License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2021.17
URN: urn:nbn:de:0030-drops-142555
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14255/
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Blondeau-Patissier, Lison ; Clairambault, Pierre

Positional Injectivity for Innocent Strategies

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LIPIcs-FSCD-2021-17.pdf (0.9 MB)

Abstract

In asynchronous games, Melliès proved that innocent strategies are positional: their behaviour only depends on the position, not the temporal order used to reach it. This insightful result shaped our understanding of the link between dynamic (i.e. game) and static (i.e. relational) semantics.
In this paper, we investigate the positionality of innocent strategies in the traditional setting of Hyland-Ong-Nickau-Coquand pointer games. We show that though innocent strategies are not positional, total finite innocent strategies still enjoy a key consequence of positionality, namely positional injectivity: they are entirely determined by their positions. Unfortunately, this does not hold in general: we show a counter-example if finiteness and totality are lifted. For finite partial strategies we leave the problem open; we show however the partial result that two strategies with the same positions must have the same P-views of maximal length.

BibTeX - Entry

@InProceedings{blondeaupatissier_et_al:LIPIcs.FSCD.2021.17,
  author =	{Blondeau-Patissier, Lison and Clairambault, Pierre},
  title =	{{Positional Injectivity for Innocent Strategies}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14255},
  URN =		{urn:nbn:de:0030-drops-142555},
  doi =		{10.4230/LIPIcs.FSCD.2021.17},
  annote =	{Keywords: Game Semantics, Innocence, Relational Semantics, Positionality}
}

Keywords: Game Semantics, Innocence, Relational Semantics, Positionality
Collection: 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)
Issue Date: 2021
Date of publication: 06.07.2021

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