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تسجيل مستخدم جديدPositional Injectivity for Innocent Strategies
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نشر من قبل
Pierre Clairambault
تاريخ النشر
2021
مجال البحث
الهندسة المعلوماتية
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English
تأليف
Lison Blondeau-Patissier
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In asynchronous games, Melli{`e}s 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 counterexample 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.
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