Affiliation:
1. Department of Computer Science, University of Toronto, Toronto, Ont., Canada. and Princeton University, Princeton, New Jersey
Abstract
Many problems, some of them quite meaningful, have been proved to be recursively unsolvable for programs in general. The paper is directed toward a class of programs where many decision problems are solvable. The equivalence problem has been proved to be unsolvable for the class
L
2
of loop programs defining the class of elementary functions. A solution is given for the class
L
1
defining the class of simple functions. Further, a set of other decision problems not directly connected with the equivalence problem is investigated. These problems are found again to be unsolvable for the class
L
2
; but as before, a solution is given for the class
L
1
. It is concluded, therefore, that there is a barrier of unsolvability between the classes
L
1
and
L
2
.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference15 articles.
1. GRZEGORCZrK A. Some classes of recursive functions. Rozprawy Matematycznc (Warsaw poland) 4 (1953) 1-46. GRZEGORCZrK A. Some classes of recursive functions. Rozprawy Matematycznc (Warsaw poland) 4 (1953) 1-46.
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