16 citations · 106 across the 22 of their papers we have counts for
22 papers
On the formalization of the notion of a concurrent algorithm
C. A. Middelburg
Previous papers give accounts of quests for satisfactory formalizations of the classical informal notion of an algorithm and the contemporary informal notion of an interactive algo…
On an ordinary expansion of first-order Belnap-Dunn logic
C. A. Middelburg
This paper concerns an expansion of first-order Belnap-Dunn logic whose connectives and quantifiers all have a counterpart in classical logic. The language and logical consequence…
Paraconsistent logic and query answering in inconsistent databases
C. A. Middelburg
This paper concerns the paraconsistent logic LPQ and an application of it in the area of relational database theory. The notions of a relational database, a…
Imperative process algebra and models of computation
C. A. Middelburg
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considere…
A classical-logic view on a paraconsistent logic
C. A. Middelburg
This paper is concerned with the paraconsistent first-order logic LPQ, Priest's LPQ enriched with an implication connective and a falsity constant. A sequent…
Using Hoare logic in a process algebra setting
J. A. Bergstra, C. A. Middelburg
This paper concerns the relation between process algebra and Hoare logic. We investigate the question whether and how a Hoare logic can be used for reasoning about how data change…
Process algebra with strategic interleaving
J. A. Bergstra, C. A. Middelburg
In process algebras such as ACP (Algebra of Communicating Processes), parallel processes are considered to be interleaved in an arbitrary way. In the case of multi-threading as fou…
Contradiction-tolerant process algebra with propositional signals
J. A. Bergstra, C. A. Middelburg
In a previous paper, an ACP-style process algebra was proposed in which propositions are used as the visible part of the state of processes and as state conditions under which proc…
Instruction sequence size complexity of parity
J. A. Bergstra, C. A. Middelburg
Each Boolean function can be computed by a single-pass instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructio…
On algorithmic equivalence of instruction sequences for computing bit string functions
J. A. Bergstra, C. A. Middelburg
Every partial function from bit strings of a given length to bit strings of a possibly different given length can be computed by a finite instruction sequence that contains only in…
On the behaviours produced by instruction sequences under execution
J. A. Bergstra, C. A. Middelburg
We study several aspects of the behaviours produced by instruction sequences under execution in the setting of the algebraic theory of processes known as ACP. We use ACP to describ…
Interest prohibition and financial product innovation
J. A. Bergstra, C. A. Middelburg
We give a rough sketch of the Judaic, Greek, Islamic and Christian positions in the matter of interest prohibition during the last few millennia and discuss the way in which intere…
An Application Specific Informal Logic for Interest Prohibition Theory
J. A. Bergstra, C. A. Middelburg
Interest prohibition theory concerns theoretical aspects of interest prohibition. We attempt to lay down some aspects of interest prohibition theory wrapped in a larger framework o…
Preliminaries to an investigation of reduced product set finance
J. A. Bergstra, C. A. Middelburg
Principles of financial product synthesis from a few basic financial products constitute an interesting research topic inspired by Islamic finance. We make an effort to answer gene…
Instruction sequence processing operators
J. A. Bergstra, C. A. Middelburg
Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the be…
A process calculus with finitary comprehended terms
J. A. Bergstra, C. A. Middelburg
We introduce the notion of an ACP process algebra and the notion of a meadow enriched ACP process algebra. The former notion originates from the models of the axiom system ACP. The…
On the expressiveness of single-pass instruction sequences
J. A. Bergstra, C. A. Middelburg
We perceive programs as single-pass instruction sequences. A single-pass instruction sequence under execution is considered to produce a behaviour to be controlled by some executio…
Data linkage dynamics with shedding
J. A. Bergstra, C. A. Middelburg
We study shedding in the setting of data linkage dynamics, a simple model of computation that bears on the use of dynamic data structures in programming. Shedding is complementary…
Data linkage algebra, data linkage dynamics, and priority rewriting
J. A. Bergstra, C. A. Middelburg
We introduce an algebra of data linkages. Data linkages are intended for modelling the states of computations in which dynamic data structures are involved. We present a simple mod…
Thread algebra for poly-threading
J. A. Bergstra, C. A. Middelburg
Threads as considered in basic thread algebra are primarily looked upon as behaviours exhibited by sequential programs on execution. It is a fact of life that sequential programs a…
Instruction sequences with dynamically instantiated instructions
J. A. Bergstra, C. A. Middelburg
We study sequential programs that are instruction sequences with dynamically instantiated instructions. We define the meaning of such programs in two different ways. In either case…
An interface group for process components
J. A. Bergstra, C. A. Middelburg
We take a process component as a pair of an interface and a behaviour. We study the composition of interacting process components in the setting of process algebra. We formalize th…