Event Structure Semantics Research Articles

Global Types and Event Structure Semantics for Asynchronous Multiparty Sessions

We propose an interpretation of multiparty sessions with asynchronous communication as Flow Event Structures. We introduce a new notion of asynchronous type for such sessions, ensuring the expected properties for multiparty sessions, including progress. Our asynchronous types, which reflect asynchrony more directly and more precisely than standard global types and are more permissive, are themselves interpreted as Prime Event Structures. The main result is that the Event Structure interpretation of a session is equivalent, when the session is typable, to the Event Structure interpretation of its asynchronous type, namely their domains of configurations are isomorphic.

Global Types and Event Structure Semantics for Asynchronous Multiparty Sessions

We propose an interpretation of multiparty sessions with asynchronous communication as Flow Event Structures. We introduce a new notion of global type for asynchronous multiparty sessions, ensuring the expected properties for sessions, including progress. Our global types, which reflect asynchrony more directly than standard global types and are more permissive, are themselves interpreted as Prime Event Structures. The main result is that the Event Structure interpretation of a session is equivalent, when the session is typable, to the Event Structure interpretation of its global type.

Event structures for the reversible early internal π-calculus

The π-calculus is a widely used process calculus, which models communications between processes and allows the passing of communication links. Various operational semantics of the π-calculus have been proposed, which can be classified according to whether transitions are unlabelled (so-called reductions) or labelled. With labelled transitions, we can distinguish early and late semantics. The early version allows a process to receive names it already knows from the environment, while the late semantics and reduction semantics do not. All existing reversible versions of the π-calculus use reduction or late semantics, despite the early semantics of the (forward-only) π-calculus being more widely used than the late. We introduce two reversible forms of the internal π-calculus; these are the first to use early semantics. The internal π-calculus is a subset of the π-calculus where every link sent by an output is private, yielding greater symmetry between inputs and outputs. One of the new reversible calculi uses static reversibility, where performing an action does not change the structure of the process, and the other uses dynamic reversibility, where performing an action moves it to a separate history. We show an operational correspondence between the two calculi. For the static calculus we define denotational event structure semantics, which generate an event structure inductively on the structure on the process. For the dynamic calculus we define operational event structure semantics, which generate an event structure based on a labelled asynchronous transition system. We describe a correspondence between the resulting event structures.

Event structure semantics of (controlled) reversible CCS

CCSK is a reversible form of CCS which is causal, meaning that actions can be reversed if and only if each action caused by them has already been reversed; there is no control on whether or when a computation reverses. We propose an event structure semantics for CCSK. For this purpose we define a category of reversible bundle event structures, and use the causal subcategory to model CCSK. We then modify CCSK to control the reversibility with a rollback primitive, which reverses a specific action and all actions caused by it. To define the event structure semantics of rollback, we change our reversible bundle event structures by making the conflict relation asymmetric rather than symmetric, and we exploit their capacity for non-causal reversibility.

A Theory of Distributed Markov Chains

We present the theory of distributed Markov chains (DMCs). A DMC consists of a collection of communicating probabilistic agents in which the synchronizations determine the probability distribution for the next moves of the participating agents. The key feature of a DMC is that the synchronizations are deterministic, in the sense that any two simultaneously enabled synchronizations involve disjoint sets of agents. Using our theory of DMCs we show how one can analyze the behavior using the interleaved semantics of the model. A key point is, the transition system which defines the interleaved semantics is—except in degenerate cases—not a Markov chain. Hence one must develop new techniques to analyze these behaviors exhibiting both concurrency and stochasticity. After establishing the core theory we develop a statistical model checking procedure which verifies the dynamical properties of the trajectories generated by the the model. The specifications consist of Boolean combinations of component-wise bounded linear time temporal logic formulas. We also provide a probabilistic Petri net representation of DMCs and use it to derive a probabilistic event structure semantics.

Towards a Categorical Representation of Reversible Event Structures

We study categories for reversible computing, focussing on reversible forms of event structures. Event structures are a well-established model of true concurrency. There exist a number of forms of event structures, including prime event structures, asymmetric event structures, and general event structures. More recently, reversible forms of these types of event structures have been defined. We formulate corresponding categories and functors between them. We show that products and co-products exist in many cases. In most work on reversible computing, including reversible process calculi, a cause-respecting condition is posited, meaning that the cause of an event may not be reversed before the event itself. Since reversible event structures are not assumed to be cause-respecting in general, we also define cause-respecting subcategories of these event structures. Our longer-term aim is to formulate event structure semantics for reversible process calculi.

Probabilistic rely-guarantee calculus

Jones' rely-guarantee calculus for shared variable concurrency is extended to include probabilistic behaviours. We use an algebraic approach that is based on a combination of probabilistic Kleene algebra with concurrent Kleene algebra. Soundness of the algebra is shown relative to a general probabilistic event structure semantics. The main contribution of this paper is a collection of rely-guarantee rules built on top of that semantics. In particular, we show how to obtain bounds on probabilities of correctness by deriving quantitative extensions of rely-guarantee rules. The use of these rules is illustrated by a detailed verification of a simple probabilistic concurrent program: a faulty Eratosthenes sieve.

Dimensional models of event structure and verbal semantics

Dimensional models of event structure and verbal semantics

Typed event structures and the linear [formula omitted]-calculus

We propose a typing system for the true concurrent model of event structures that guarantees the interesting behavioural properties known as conflict freeness and confusion freeness. Conflict freeness is the true concurrent version of the notion of confluence. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. Ours is the first typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the π -calculi with internal mobility. The semantics we provide is the first event structure semantics of the π -calculus and generalises Winskel’s original event structure semantics of CCS.

Event Structures with Symmetry

category of event structures with symmetry is introduced and its categorical properties investigated. Applications to the event-structure semantics of higher order processes, nondeterministic dataflow and the unfolding of Petri nets with multiple tokens are sketched.

Typed Event Structures and the π-Calculus: Extended Abstract

We propose a typing system for the true concurrent model of event structures that guarantees the interesting behavioural properties known as conflict freeness and confusion freeness. Conflict freeness is the true concurrent version of the notion of confluence. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. Ours is the first typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the π-calculi with internal mobility. The semantics we provide is the first event structure semantics of the π-calculus and generalises Winskel's original event structure semantics of CCS.

Domain and event structure semantics for Petri nets with read and inhibitor arcs

We propose a functorial concurrent semantics for Petri nets extended with read and inhibitor arcs, that we call inhibitor nets. Along the lines of the seminal work by Winskel on safe (ordinary) nets, the truly concurrent semantics is given at a categorical level via a chain of coreflections leading from the category SW- IN of semi-weighted inhibitor nets to the category Dom of finitary prime algebraic domains (equivalent to the category PES of prime event structures). As an intermediate semantic model, we introduce inhibitor event structures, an event-based model able to faithfully capture the dependencies among events which arise in the presence of read and inhibitor arcs. Inhibitor event structures generalise several event structure models in the literature, like prime, asymmetric and bundle event structures.

Domain and event structure semantics for Petri nets with read and inhibitor arcs*1

We propose a functorial concurrent semantics for Petri nets extended with read and inhibitor arcs, that we call inhibitor nets . Along the lines of the seminal work by Winskel on safe (ordinary) nets, the truly concurrent semantics is given at a categorical level via a chain of coreflections leading from the category SW - IN of semi-weighted inhibitor nets to the category Dom of finitary prime algebraic domains (equivalent to the category PES of prime event structures). As an intermediate semantic model, we introduce inhibitor event structures , an event-based model able to faithfully capture the dependencies among events which arise in the presence of read and inhibitor arcs. Inhibitor event structures generalise several event structure models in the literature, like prime, asymmetric and bundle event structures.

Event Structure Semantics for CCS and Related Languages

<p>We give denotational semantics to a wide range of parallel programming languages based on the ideas of Milner's CCS, that processes communicate by events of mutual synchronisation.</p><p>Processes are denoted by labelled event structures. Event structures represent concurrency rather directly as in net theory.</p><p>The semantics does not simulate concurrency by non-deterministic interleaving.</p>

Contextual Petri Nets, Asymmetric Event Structures, and Processes

We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (read-only operations). A basic role is played by asymmetric event structures, a generalization of Winskel's prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskel's seminal work on safe nets, the truly concurrent event-based semantics of contextual nets is given at categorical level via a chain of coreflections leading from the category SW-CN of semi-weighted contextual nets to the category Dom of finitary prime algebraic domains. First an unfolding construction generates from a contextual net a corresponding occurrence contextual net, from where an asymmetric event structure is extracted. Then the configurations of the asymmetric event structure, endowed with a suitable order, are shown to form a finitary prime algebraic domain. We also investigate the relation between the proposed unfolding semantics and several deterministic process semantics for contextual nets in the literature. In particular, the domain obtained via the unfolding is characterized as the collection of the deterministic processes of the net endowed with a kind of prefix ordering.

Partial order models for quantitative extensions of LOTOS

Event structures are a prominent model for non-interleaving concurrency. The use of event structures for providing a compositional non-interleaving semantics to LOTOS without data is studied. In particular, several quantitative extensions of event structures are proposed that incorporate notions like time – both of deterministic and stochastic nature – and probability. The suitability of these models for giving a non-interleaving semantics to a timed, stochastic and probabilistic extension of LOTOS is investigated. Consistency between the event structure semantics and an (event-based) operational semantics is addressed for the different quantitative variants of LOTOS and is worked out for the timed case in more detail. These consistency results facilitate the coherent use of an interleaving and a non-interleaving semantic view in a single design trajectory and provide a justification for the event structure semantics. As a running example an infinite buffer is used in which gradually timing constraints on latency and rates of accepting and producing data and the probability of loss of messages are incorporated.

A Consistent Causality-Based View on a Timed Process AlgebraIncluding Urgent Interactions

This paper discusses a timed variant of a process algebra akin to LOTOS, baptized UPA, in a causality-based setting. Two timed features are incorporated—a delay function which constrains the occurrence time of atomic actions and an urgency operator that forces (local or synchronized) actions to happen urgently. Timeouts are typical urgent phenomena. A novel timed extension of event structures is introduced and used as a vehicle to provide a denotational causality-based semantics for UPA. Recursion is dealt with by using standard fixpoint theory. In addition, an operational semantics is presented based on separate time- and action-transitions that is shown to be consistent with the event structure semantics. An interleaving semantics for UPA is immediately obtained from the operational semantics. By adopting this dual approach the well-developed timed interleaving view is extended with a consistent timed partial order view and a comparison is facilitated of the partial order model and the variety of existing (interleaved) timed process algebras.

An event structure semantics for general Petri nets

In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? As a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called UL-event structures. We propose that UL-event structures are appropriate for capturing the behaviour of general Petri nets. Our answer is a partial one in that in the proposed event structure semantics, auto-concurrency is filtered out from the behaviour of Petri nets. It turns out that this limited event structure semantics for Petri nets is nevertheless a non-trivial and conservative extension of the (prime) event structure semantics of 1-safe Petri nets provided in Nielsen et al. (1981). We also show that the strong relationship between prime event structures and 1-safe Petri nets established in a categorical framework in Winskel (1987) can be extended to the present setting, provided we restrict our attention to the subclass of Petri nets whose behaviours do not exhibit any auto-concurrency. Finally, we show that Winskel's general and stable event structures can be smoothly related to local event structures and that similarly prime event structures can be related to UL-event structures.

DPO Rewriting and Abstract Semantics via Opfibrations

The classical DPO graph rewriting construction is re-expressed using the opfibration approach introduced originally for term graph rewriting. Using a skeleton category of graphs, a base of canonical graphs-in-context, with DPO rules as arrows, and with categories of redexes over each object in the base, yields a category of rewrites via the discrete Grothendieck construction. The various possible ways of combining rules and rewrites leads to a variety of functors amongst the various categories formed. Categories whose arrows are rewriting sequences have counterparts where the arrows are elementary event structures, and an event structure semantics for arbitrary graph grammars emerges naturally.

The connection between an event structure semantics and an operational semantics forTCSP

The relation between an operational interleaving semantics for TSCP based on a transition system and a compositional true concurrency semantics based on event structures is studied. In particular we extend the consistency result of U. Goltz and R. Loogen [Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 14, 39-73 (1991; Zbl 0717.68028)] for TCSP processes without recursion to the general case. Thus, we obtain for every TCSP process P that its operational meaning O(P) and the interleaving behaviour O(M[[P]]) which is derived from the event structure M[[P]] associated with P are bisimilar. (aus: Zentralblatt MATH)