Papers by J. van der Woude
Springer eBooks, 1990
Predicate transformer semantics (PTS) has proved to be very fruitful, in particular for program d... more Predicate transformer semantics (PTS) has proved to be very fruitful, in particular for program derivation. It is well known, although not very well documented, that the version of PTS with universal conjunctivity for wlp and without the law of the excluded miracle is equivalent to some relation semantics (RS).
Journal of Logical and Algebraic Methods in Programming, 2021
Central to algorithmic graph theory are the concepts of acyclicity and strongly connected compone... more Central to algorithmic graph theory are the concepts of acyclicity and strongly connected components of a graph, and the related search algorithms. This article is about combining mathematical precision and concision in the presentation of these concepts. Concise formulations are given for, for example, the reflexive-transitive reduction of an acyclic graph, reachability properties of acyclic graphs and their relation to the fundamental concept of "definiteness", and the decomposition of paths in a graph via the identification of its strongly connected components and a pathwise homomorphic acyclic subgraph. The relevant properties are established by precise algebraic calculation. The combination of concision and precision is achieved by the use of point-free relation algebra capturing the algebraic properties of paths in graphs, as opposed to the use of pointwise reasoning about paths between nodes in graphs.
With relational transformational programming in mind, an extension of a "lawless &qu... more With relational transformational programming in mind, an extension of a "lawless " relational theory of datatypes is proposed in order to study and manipulate quotient types within a Tarski-like calculus of relations. The extended notion of type, pertype (from partial equivalence relation), is shown to admit a complete lattice structure by constructing the order via a Galois connection. A pertyping of relations is developed and inductive pertypes generated by equations are discussed. Pertypes do occur in model theory for -calculus but we are unaware of manipulations with inductive "lawful" types based on a simple relational calculus. 1 Introduction Program construction and its theory are developing steadily towards an algebraic discipline combining methods from category theory, algebraic logic and lattice theory. The driving forces are the needs for uninterpreted manipulation, problem structuring and generalisation, and polymorphy, with a major role for calculational type theo...
Lecture Notes in Computer Science, 1989
Lecture Notes in Computer Science, 2011
Siam Journal on Computing - SIAMCOMP, 1984
In this expository paper we discuss some notions from (abstract) Topological Dynamics. Moreover, ... more In this expository paper we discuss some notions from (abstract) Topological Dynamics. Moreover, we present self-contained simple proofs of the following results. Let <J>: X-* • Y be an open extension of minimal flows and suppose that <(> admits a relatively invariant measure. Then Q ±-E, f i.e. the relative regionally proximal relation is an equivalence relation. Also, if E. = R. (that is, 4> has no non-trivial almost periodic factor), then <J> is weakly mixing.
Pacific Journal of Mathematics, 1987
Consider homomorphisms φ: X-* Y and ψ: Y-> Z, where φ is open and N-to-one, ψ is almost periodic.... more Consider homomorphisms φ: X-* Y and ψ: Y-> Z, where φ is open and N-to-one, ψ is almost periodic. In the paper by R. J Sacker and G. R. Sell, it was shown that, under a certain condition on the phase group, the composition ψ ° φ: X-» Z is almost periodic (provided that Z is trivial and X is minimal). In this paper almost periodicity of ψ ° φ is studied under connectedness conditions on the fibers of ψ. For instance it is shown that if ψ is almost periodic with connected fibers than ψ φ is almost periodic. If ψ is locally almost periodic with locally connected fibers then φ ° ψ is locally almost periodic.
Pacific Journal of Mathematics, 1985
CHARACTERIZATIONS OF (H)PI EXTENSIONS JAAP VAN DER WOUDE A generalization of I. U. Bronstein's ch... more CHARACTERIZATIONS OF (H)PI EXTENSIONS JAAP VAN DER WOUDE A generalization of I. U. Bronstein's characterization for PD extensions is given and, exploiting similar ideas, HPI extensions are characterized intrinsically.
Ergodic Theory and Dynamical Systems, 1981
We study minimal flows and their extensions by means of the associated maximally highly proximal ... more We study minimal flows and their extensions by means of the associated maximally highly proximal flows. These, in turn, can be represented by highly proximal generators, which are certain subsets of the universal minimal flow. From this point of view we obtain information on relative disjointness, coalescence, the Bronstein property, and RIC extensions.
Ergodic Theory and Dynamical Systems, 1984
We discuss weak disjointness of homomorphisms of minimal transformation groups and use the techni... more We discuss weak disjointness of homomorphisms of minimal transformation groups and use the techniques involved to deepen our knowledge of the equicontinuous structure relation.
Science of Computer Programming, 1989
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
The notions of domain operator and domain kind are introduced. Several examples are presented. In... more The notions of domain operator and domain kind are introduced. Several examples are presented. In particular, it is shown that the partial equivalence relations form a domain kind. The proof involves the construction of a Galois connection demonstrating that the partial equivalence relations form a complete lattice under the so-called domain ordering, thus providing another illustration of the importance of the early recognition of Galois connections.
We give a concise, structured, and calculational proof of a theorem that yields a program specifi... more We give a concise, structured, and calculational proof of a theorem that yields a program specification for a given, specific, program simulation.
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Papers by J. van der Woude