Cycling in proofs and feasibility

Cycling in proofs and feasibility (1998)

by A. Carbone

Venue:	Transactions of the American Mathematical Society
Citations:	8 - 4 self

Datum	Value	Source
TITLE	Cycling in proofs and feasibility	INFERENCE
AUTHOR NAME	A. Carbone	SVM HeaderParse 0.2
ABSTRACT	Abstract. There is a common perception by which small numbers are considered more concrete and large numbers more abstract. A mathematical formalization of this idea was introduced by Parikh (1971) through an inconsistent theory of feasible numbers in which addition and multiplication are as usual but for which some very large number is defined to be not feasible. Parikh shows that sufficiently short proofs in this theory can only prove true statements of arithmetic. We pursue these topics in light of logical flow graphs of proofs (Buss, 1991) and show that Parikh’s lower bound for concrete consistency reflects the presence of cycles in the logical graphs of short proofs of feasibility of large numbers. We discuss two concrete constructions which show the bound to be optimal and bring out the dynamical aspect of formal proofs. For this paper the concept of feasible numbers has two roles, as an idea with its own life and as a vehicle for exploring general principles on the dynamics and geometry of proofs. Cycles can be seen as a measure of how complicated a proof can be. We prove that short proofs must have cycles. 1.	SVM HeaderParse 0.2
YEAR	1998	INFERENCE
VENUE	Transactions of the American Mathematical Society	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	2049--2075	INFERENCE
VOLUME	5	INFERENCE
CITATIONS	34 found	ParsCit 1.0