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The History of Artificial Intelligence

The convergence of functions to fixedpoints of recursive definitions.

purl.stanford.edu/pw969qk2499
Title:
The convergence of functions to fixedpoints of recursive definitions.
Author:
Manna, Z ohar and Shamir, Adi
Author (no Collectors):
Manna, Z ohar and Shamir, Adi
Description:
The classical method for constructing the least fixedpoint of a recursive definition is to generate a sequence of functions whose initial element is the totally undefined function and which converges to the desired least fixedpoint. This method, due to Kleene, cannot be generalized to allow the construction of other fixedpoints. In this paper we present an alternate definition of convergence and a new fixedpoint access method of generating sequences of functions for a given recursive definition. The initial function of the sequence can be an arbitrary function, and the sequence will always converge to a fixedpoint that is "close" to the initial function. This defines a monotonic mapping from the set of partial functions onto the set of all fixedpoints of the given recursive definition.
Topic:
Computer science
Subject:
Stanford University. Computer Science Department
Language:
English
Physical Description:
1 text file
Publication Info:
cau and Stanford (Calif.)
Date:
May 01, 1977
Place created:
Stanford (Calif.)
Imprint:
Stanford (Calif.), May 1, 1977
Genre:
technical reports
Identifier:
CS-TR-1977-614
Repository:
Stanford University. Libraries. Department of Special Collections and University Archives
Collection:
Stanford University, Department of Computer Science, Technical Reports and Stanford Artificial Intelligence Laboratory records, 1963-2009
Manuscript number:
3840/2