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Modelling Concurrency with Partial Orders
, 1986
"... Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a n ..."
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Cited by 263 (18 self)
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Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia. In this paper we extract from these three approaches a single hybrid approach having a rich language that mixes algebra and logic and having a natural class of models of concurrent processes. The heart of the approach is a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordered multisets or pomsets. Just as sets of strings form languages, so do sets of pomsets form processes. We introduce a number of operations useful for specifying concurrent processes and demonstrate their utility on some basic examples. Although none of the operations is particularly oriented to nets it is nevertheless possible to use them to express processes constructed as a net of subprocesses, and more generally as a system consisting of components. Th...
Concurrent Transition Systems
 Theoretical Computer Science
, 1989
"... : Concurrent transition systems (CTS's), are ordinary nondeterministic transition systems that have been equipped with additional concurrency information, specified in terms of a binary residual operation on transitions. Each CTS C freely generates a complete CTS or computation category C , ..."
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Cited by 42 (5 self)
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: Concurrent transition systems (CTS's), are ordinary nondeterministic transition systems that have been equipped with additional concurrency information, specified in terms of a binary residual operation on transitions. Each CTS C freely generates a complete CTS or computation category C , whose arrows are equivalence classes of finite computation sequences, modulo a congruence induced by the concurrency information. The categorical composition on C induces a "prefix" partial order on its arrows, and the computations of C are conveniently defined to be the ideals of this partial order. The definition of computations as ideals has some pleasant properties, one of which is that the notion of a maximal ideal in certain circumstances can serve as a replacement for the more troublesome notion of a fair computation sequence. To illustrate the utility of CTS's, we use them to define and investigate a dataflowlike model of concurrent computation. The model consists of machines, which ...
Operators and Laws for Combining Preference Relations
, 2002
"... The paper is a theoretical study of a generalization of the lexicographic rule for combining ordering relations. We define the concept of priority operator: a priority operator maps a family of relations to a single relation which represents their lexicographic combination according to a certain pri ..."
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Cited by 40 (0 self)
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The paper is a theoretical study of a generalization of the lexicographic rule for combining ordering relations. We define the concept of priority operator: a priority operator maps a family of relations to a single relation which represents their lexicographic combination according to a certain priority on the family of relations. We present four kinds of results. We show
Abstraction for Concurrent Objects ⋆
"... Abstract. Concurrent data structures are usually designed to satisfy correctness conditions such as sequential consistency and linearizability. In this paper, we consider the following fundamental question: what guarantees are provided by these conditions for client programs? We formally show that t ..."
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Cited by 32 (10 self)
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Abstract. Concurrent data structures are usually designed to satisfy correctness conditions such as sequential consistency and linearizability. In this paper, we consider the following fundamental question: what guarantees are provided by these conditions for client programs? We formally show that these conditions can be characterized in terms of observational refinement. Our study also provides a new understanding of sequential consistency and linearizability in terms of abstraction of dependency between computation steps of client programs. 1
Temporal Structures
, 1990
"... We combine the principles of the FloydWarshallKleene algorithm, enriched categories, and Birkhoff arithmetic, to yield a useful class of algebras of transitive vertexlabeled spaces. The motivating application is a uniform theory of abstract or parametrized time in which to any given notion of tim ..."
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Cited by 31 (22 self)
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We combine the principles of the FloydWarshallKleene algorithm, enriched categories, and Birkhoff arithmetic, to yield a useful class of algebras of transitive vertexlabeled spaces. The motivating application is a uniform theory of abstract or parametrized time in which to any given notion of time there corresponds an algebra of concurrent behaviors and their operations, always the same operations but interpreted automatically and appropriately for that notion of time. An interesting side application is a language for succinctly naming a wide range of datatypes. 1 Introduction Posets, metric spaces, "closed" automata, and categories have in common the notion of a space of points with distances between points. These distances are respectively truth values, reals, languages, and sets. Distances have two facets, logical and metrical. The logical facet is expressed respectively via implications p ! q between truth values, comparisons x y between reals, inclusions L ` M between langua...
Higher Dimensional Automata Revisited
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
"... ..."
An Algebra for Pomsets
, 1995
"... We study languages for manipulating partially ordered structures with duplicates (e.g. trees, lists). As a general framework, we consider the pomset (partially ordered multiset) data type. We introduce an algebra for pomsets, which generalizes traditional algebras for (nested) sets, bags and list ..."
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Cited by 21 (3 self)
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We study languages for manipulating partially ordered structures with duplicates (e.g. trees, lists). As a general framework, we consider the pomset (partially ordered multiset) data type. We introduce an algebra for pomsets, which generalizes traditional algebras for (nested) sets, bags and lists. This paper is motivated by the study of the impact of different language primitives on the expressive power. We show that the use of partially ordered types increases the expressive power significantly. Surprisingly, it turns out that the algebra when restricted to both unordered (bags) and totally ordered (lists) intermediate types, yields the same expressive power as fixpoint logic with counting on relational databases. It therefore constitutes a rather robust class of relational queries. On the other hand, we obtain a characterization of PTIME queries on lists by considering only totally ordered types.
Passivity and independence
 In Proceedings, Ninth Annual IEEE Symposium on Logic in Computer Science
, 1994
"... Most programming languages have certain phrases (like expressions) which only read information from the state and certain others (like commands) which write information to the state. These are called passive and active phrases respectively. Semantic models which make these distinctions have been har ..."
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Cited by 12 (7 self)
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Most programming languages have certain phrases (like expressions) which only read information from the state and certain others (like commands) which write information to the state. These are called passive and active phrases respectively. Semantic models which make these distinctions have been hard to find. For instance, most semantic models have expression denotations that (temporarily) change the state. Common reasoning principles, such as the Hoare’s assignment axiom, are not valid in such models. We define here a semantic model which captures the notions of “change”, “absence of change” and “independent change ” etc. This is done by extending the author’s “linear logic model of state ” with dependence/independence relations so that sequential traces give way to pomset traces. 1
Spaces: Complementarity and Uncertainty in Rational Mechanics
, 1994
"... 1 Introduction to Chu spaces 1.1 Basic notions A Boolean Chu space A = (X, =, A) consists of two sets X and A and a binary relation  = ⊆ X × A from X to A. We call the elements x, y,... of X states or opens, and the elements a, b,... of A points, propositions, or events. We ..."
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Cited by 12 (0 self)
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1 Introduction to Chu spaces 1.1 Basic notions A Boolean Chu space A = (X, =, A) consists of two sets X and A and a binary relation  = ⊆ X × A from X to A. We call the elements x, y,... of X states or opens, and the elements a, b,... of A points, propositions, or events. We