Probabilistic Event Structures and Domains
TL;DR: In this article, the authors study how to adjoin probability to event structures, leading to the model of probabilistic event structures and show that continuous valuations on the domain of a confusion-free event structure correspond to the event structures it supports.
Abstract: This paper studies how to adjoin probability to event structures, leading to the model of probabilistic event structures. In their simplest form, probabilistic choice is localised to cells, where conflict arises; in which case probabilistic independence coincides with causal independence. An event structure is associated with a domain--that of its configurations ordered by inclusion. In domain theory, probabilistic processes are denoted by continuous valuations on a domain. A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion-free event structure correspond to the probabilistic event structures it supports. We explore how to extend probability to event structures which are not confusion-free via two notions of probabilistic runs of a general event structure. Finally, we show how probabilistic correlation and probabilistic event structures with confusion can arise from event structures which are originally confusion-free by using morphisms to rename and hide events.
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21 Jun 2011
TL;DR: A bi category of very general nondeterministic concurrent games and strategies is presented to formalize distributed games in which both Player and Opponent can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate.
Abstract: A bi category of very general nondeterministic concurrent games and strategies is presented. The intention is to formalize distributed games in which both Player (or a team of players) and Opponent (or a team of opponents) can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate.
88 citations
Cites background from "Probabilistic Event Structures and ..."
...Nondeterministic strategies can potentially support probability as probabilistic or stochastic event structures [14] to become probabilistic or stochastic strategies....
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TL;DR: A new class of event structures, called locally finite, that extend confusion-free event structure are considered that have the property that ''concurrent processes are independent in the probabilistic sense.
Abstract: This paper is devoted to probabilistic models for concurrent systems under their true-concurrency semantics. Here we address probabilistic event structures. We consider a new class of event structures, called locally finite, that extend confusion-free event structure. In locally finite event structures, maximal configurations can be tiled with branching cells: branching cells are minimal and finite sub-structures capturing the choices performed while scanning a maximal configuration. The probabilistic event structures that we introduce have the property that ''concurrent processes are independent in the probabilistic sense.''
42 citations
Cites background from "Probabilistic Event Structures and ..."
...the role of the non-leaking valuations in [4]....
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...We recognize thus in the branching cells of E the cells defined in [4] for confusion-free event structures....
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...This particular result for confusion-free event structures is stated in [4], in the framework of so-called “non-leaking valuations with independence”....
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...In [4], the randomization of event structures is studied from the domain theory point of view, by using continuous valuations defined on the domain of configurations of an event structure....
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TL;DR: It is shown how consistent parts of a quantum event structure are automatically probabilistic event structures, and so possess a probability measure, which gives a non-traditional take on the consistent-histories approach to quantum theory.
35 citations
Cites background from "Probabilistic Event Structures and ..."
...Existing definitions of probabilistic event structures [2], [3] are not general enough to ascribe probabilities to the results of the sometimes partial interaction between strategies....
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...This description of a probabilistic event structure extends the definitions in [3]....
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25 Jun 2012
TL;DR: A positive answer to the question of whether concurrent games with winning conditions are determined is given when the games are well-founded and satisfy a structural property, race-freedom, which prevents one player from interfering with the moves available to the other.
Abstract: A bicategory of concurrent games, where nondeterministic strategies are formalized as certain maps of event structures, was introduced recently. This paper studies an extension of concurrent games by winning conditions, specifying players' objectives. The introduction of winning conditions raises the question of whether such games are determined, that is, if one of the players has a winning strategy. This paper gives a positive answer to this question when the games are well-founded and satisfy a structural property, race-freedom, which prevents one player from interfering with the moves available to the other. Uncovering the conditions under which concurrent games with winning conditions are determined opens up the possibility of further applications of concurrent games in areas such as logic and verification, where both winning conditions and determinacy are most needed. A concurrent-game semantics for predicate calculus is provided as an illustration.
31 citations
Cites background from "Probabilistic Event Structures and ..."
...There are several ways of extending the work on concurrent games with winning conditions: stochastic behaviour, perhaps with the use of probabilistic event structures [13], so as to define profiles of mixed strategies and Nash equilibria; imperfect information as the key concept for reasoning, more faithfully, about real-life distributed systems; and determinacy results for games with infinite behaviour so that more complex winning conditions can be handled, e....
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TL;DR: The semantics provided is the first event structure semantics of the @p-calculus and generalises Winskel's original event structure morphology of CCS and is theFirst typing system to control behaviour in a true concurrent model.
24 citations
Cites background or methods from "Probabilistic Event Structures and ..."
...Finally, confusion freeness has been recognised as an important property in the context of probabilistic models [32, 1]....
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...Future works include extending this approach to a probabilistic framework, for instance the probabilistic π-calculus [16], by using a typed version of probabilistic event structures [32]....
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...The above definition was introduced in [32]....
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References
More filters
21 Jun 2011
TL;DR: A bi category of very general nondeterministic concurrent games and strategies is presented to formalize distributed games in which both Player and Opponent can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate.
Abstract: A bi category of very general nondeterministic concurrent games and strategies is presented. The intention is to formalize distributed games in which both Player (or a team of players) and Opponent (or a team of opponents) can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate.
88 citations
TL;DR: A new class of event structures, called locally finite, that extend confusion-free event structure are considered that have the property that ''concurrent processes are independent in the probabilistic sense.
Abstract: This paper is devoted to probabilistic models for concurrent systems under their true-concurrency semantics. Here we address probabilistic event structures. We consider a new class of event structures, called locally finite, that extend confusion-free event structure. In locally finite event structures, maximal configurations can be tiled with branching cells: branching cells are minimal and finite sub-structures capturing the choices performed while scanning a maximal configuration. The probabilistic event structures that we introduce have the property that ''concurrent processes are independent in the probabilistic sense.''
42 citations
TL;DR: It is shown how consistent parts of a quantum event structure are automatically probabilistic event structures, and so possess a probability measure, which gives a non-traditional take on the consistent-histories approach to quantum theory.
35 citations
25 Jun 2012
TL;DR: A positive answer to the question of whether concurrent games with winning conditions are determined is given when the games are well-founded and satisfy a structural property, race-freedom, which prevents one player from interfering with the moves available to the other.
Abstract: A bicategory of concurrent games, where nondeterministic strategies are formalized as certain maps of event structures, was introduced recently. This paper studies an extension of concurrent games by winning conditions, specifying players' objectives. The introduction of winning conditions raises the question of whether such games are determined, that is, if one of the players has a winning strategy. This paper gives a positive answer to this question when the games are well-founded and satisfy a structural property, race-freedom, which prevents one player from interfering with the moves available to the other. Uncovering the conditions under which concurrent games with winning conditions are determined opens up the possibility of further applications of concurrent games in areas such as logic and verification, where both winning conditions and determinacy are most needed. A concurrent-game semantics for predicate calculus is provided as an illustration.
31 citations
11 Jul 2010
TL;DR: This paper establishes a bridge between presheaf models for concurrency and the more operationally-informative world of event structures by showing how with the introduction of symmetry event structures represent all presheaves over finite partial orders.
Abstract: This paper establishes a bridge between presheaf models for concurrency and the more operationally-informative world of event structures. It concentrates on a particular presheaf category, consisting of presheaves over finite partial orders of events; such presheaves form a model of nondeterministic processes in which the computation paths have the shape of partial orders. It is shown how with the introduction of symmetry event structures represent all presheaves over finite partial orders. This is in contrast with plain event structures which only represent certain separated presheaves. Specifically a coreflection from the category of presheaves to the category of event structures with symmetry is exhibited. It is shown how the coreflection can be cut down to an equivalence between the presheaf category and the subcategory of graded event structures with symmetry. Event structures with strong symmetries are shown to represent precisely all the separated presheaves. The broader context and specific applications to the unfolding of higher-dimensional automata and Petri nets, and weak bisimulation on event structures are sketched.
13 citations