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91
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
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Cited by 263 (33 self)
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The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
A brief history of process algebra
 Theor. Comput. Sci
, 2004
"... Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The a ..."
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Cited by 56 (1 self)
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Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.
Modeling and Analysis of Timed Petri Nets Using Heaps of Pieces
, 1997
"... We show that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkievicz of the behavior of safe Petri nets by trace monoids and trace languages. Fo ..."
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Cited by 44 (15 self)
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We show that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkievicz of the behavior of safe Petri nets by trace monoids and trace languages. For a subclass including all safe Free Choice Petri nets, we obtain reduced heap realizations using structural properties of the net (covering by safe state machine components). We illustrate the heapbased modeling by the typical case of safe jobshops. For a periodic schedule, we obtain a heapbased throughput formula, which is simpler to compute than its traditional timed event graph version, particularly if one is interested in the successive evaluation of a large number of possible schedules. Keywords Timed Petri nets, automata with multiplicities, heaps of pieces, (max,+) semiring, scheduling. I. Introduction The purpose of this paper 1 is to prove the following result: Timed safe Pe...
An Expressively Complete Linear Time Temporal Logic for Mazurkiewicz Traces
, 1997
"... A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. ..."
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Cited by 42 (5 self)
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A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. These partial orders arise in a variety of contexts in concurrency theory and they provide the conceptual basis for many of the partial order reduction methods that have been developed in connection with LTLspecifications. We show that LTrL, our linear time temporal logic, is equal in expressive power to the first order theory of traces when interpreted over (finite and) infinite traces. This result fills a prominent gap in the existing logical theory of infinite traces. LTrL also constitutes a characterisation of the so called trace consistent (robust) LTLspecifications. These are specifications expressed as LTL formulas that do not distinguish between different linearisations of the same trace and hence are amenable to partial order reduction methods.
Dynamic Linear Time Temporal Logic
 IN ANNALS OF PURE AND APPLIED LOGIC
, 1997
"... A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S ..."
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Cited by 42 (3 self)
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A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S1S, the monadic secondorder theory of !sequences. In fact a sublogic of DLTL which corresponds to propositional dynamic logic with a linear time semantics is already as expressive as S1S. We pin down in an obvious manner the sublogic of DLTL which correponds to the first order fragment of S1S. We show that DLTL has an exponential time decision procedure. We also obtain an axiomatization of DLTL. Finally, we point to some natural extensions of the approach presented here for bringing together propositional dynamic and temporal logics in a linear time setting.
Message Sequence Graphs and Decision Problems on Mazurkiewicz Traces
 In Proc. of MFCS'99, LNCS 1672
, 1999
"... Message sequence charts (MSC) are a graphical specification language widely used for designing communication protocols. Our starting point are two decision problems concerning the correctness and the consistency of a design based by MSC graphs. Both problems are shown to be undecidable, in gener ..."
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Cited by 41 (11 self)
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Message sequence charts (MSC) are a graphical specification language widely used for designing communication protocols. Our starting point are two decision problems concerning the correctness and the consistency of a design based by MSC graphs. Both problems are shown to be undecidable, in general. Using a natural connectivity assumption from Mazurkiewicz trace theory we show both problems to be EXPSPACEcomplete for locally synchronized graphs. The results are based on new complexity results for starconnected rational trace languages.
Asynchronous Games 2  The true concurrency of innocence
, 2004
"... In game semantics, the higherorder value passing mechanisms of the #calculus are decomposed as sequences of atomic actions exchanged by a Player and its Opponent. Seen from this angle, game semantics is reminiscent of trace semantics in concurrency theory, where a process is identified to the sequ ..."
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Cited by 29 (6 self)
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In game semantics, the higherorder value passing mechanisms of the #calculus are decomposed as sequences of atomic actions exchanged by a Player and its Opponent. Seen from this angle, game semantics is reminiscent of trace semantics in concurrency theory, where a process is identified to the sequences of requests it generates in the course of time. Asynchronous game semantics is an attempt to bridge the gap between the two subjects, and to see mainstream game semantics as a refined and interactive form of trace semantics. Asynchronous games are positional games played on Mazurkiewicz traces, which reformulate (and generalize) the familiar notion of arena game. The interleaving semantics of #terms, expressed as innocent strategies, may be analyzed in this framework, in the perspective of true concurrency. The analysis reveals that innocent strategies are positional strategies regulated by forward and backward confluence properties. This captures, we believe, the essence of innocence. We conclude the article by defining a non uniform variant of the #calculus, in which the game semantics of a #term is formulated directly as a trace semantics, performing the syntactic exploration or parsing of that #term.
Shuffle on Trajectories: Syntactic Constraints
 Theor. Comp. Sci
, 1998
"... We introduce and investigate new methods to define parallel composition of words and languages. The operation of parallel composition leads to new shufflelike operations defined by syntactic constraints on the usual shuffle operation. The approach is applicable to concurrency, providing a method to ..."
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Cited by 25 (5 self)
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We introduce and investigate new methods to define parallel composition of words and languages. The operation of parallel composition leads to new shufflelike operations defined by syntactic constraints on the usual shuffle operation. The approach is applicable to concurrency, providing a method to define parallel composition of processes. It is also applicable to parallel computation. The operations are introduced using a uniform method based on the notion of trajectory. As a consequence, we obtain a very intuitive geometrical interpretation of the parallel composition operation. These operations lead in a natural way to a large class of semirings. The approach is amazingly flexible, diverse concepts from the theory of concurrency can be introduced and studied in this framework. For instance, we provide examples of applications to fairness property and to parallelization of noncontextfree languages in terms of contextfree and even regular languages. This paper concetrates on syntactic constraints. Semantic constraints will be dealt with in a forthcoming contribution. TUCS Research Group
Infinitestate highlevel MSCs: Modelchecking and realizability
 In ICALP 2002, volume 2380 of LNCS
, 2002
"... Abstract. We consider three natural classes of infinitestate HMSCs: ..."
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Cited by 25 (5 self)
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Abstract. We consider three natural classes of infinitestate HMSCs: