Strategies with Parallel Causes

TL;DR

This paper introduces an extended event structure framework supporting parallel causes, hiding, and probabilistic strategies, enabling a bicategory of probabilistic distributed strategies for parallel programming.

Contribution

It develops a novel extension of event structures that supports parallel causes, hiding, and probabilistic nondeterminism, facilitating advanced strategy composition.

Findings

Supports parallel causes in event structures

Enables probabilistic distributed strategies with hiding

Constructs a bicategory of strategies for parallel programming

Abstract

In a distributed game we imagine a team Player engaging a team Opponent in a distributed fashion. Such games and their strategies have been formalised in concurrent games based on event structures. However there are limitations in founding strategies on traditional event structures. Sometimes a probabilistic distributed strategy relies on certain benign races where, intuitively, several members of team Player may race each other to make a common move. Although there are event structures which support such parallel causes, in which an event is enabled in several compatible ways, they do not support an operation of hiding central to the composition of strategies; nor do they support probability adequately. An extension of traditional event structures is devised which supports parallel causes and hiding, as well as the mix of probability and nondeterminism needed to account for probabilistic distributed strategies. The extension is tested in the construction of a bicategory of probabilistic distributed strategies with parallel causes. The bicategory is rich in operations relevant to probabilistic as well as deterministic parallel programming.