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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05 May 1969TL;DR: A “processor” is a Turing-like automaton with auxiliary storage that consists of all processors that use the storage in the same way and properties common to all AFP are derived.
Abstract: A “processor” is a Turing-like automaton with auxiliary storage. An “abstract family” of processors (AFP) consists of all processors that use the storage in the same way. Properties common to all AFP are derived. For a family of operations to be the output functions of some AFP, it is necessary and sufficient that certain word-sets representing its members form a full AFL (in the sense of Ginsburg and Greibach) closed under intersection and iterated finite substitution.2 For a family of word-sets to be the accepted languages of some AFP, it is necessary and sufficient that it be a full AFL closed under intersection and iterated finite substitution. The smallest full AFL of this kind is the family of all recursively enumerable sets.
4 citations
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TL;DR: In this article, the only remaining step in the Chomsky hierarchy is to consider those groups with a context-sensitive word problem and prove some results about these groups, and also establish some results for other context sensitive decision problems in groups.
Abstract: There already exist classifications of those groups which have regular, context-free or recursively enumerable word problem. The only remaining step in the Chomsky hierarchy is to consider those groups with a context-sensitive word problem. In this paper we consider this problem and prove some results about these groups. We also establish some results about other context-sensitive decision problems in groups.
4 citations
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22 Jul 2013
TL;DR: In this paper, Csuhaj-Varjuvju et al. showed that the power of centralized pushdown automata in non-returning mode can be improved to two for recursively enumerable languages with non-centralized systems.
Abstract: In (Csuhaj-Varju et. al. 2000) parallel communicating systems of pushdown automata (PCPA) were introduced and in their centralized variants shown to be able to simulate nondeterministic one-way multi-head pushdown automata. A claimed converse simulation for returning mode (Balan 2009) turned out to be incomplete (Otto 2012) and a language was suggested for separating these PCPA of degree two (number of pushdown automata) from nondeterministic one-way two-head pushdown automata. We show that the suggested language can be accepted by the latter computational model. We present a different decidable example over a single letter alphabet indeed ruling out the possibility of a simulation between the models. The open question about the power of centralized PCPA working in returning mode is then settled by showing them to be universal. Since the construction is possible using systems of degree two, this also improves the previous bound three for accepting all recursively enumerable languages with non-centralized systems. A similar technique can be applied to centralized PCPA working in non-returning mode improving the previous bound on the number of components to two for accepting all recursively enumerable languages. Finally PCPAs are restricted in such a way that a simulation by multi-head automata is possible.
4 citations
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TL;DR: It is shown that explanatorily learnable and recursively enumerable classes always have a splitting into two incomparable classes; this gives an inductive inference counterpart of the Sacks splitting theorem from recursion theory.
Abstract: For the natural notion of splitting classes into two disjoint subclasses via a recursive classifier working on texts, the question of how these splittings can look in the case of learnable classes is addressed. Here the strength of the classes is compared using the strong and weak reducibility from intrinsic complexity. It is shown that, for explanatorily learnable classes, the complete classes are also mitotic with respect to weak and strong reducibility, respectively. But there is a weakly complete class that cannot be split into two classes which are of the same complexity with respect to strong reducibility. It is shown that, for complete classes for behaviorally correct learning, one-half of each splitting is complete for this learning notion as well. Furthermore, it is shown that explanatorily learnable and recursively enumerable classes always have a splitting into two incomparable classes; this gives an inductive inference counterpart of the Sacks splitting theorem from recursion theory.
4 citations