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GAME SEMANTICS AND THE GEOMETRY OF BACKTRACKING: A NEW COMPLEXITY ANALYSIS OF INTERACTION

Published online by Cambridge University Press:  19 June 2017

FEDERICO ASCHIERI
FEDERICO ASCHIERI*
Affiliation:
INSTITUT FÜR DISKRETE MATHEMATIK UND GEOMETRIE TECHNISCHE UNIVERSITÄT WIEN WIEDNER HAUPTSTRAßE 8-10/104, 1040 VIENNA, AUSTRIAE-mail: federico.aschieri@tuwien.ac.at
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Abstract

We present abstract complexity results about Coquand and Hyland–Ong game semantics, that will lead to new bounds on the length of first-order cut-elimination, normalization, interaction between expansion trees and any other dialogical process game semantics can model and apply to. In particular, we provide a novel method to bound the length of interactions between visible strategies and to measure precisely the tower of exponentials defining the worst-case complexity. Our study improves the old estimates on average by several exponentials.

Keywords

F.4.1Hyland–Ong Coquand game semanticsfirst-order logicboundsstrategy interactionscut-eliminationnormalization
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 2 , June 2017 , pp. 672 - 708
Copyright
Copyright © The Association for Symbolic Logic 2017 

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