Underspecification for process algebras

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Infinite possible worlds for process algebras

[VD98] propose to view a finite nondeterministic process as a specification for a set of deterministic implementations: its possible worlds or model space. Refinement amounts to inclusion of possible worlds. We consider here the extension to infinite processes. We study the properties of possible worlds semanties, answer in particular an open question concerning the relation between bisimulation and possible worlds equivalence and discuss operational aspects

On redundancy, anomalies and on the question "what do normal forms really do"

In this paper we first survey various examples for anomalies given in the literature [1,3,8]. We discuss the formalizations and relate them to each other and the examples. We give arguments that show that decomposition of a relation scheme can help in getting rid of deletion/insertion anomalies and can fail in getting rid of update anomalies in the decomposed case

Some comments on CPO-semantics and metric space semantics for imperative languages

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Ensuring the existence of a BCNF-decomposition that preserves functional dependencies in O (N2) time

A simple condition is presented that ensures that a relation scheme R with a set F of functional dependencies has a Boyce-Codd normal form (BCNF)-decomposition that has the lossless-join property and preserves functional dependencies

On the uniqueness of fixed points endofunctors in a category of complete metric spaces

In de Bakker and Zucker proposed to use complete metric spaces for the semantic definition of programming languages that allow for concurrency and synchronisation. The use of the tools of metric topology has been advocated by Nivat and his colleagues already in the seventies and metric topology was successfully applied to various problems. Recently, the question under which circumstances fixed point equations involving complete metric spaces can be (unsquely) solved has attracted attention, e.g. [1,10]. In [1], a criterion for the existence of a solution, namely the contractiveness of the respectitve functor, is provided. Contractiveness together with an addtional criterton, the hom-contractiveness was shown in [1] to guarantee uniqueness. The problem of uniqueness is the topic of our contribution

Reachability in Cooperating Systems with Architectural Constraints is PSPACE-Complete

The reachability problem in cooperating systems is known to be PSPACE-complete. We show here that this problem remains PSPACE-complete when we restrict the communication structure between the subsystems in various ways. For this purpose we introduce two basic and incomparable subclasses of cooperating systems that occur often in practice and provide respective reductions. The subclasses we consider consist of cooperating systems the communication structure of which forms a line respectively a star.Comment: In Proceedings GRAPHITE 2013, arXiv:1312.706

The contraction property is sufficient to guarantee the uniqueness of fixed points of endofunctors in a category of acomplete metric spaces

In de Bakker and Zucker proposed to use complete metric spaces for the semantic definition of programming languages that allow for concurrency and synchronisation. The use of the tools of metric topology has been advocated by Nivat and his colleagues already in the seventies and metric topology was successfully applied to various problems (12, 13). Recently, the question under which circumstances fixed point equations involving complete metric spaces can be (uniquely) solved has attracted attention, e.g. (1,11). The solution of such equation provides the basis for the semantics of a given language and is hence of practical relevance. In (1), a criterion for the existence of a solution, namely that the respective functor is contracting, is provided. This property together with an additional criterion, namely that the respective functor is hom-contracting, was shown in (1) to guarantee uniqueness. In this paper we show that the contraction property is already sufficient to guarantee the uniqueness

A definition of redundancy in relational databases

The relational data model as proposed by Codd is a well-established method for data abstraction. Two essential aspects in this model are the definition of the data structure via the relation scheme and the data semantics via data dependencies. Various classes of data dependencies have been studied in the past. In the presence of data dependencies "update dependencies" (or anomalies) and "redundancy" may occur as first observed by Codd. Normal forms have been proposed as a means to control update anomalies and redundancy. But as the notion of redundancy has never been formally defined, one cannot make any precise statement concerning the presence or absence of redundancy for a given design. In this paper we attempt to provide a formal definition of the notion of redundancy for the case of a single relation respectively relation scheme. We first give a static semantic definition of redundancy and then present an operational analogue. Intuitively speaking a relation r contains redundancy, if some "part" of the information given in r can be "determined" from the "rest" of r. And a relation scheme with a given set of data dependencies admits redundancy if there is a relation belonging to this scheme that contains redundancy. The paper is organized in six sections. Section 1 contains the definition of the relational model that we use. We make use of partial "relations" that are built from constants and variables. In section 2 we present the semantic definition of redundancy. Section 3 introduces a class of data dependencies, i.e. implicational dependencies and a chase procedure for partial relations. Section 4 gives an operational characterization of redundancy. The main theorem in this section is theorem 4.3. It states that a relation r in a class of relations sat(D) contains redundancy if there exists a partial relation q that "contains less information" than rand for which chase D(q

On two different characterizations of bisimulation

Aczel89 and Joyal94 give distinct characterizations of bisimulation on labelled transition systems in terms of category theory. This paper discusses the differences between their formalisms and shows how to translate these approaches into one another