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On The Specification Of Concurrent Systems
, 1991
"... In models of concurrent processes constraints on the order of events are often represented by partial orders, and schedules of events are then defined using an algebra of standard operations such as sequential and parallel composition. In this dissertation the notion of partial order is replaced by ..."
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In models of concurrent processes constraints on the order of events are often represented by partial orders, and schedules of events are then defined using an algebra of standard operations such as sequential and parallel composition. In this dissertation the notion of partial order is replaced by that of a set with a metric which takes values in a given ordered monoid. Partial orders are the simple case of a monoid whose two elements represent the presence or absence of a constraint. An ordered monoid can be seen as a monoidal category, and schedules based on it are categories enriched in the monoid. Algebraic operations on schedules can then be defined as constructions in the category of schedules. These definitions rely on certain properties of a category of schedules, such as closure and completeness. To simplify proofs of these properties, two constructions are defined. The first creates a category of unlabeled schedules from a system of constraints. The second adds labels to unl...
The Shuffle Hopf Algebra and Noncommutative Full Completeness
, 1999
"... We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformati ..."
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We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffle algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cutfree proofs in CyLL+MIX. This can be viewed as a fully faithful representation of a free *autonomous category, canonically enriched over vector spaces. This paper
Towards a Calculus for UMLRT Specifications
, 1998
"... The unified modeling language (UML) developed under the coordination of the Object Management Group (OMG) is one of the most importantstandards for the specification and design of objectoriented systems. This standard is currently tuned for realtime applications in the form of a new proposal, ..."
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The unified modeling language (UML) developed under the coordination of the Object Management Group (OMG) is one of the most importantstandards for the specification and design of objectoriented systems. This standard is currently tuned for realtime applications in the form of a new proposal, UML for RealTime (UMLRT), by Rational Software Corporation and ObjecTime Limited. Because of the importance of UMLRTwe are investigating its formal foundation in a joint project between ObjecTime Limited, Technische Universitat Munchen and the University of Bucharest. In this paper we present part of this foundation, namely the theory of flowgraphs.
A Noncommutative Full Completeness Theorem (Extended Abstract)
 Elsevier Science B.V
, 1996
"... ) R.F. Blute 1 P.J. Scott 1 Dept. of Mathematics University of Ottawa Ottawa, Ontario K1N 6N5 CANADA E. N. T. C. S. Elsevier Science B. V. Abstract We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic known as cyclic linear logic (Cy ..."
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) R.F. Blute 1 P.J. Scott 1 Dept. of Mathematics University of Ottawa Ottawa, Ontario K1N 6N5 CANADA E. N. T. C. S. Elsevier Science B. V. Abstract We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic known as cyclic linear logic (CyLL), first defined by Yetter. The semantics is obtained by considering dinatural transformations on a category of topological vector spaces which are invariant under certain actions of a noncocommutative Hopf algebra, called the shuffle algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that the space has the denotations of cutfree proofs in CyLL+MIX as a basis. This work is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic. In that paper, we consider dinaturals which are invariant under certain actions of the additive group of integers. The passage from group...
Types and Dynamics in Partially Additive Categories
, 1995
"... this paper can be directly applied in order to give a semantics of reduction for the multiplicative fragment of linear logic: in order to capture larger fragments it should be extended dealing with infinitary objects and more generally, this approach allows to investigate an algebraic theory of comp ..."
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this paper can be directly applied in order to give a semantics of reduction for the multiplicative fragment of linear logic: in order to capture larger fragments it should be extended dealing with infinitary objects and more generally, this approach allows to investigate an algebraic theory of computation based on the cutelimination of proofs. 6 Conclusions and Related Works