Accession Number : AD0708529

Title :   ON THE EXISTENCE AND USE OF ALGORITHMS.

Descriptive Note : Final rept.,

Corporate Author : NEW YORK UNIV N Y

Personal Author(s) : Davis,Martin D.

Report Date : JUN 1970

Pagination or Media Count : 10

Abstract : A complete solution to the problem of locating a sharper estimate than Bachmann for the closure of Finsler's arithmetic operations was sought and found. A proof was also developed to show a correspondence between Schutte's ordinal notation and Takeuti's system of ordinal diagrams. Significant work was done in identifying certain sets as Diophantine. Five solvable cases of word problems for semi-groups were identified as solvable, and three systems of unary second order languages were studied with respect to finite axiomaticability, decision problems, and classification of equivalence models. This work effort should materially contribute to work on mechanized theorem proving and should significantly reduce the amount of time needed to reach solutions conventionally obtained under standard encoding methods and execution techniques. (Author)

Descriptors :   (*MATHEMATICAL LOGIC, PROBLEM SOLVING), GROUPS(MATHEMATICS), NUMBER THEORY, RECURSIVE FUNCTIONS, ALGORITHMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE