Games with 1-backtracking
Artikel i vetenskaplig tidskrift, 2010

We associate with any game G another game, which is a variant of it, and which we call bck(G). Winning strategies for bck(G) have a lower recursive degree than winning strategies for G: if a player has a winning strategy of recursive degree 1 over G, then it has a recursive winning strategy over bck(G), and vice versa. Through bck(G) we can express in algorithmic form, as a recursive winning strategy, many (but not all) common proofs of non-constructive Mathematics, namely exactly the theorems of the sub-classical logic Limit Computable Mathematics (Hayashi (2006) [6], Hayashi and Nakata (2001) [7]). (C) 2010 Elsevier B.V. All rights reserved.

Limit computable

Recursive degree

Game semantics

Learning in the limit

mathematics

Classical logic

Backtracking

Författare

S. Berardi

Universita degli Studi di Torino

Thierry Coquand

Chalmers, Data- och informationsteknik, Datavetenskap

S. Hayashi

Kyoto University

Annals of Pure and Applied Logic

0168-0072 (ISSN)

Vol. 161 1254-1269

Ämneskategorier

Annan matematik

DOI

10.1016/j.apal.2010.03.002