Straight-line instruction sequence completeness for total calculation on cancellation meadows (2009)
Bergstra, Jan A., Bethke, Inge
A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the...
The structure of finite meadows (2009)
Bethke, Inge, Rodenburg, Piet, Sevenster, Arjen
A meadow is a commutative ring with a total inverse operator satisfying 0^{-1}=0. We show that the class of finite meadows is the closure of the class of Galois fields under finite products. As a...
A \emph{meadow} is a commutative ring with an inverse operator satisfying $0^{-1}=0$. We determine the initial algebra of the meadows of characteristic 0 and show that its word problem is decidable.
Some properties of finite meadows (2007)
The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary,...
Abstract. We propose an extension of purely equational reasoning with an induction rule, to obtain an intermediate between the equational theory of an algebraic specification and its!-closure. 1.
Note Coherence spaces are untopological (2007)
The purpose of this note is to show that stability is not a topological property. That is, that coherence spaces- except for the so-called flat ones- cannot be equipped with a topology such that the...
Jan A. Bergstra, Inge Bethke, Alban Ponse
We introduce iteration in process algebra by means of (the binary version of) Kleene's star operator: x y is the process that chooses between x and y, and upon termination of x has this choice...
A process algebra based framework for promise theory (2007)
Bergstra, Jan, Bethke, Inge, Burgess, Mark
We present a process algebra based approach to formalize the interactions of computing devices such as the representation of policies and the resolution of conflicts. As an example we specify how...
Autoconfiscation of Imake Configured (2007)
Ivo Tamboer, Supervisor(s) Bob Diertens, Inge Bethke
Signed: 2
Elementary Algebraic Specification of String Theory (2006)
Abstract. We discuss the data types Strings, Lines, and Pages which are the first steps into the direction of an algebraic specification of the daily practice of writing HTML texts. 1
Program Algebra and Thread Algebra (2006)
Jan A. Bergstra, Inge Bethke, Alban Ponse, I. Bethke, A. Ponse
These lecture notes comprise slightly abbreviated versions of a number of papers on program algebra and thread algebra. Program algebra in the form of PGA, an algebra of imperative programs dates...
Decision Problems for Pushdown Threads (2005)
Jan A. Bergstra, Inge Bethke, Alban Ponse
Abstract. Threads as contained in a thread algebra emerge from the behavioral abstraction from programs in an appropriate program algebra. Threads may make use of services such as stacks, and a...
Polarized process algebra and program equivalence (2003)
ingelscience.uva.nl Abstract. The basic polarized process algebra is completed yielding as a projective limit a cpo which also comprises infinite processes. It is shown that this model serves in a...
Extending partial combinatory algebras (1999)
We give a negative answer to the question whether every partial combinatory algebra can be completed. The explicit counterexample will be an intricately constructed term model, the construction and...
Descendants and Origins in Term Rewriting (1999)
I. Bethke, Jan W. Klop, R. De Vrijer, Inge Bethke, Jan Willem Klop, Roel De Vrijer
In this paper we treat various aspects of a notion that is central in term rewriting, namely that of descendants or residuals. We address both first order term rewriting and -calculus, their finitary...
Collapsing partial combinatory algebras (1996)
Abstract. Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general...
Completing Partial Combinatory Algebras with Unique Head-Normal Forms (1995)
I. Bethke, J. W. Klop, R. De Vrijer, Issn -x, Inge Bethke, Jan Willem Klop, ...
In this note, we prove that having unique head-normal forms is a sufficient condition on partial combinatory algebras to be completable. As application, we show that the pca of strongly normalizing...
Process Algebra with Combinators (1994)
Jan A. Bergstra, Inge Bethke, Alban Ponse
We introduce typed combinatory process algebra, a system combining process algebra with types and combinators. We describe its syntax and semantics, and by way of example, verify within this...
A Car Registration Authority, a Concise PSF-Specification (1993)
A PSF specification of a Car Registration Authority is given. Typical is the use of encapsulation of actions having certain data values, and data parametric communication and recursion. The PSF...
Finite type structures within combinatory algebras (1991)
Inge Bethke, For In Particular
Inside a combinatory algebra, there are 'internal ' versions of the finite type structure over!, which form models of various systems of finite type arithmetic. This paper compares internal...