to the statement that every branch of a recursively enumerable tree of bounded width is recursive. There is no algorithm which computes a branch from the index of the tree, but there are nontrivial positive results by weakening the requirements as follows: For some fixed number k, an algorithm is wanted which, given an index of a tree, outputs a list of k programs such that at least one of them computes a branch of the tree up to finitely many errors. What is the least k for which this works? In this paper it is shown that, for recursively enumerable trees of width at most n, the least possible k is 2n−1. For trees arising from Trakhtenbrot's Theorem with parameters m, n, the optimal value is k = n − m + 1. In addition, several other, related classes of trees are investigated.
13 citations
05 Jun 2017
TL;DR: It is shown that pure MIS of size (3) (i.e., having ternary matrices inserting one symbol in two symbol context) can characterize all recursively enumerable languages.
Abstract: We study matrix insertion grammars (MIS) towards representation of recursively enumerable languages with small size. We show that pure MIS of size (3; 1, 2, 2) (i.e., having ternary matrices inserting one symbol in two symbol context) can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language or an intersection with a regular language followed by a weak coding. The obtained results complete known results on insertion-deletion systems from DNA computing area.
13 citations