Topic
Recursive language
About: Recursive language is a research topic. Over the lifetime, 403 publications have been published within this topic receiving 10496 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Oct 1969
TL;DR: The purpose of the paper is to formalize properties (such as termination, correctness and equivalence) of these partial functions by means of the satisfiability or validity of certain formulas in partial function logic.
Abstract: : Recursive definitions are considered which consist of Algol-like conditional expressions. By specifying a computation rule for evaluating such recursive definition, it determines a partial function. However, for different computation rules, the same recursive definition may determine different partial functions. Two types of computation rules are distinguished: sequential and parallel. The purpose of the paper is to formalize properties (such as termination, correctness and equivalence) of these partial functions by means of the satisfiability or validity of certain formulas in partial function logic.
81 citations
TL;DR: This chapter presents an expository treatment of the elements of recursive function theory, and discusses oracles and functional, recursive enumerability, logic and recursions theory, degrees of unsolvability, definability and recursion, creative and lesser sets, and recursive analogs of classical objects.
Abstract: Publisher Summary This chapter presents an expository treatment of the elements of recursive function theory. The chapter also discusses informal computability, Turing machines, Church's thesis, universal machines, and normal form. The simplest conception of recursive functions is effectively computable functions. There are many equivalent ways of formulating the definition of recursiveness. A version phrased in terms of imaginary computing machines was given by the English mathematician Alan Turing. The chapter also discusses oracles and functional, recursive enumerability, logic and recursion theory, degrees of unsolvability, definability and recursion, creative and lesser sets, and recursive analogs of classical objects.
81 citations
TL;DR: A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory to support the formalization of particular recursive definitions for use in verification, semantics proofs, and other computational reasoning.
Abstract: A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs, and other computational reasoning.
79 citations
TL;DR: In this article, the problem of when a nonlinear system can be represented as a quotient of two stable non-linear systems is considered, where recursive means that the relationship between an input sequence and the corresponding output sequence can be expressed in terms of a finite number of recursive equations.
Abstract: The problem of when a non-linear system can be represented as a quotient of two stable non-linear systems is considered. Attention is mainly directed toward nonlinear discrete-time recursive systems, where recursive means that the relationship between an input sequence and the corresponding output sequence can be expressed in terms of a finite number of recursive equations. Necessary and sufficient conditions are derived for the existence of a fraction representation of a recursive system, where the numerator and the denominator are stable recursive systems. The explicit construction of such a fraction representation is described.
77 citations
TL;DR: The survey at hand picks out important studies on learning indexed families of recursive languages (including basic as well as recent research), summarizes and illustrates the corresponding results, and points out links to related fields such as grammatical inference, machine learning, and artificial intelligence in general.
75 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
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| 2021 | 1 |
| 2020 | 1 |
| 2019 | 3 |
| 2018 | 2 |
| 2017 | 4 |
| 2016 | 10 |