Showing papers by "Maciej Koutny published in 1997"
TL;DR: For a number of different classes of structures, it is shown that any structure can be represented as the intersection of its maximal extensions, which can be seen as a generalisation of Szpilrajn's theorem.
Abstract: We consider relational structures \((X,R_1,R_2)\) such that \(X\) is a set and \(R_1,R_2\) are two binary relations on \(X\). For a number of different classes of structures we show that any structure can be represented as the intersection of its maximal extensions. Such a property – called extension completeness – can be seen as a generalisation of Szpilrajn's theorem which states that each partial order is the intersection of its total order extensions. When \(R_1\) can be interpreted as causality and \(R_2\) as ‘weak’ causality we obtain a model of concurrent histories generalising that based on causal partial orders.
44 citations
TL;DR: In this paper, the correctness of distributed systems made up of replicated processes that communicate by message passing is investigated, and the notion of correctness is based on a relation that formally expresses the conformance of an implementation process with the target process it is intended to implement.
Abstract: This paper studies the correctness of distributed systems made up of replicated processes that communicate by message passing. Processes are described within the divergence model of CSP. The notion of correctness introduced is based on a relation that formally expresses the conformance of an implementation process with the target process it is intended to implement. A weak and a strong version of the relation are introduced, aimed at treating acyclic and cyclic process networks respectively. Both allow the study of (total) correctness and may cope with non-deterministic targets and implementations. We then show how a target process may be implemented (in the formal sense introduced) by replicating it in a set of copies, a majority of which is non-faulty.
9 citations
01 Jan 1997
TL;DR: This paper transfers the notion of duplication equivalence to the domain of box expressions and investigates the relationship between duplication equivalent boxes and box expressions.
Abstract: The Petri Box Calculus (PBC) consists of an algebra of box expressions, and a corresponding algebra of boxes (a class of labelled Petri nets). A compositional semantics provides a translation from box expressions to boxes. There are several alternative ways of defining an equivalence notion for boxes, the strongest one being net isomorphism. In this paper we consider slightly weaker notion of equivalence, called duplication equivalence, which still can be argued to capture a very close structural similarity of concurrent systems represented by boxes. We transfer the notion of duplication equivalence to the domain of box expressions and investigate the relationship between duplication equivalent boxes and box expressions. The main result of this investigation is a sound and complete axiomatisation of duplication equivalence for a fragment of recursion-free PBC.
3 citations