An introduction to event structures

Winskel, Glynn

doi:10.1007/bfb0013026

Cited by 177 publications

(160 citation statements)

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“…The semantics of a PPO can be described in terms of a labeled transition system, referred to as the configuration structure of the PPO (see [8,33]). The states of a configuration structure are configurations, finite sets of events that have already occurred.…”

Section: From Ppos To Configuration Structuresmentioning

confidence: 99%

Modeling task systems using parameterized partial orders

Houben

Igna

Vaandrager

2012

Int J Softw Tools Technol Transfer

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Abstract. Inspired by work on model-based design of printers, the notion of a parametrized partial order (PPO) was introduced recently. PPOs are a simple extension of partial orders, expressive enough to compactly represent large task graphs with finite repetitive behavior. We present a translation of the PPO subclass to timed automata and prove that the transition system induced by the Uppaal models is isomorphic to the configuration structure of the original PPO. Moreover, we introduce real-time task systems (RTTS), a general model for real-time embedded systems that we have used to describe the data paths of realistic printer designs. In an RTTS, tasks are represented as PPOs and the pace of a task instance may vary, depending on the resources that are allocated to it. We describe a translation of a subclass of RTTSs to Uppaal, and establish, for an even smaller subclass, bisimulation equivalence between the timed configuration semantics of an RTTS and the transition system induced by the corresponding Uppaal translation. Lastly, we report on a series of experiments which demonstrates that the resulting Uppaal models are more tractable than handcrafted models of the same systems used in earlier case studies.

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Section: From Ppos To Configuration Structuresmentioning

confidence: 99%

Modeling task systems using parameterized partial orders

Houben

Igna

Vaandrager

2012

Int J Softw Tools Technol Transfer

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Section: Processes As Trace Setsmentioning

confidence: 99%

“…So we can identify P with the partial order of downwards-closed subsets of P, ordered by inclusion; the order P has joins got simply via unions with the empty join being the least element ∅. The partial orders obtained in this way are precisely the infinitelydistributive algebraic lattices (see e.g., [27,28]) and these are just the same as prime algebraic lattices [25], and free join completions of partial orders.We are thinking of P as a nondeterministic domain [15,14]. An object in P is thought of as a denotation of a nondeterministic process which can realise path shapes in P. An object in P is a trace set, like those originally, in [16], but for general path shapes, standing for the set of computation paths a process can perform.…”

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confidence: 99%

Linearity and Nonlinearity in Distributed Computation

Winskel

2004

Linear Logic in Computer Science

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The copying of processes is limited in the context of distributed computation, either as a fact of life, often because remote networks are simply too complicated to have control over, or deliberately, as in the design of security protocols. Roughly, linearity is about how to manage without a presumed ability to copy. The meaning and mathematical consequences of linearity are studied for path-based models of processes which are also models of affine-linear logic. This connection yields an affine-linear language for processes in which processes are typed according to the kind of computation paths they can perform. One consequence is that the affine-linear language automatically respects open-map bisimulation. A range of process operations (from CCS, CCS with process-passing, mobile ambients, and dataflow) can be expressed within the affine-linear language showing the ubiquity of linearity. Of course, process code can be sent explicitly to be copied. Following the discipline of linear logic, suitable nonlinear maps are obtained as linear maps whose domain is under an exponential. Different ways to make assemblies of processes lead to different choices of exponential; the nonlinear maps of only some of which will respect bisimulation. IntroductionIn the film "Groundhog Day" the main character comes to relive and remember the same day repeatedly, until finally he gets it right (and the girl). Real life isn't like that. The world moves on and we cannot rehearse, repeat or reverse the effects of the more important decisions we take. 2 Glynn WinskelAs computation becomes increasingly distributed and interactive the more it resembles life in this respect, and the more difficult or impossible it is for a state of computation to be frozen and copied, so that interaction is most often conducted in a single irreversible run. Mathematically, this amounts to a form of linearity, as it is understood within models of linear logic.Although it can be hard for processes to copy processes, it is generally easy for processes to ignore other processes. For this reason distributed computation often involves affine-linear maps.To get an idea of the nature of affine-linear maps, imagine a network of interacting processes with a single hole, into which a process, the input process, may be plugged to form a complete process, the output process. The network with the hole represents an affine-linear map; given an input process, one obtains an output process.The input process cannot be copied, but can be ignored. Consequently, any computation path (or run) of the output process will have depended on at most one computation path (or run) of the input. This property of affine-linear maps rests on an understanding of the nature of the computation paths of a process. The property can be simplified provided we understand a computation path of the input processes to also admit the empty computation path-a computation path obtained even when the input process is ignored. Any output got while ignoring the input process, results from the empty...

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“…2 Incidentally, their motivation was to extend Scott's thesis (stating that the functions between datatypes computable by sequential programs are the continuous functions) to concurrent programs. The theory of unfoldings was further developed by Engelfriet, Nielsen, Rozenberg, Thiagarajan, Winskel, and others in [52,53,60,61,18].All this research was taking place in the area of semantics, with semantic goals: to provide a precise, formal definition of the behaviour of a concurrent system that could be used as a reference object to prove the correctness of, for instance, proof systemsà la Hoare. The success of model checking introduced a new way of looking at semantics: semantical objects were not only mathematical objects that allowed to formally prove the correctness or completeness of proof systems; they could also be constructed and stored in a computer, and used to automatically check behavioural properties.…”

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confidence: 99%

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A False History of True Concurrency: From Petri to Tools

Esparza

2010

Model Checking Software

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Abstract. I briefly review the history of the unfolding approach to model checking.Carl Adam Petri passed away on July 2, 2010. I learnt about his death three days later, a few hours after finishing this text. He was a very profound and highly original thinker, and will be sadly missed. This note is dedicated to his memory.In some papers and talks, Moshe Vardi has described the history of the automatatheoretic approach to model checking, the verification technique that inspired the SPIN model checker and other tools. He traces it back to the work of theoreticians like Büchi, Prior, Trakhtenbrot and others, whose motivations were surprisingly far away from the applications that their ideas found down the line. Inspired by this work, in this note I briefly present the origins of the unfolding approach to model checking [21], a branch of the automata-theoretic approach that alleviates the state-explosion problem caused by concurrency.Since the unfolding approach is based on the theory of true concurrency, describing its origins requires to speak about the origin of true concurrency itself. However, here I only touch upon those aspects of the theory that directly inspired the unfolding approach. This leaves many important works out, and so this is a very partial and "false" history of true concurrency.The theory of true concurrency starts with two fundamental contributions by Carl Adam Petri, described in detail by Brauer and Reisig in an excellent article [11]. Both were a result of Petri's interest in analyzing the connection between mathematical, abstract computing machines, and their physical realizations. In his dissertation "Kommunikation mit Automaten", defended in 1962, Petri observes that the performance of a physically implemented Turing machine will degrade over time if the machine uses more and more storage space, because in this case signals have to travel longer and longer distances over longer and longer wires. To solve this problem he proposes an asynchronous architecture in which the storage space can be extended while the machine continues to operate. In the dissertation this abstract machine is described with the help of several semi-formal representations, but three years later Petri has already distilled the first mathematical formalism for asynchronous computation, and, arguably, the beginning of concurrency theory: Petri nets.Petri's second contribution is an analysis of the notion of execution of a machine as a sequence of global states, or as a sequence of events ordered by their occurrence times with respect to some global clock. He observes that global states or global clocks are again a mathematical construct that cannot be "implemented": since information can only travel at finite speed, no part of a system can know the state of all its components at a certain moment in time. 1 He proposes to replace executions by nonsequential processes, sets of events ordered not by the time at which they occur, but by the causality relation, which is independent of the observer. The theory of nonseque...

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An introduction to event structures

Cited by 177 publications

References 12 publications

Modeling task systems using parameterized partial orders

Modeling task systems using parameterized partial orders

Linearity and Nonlinearity in Distributed Computation

A False History of True Concurrency: From Petri to Tools

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