Algorithms for ordinal arithmetic

Algorithms for ordinal arithmetic (2003)

by Panagiotis Manolios , Daron Vroon

Venue:	In 19th International Conference on Automated Deduction (CADE
Citations:	10 - 5 self

Datum	Value	Source
TITLE	Algorithms for ordinal arithmetic	INFERENCE
AUTHOR NAME	Panagiotis Manolios	SVM HeaderParse 0.2
AUTHOR AFFIL	Georgia Institute of Technology, College of Computing, CERCS Lab; 801 Atlantic Drive, Atlanta, Georgia, 30332	SVM HeaderParse 0.2
AUTHOR ADDR	USA,	SVM HeaderParse 0.2
AUTHOR NAME	Daron Vroon	SVM HeaderParse 0.2
AUTHOR AFFIL	Georgia Institute of Technology, College of Computing, CERCS Lab; 801 Atlantic Drive, Atlanta, Georgia, 30332	SVM HeaderParse 0.2
AUTHOR ADDR	USA,	SVM HeaderParse 0.2
ABSTRACT	Abstract. Proofs of termination are essential for establishing the correct behavior of computing systems. There are various ways of establishing termination, but the most general involves the use of ordinals. An example of a theorem proving system in which ordinals are used to prove termination is ACL2. In ACL2, every function defined must be shown to terminate using the ordinals up to ɛ0. We use a compact notation for the ordinals up to ɛ0 (exponentially more succinct than the one used by ACL2) and define efficient algorithms for ordinal addition, subtraction, multiplication, and exponentiation. In this paper we describe our notation and algorithms, prove their correctness, and analyze their complexity. 1	SVM HeaderParse 0.2
YEAR	2003	INFERENCE
VENUE	In 19th International Conference on Automated Deduction (CADE	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	243--257	INFERENCE
CITATIONS	34 found	ParsCit 1.0