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: A functional programming language suitable for describing data-parallel algorithms on recursively defined data in a declarative way is proposed, with an ML style polymorphic type system and a type sound operational semantics that uniformly integrates the parallel evaluation mechanism with the semantics of a typed functional language.
Abstract: This article proposes a new language mechanism for data-parallel processing of dynamically allocated recursively defined data. Different from the conventional array-based data- parallelism, it allows parallel processing of general recursively defined data such as lists or trees in a functional way. This is achieved by representing a recursively defined datum as a system of equations, and defining new language constructs for parallel transformation of a system of equations. By integrating them with a higher-order functional language, we obtain a functional programming language suitable for describing data-parallel algorithms on recursively defined data in a declarative way. The language has an ML style polymorphic type system and a type sound operational semantics that uniformly integrates the parallel evaluation mechanism with the semantics of a typed functional language. We also show the intended parallel execution model behind the formal semantics, assuming an idealized distributed memory multicomputer.
13 citations
Journal Article•
TL;DR: It turns out that starting from a Turing machine M with alphabet A and finite set of states Q which generates a given recursively enumerable language L, you need around 2 × |I| + 2 rules in order to define an extended H system which generates L.
Abstract: In this paper, we look at extended splicing systems (i.e., H systems) in order to find how small such a system can be in order to generate a recursively enumerable language. It turns out that starting from a Turing machine M with alphabet A and finite set of states Q which generates a given recursively enumerable language L, we need around 2×|I|+2 rules in order to define an extended H system H which generates L, where I is the set of instructions of Turing machine M. Next, coding the states of Q and the non-terminal symbols of L, we obtain an extended H system H 1 which generates L using |A|+2 symbols. At last, by encoding the alphabet, we obtain a splicing system U which generates a universal recursively enumerable set using only two letters.
13 citations
TL;DR: In this note, natural reference sets are presented which belong to the complete degrees at each level of the arithmetic hierarchy and provide simple methods of determining the degrees of unsolvability for several well-known problems.
13 citations
TL;DR: It is shown that Rocl, the family of one counter languages is closed under quotient by a context-free language, and every recursively enumerable language is the quotient of two linear languages.
Abstract: We study, first, the operation of quotient in connection with rational transductions. We show, afterwards, that Rocl, the family of one counter languages is closed under quotient by a context-free language. On the contrary, every recursively enumerable language is the quotient of two linear languages.
13 citations
TL;DR: The first proof is a variation on the construction of Soare and Stob (1982), the second combines highness with a modified version of the proof strategy of Cooper et al. (1989), and the third theorem is a rather surprising result with a somewhat unusual proof strategy.
13 citations