[Paper Review] Strategies with Parallel Causes

Marc de Visme, Glynn Winskel|arXiv (Cornell University)|Jul 13, 2016

Advanced Database Systems and Queries3 citations

TL;DR

This paper introduces event structure with duplication and causality (edc) strategies to model probabilistic distributed games with parallel causes, where a single move can be triggered by multiple independent events. It extends traditional event structures to support probabilistic independence, hiding, and composition, enabling a bicategory of probabilistic strategies that accurately models winning strategies with concurrent, independent triggers—resolving limitations in prior models where conflicting events forced suboptimal probability assignments.

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.

Motivation & Objective

• To address the limitation of traditional event structures in modeling strategies where a single move can be causally enabled by multiple independent events (parallel causes).
• To develop a formalism that supports probabilistic independence (via the Limited Markov Condition) even when events are in conflict.
• To enable hiding and composition of strategies in a way that preserves probabilistic and causal structure.
• To construct a bicategory of probabilistic distributed strategies that supports operations relevant to both probabilistic and deterministic parallel programming.

Proposed method

• Introduces event structures with duplication and causality (edc), extending traditional event structures to allow parallel causes and compatible enabling of events.
• Defines a new class of strategies based on edc event structures that support probabilistic sums, composition, and conjunction.
• Introduces copycat terms that reflect compatibility conditions, enabling causal wiring and subsuming operations like λ-abstraction and prefixing.
• Develops a duplication strategy δA that allows recursive definition of strategies, with deterministic behavior when the game is deterministic for Opponent.
• Uses a complete partial order with a bottom element to define recursive strategies via fixed-point semantics.
• Applies the Limited Markov Condition to ensure that causally independent moves remain probabilistically independent in the strategy model.

Experimental results

Research questions

• RQ1 How can event structures model strategies where a single move is enabled by multiple independent, concurrent causes?
• RQ2 Can probabilistic strategies be composed while preserving the Limited Markov Condition, ensuring that causally independent events remain probabilistically independent?
• RQ3 How can hiding and composition be supported in a model that allows parallel causes and probabilistic choice?
• RQ4 What structural extensions to event structures are needed to support both probabilistic independence and conflict between alternative triggers?
• RQ5 Can a bicategory of probabilistic strategies be constructed that supports rich operations like recursion, duplication, and parallel composition?

Key findings

• The paper successfully constructs a bicategory of probabilistic distributed strategies with parallel causes, resolving the issue of suboptimal probability assignments in prior models.
• By allowing parallel causes, the model correctly captures strategies where multiple watchers independently trigger a single move, preserving probabilistic independence as required by the Limited Markov Condition.
• The duplication strategy δA is deterministic when the game is deterministic for Opponent, enabling recursive definitions and ensuring associativity in composition.
• The model supports probabilistic sums, conjunctions, and composition, forming a rich framework for probabilistic and deterministic parallel programming.
• The framework generalizes prior models by supporting hiding, probabilistic independence, and composition without forcing conflicting event structures.
• The approach enables accurate modeling of strategies such as the 'two-watchers' game, where a single move wins with certainty despite probabilistic reliability, by allowing parallel enabling without conflict between triggers.