25 citations · 290 across the 54 of their papers we have counts for
10 papers · 1 filter
Autosolvability of halting problem instances for instruction sequences
J. A. Bergstra, C. A. Middelburg
We position Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain ki…
Functional units for natural numbers
J. A. Bergstra, C. A. Middelburg
Interaction with services provided by an execution environment forms part of the behaviours exhibited by instruction sequences under execution. Mechanisms related to the kind of in…
Partial Komori fields and imperative Komori fields
J. A. Bergstra, C. A. Middelburg
This paper is concerned with the status of 1/0 and ways to deal with it. These matters are treated in the setting of Komori fields, also known as non-trivial cancellation meadows.…
Indirect jumps improve instruction sequence performance
J. A. Bergstra, C. A. Middelburg
Instruction sequences with direct and indirect jump instructions are as expressive as instruction sequences with direct jump instructions only. We show that, in the case where the…
Arithmetical meadows
J. A. Bergstra, C. A. Middelburg
An inversive meadow is a commutative ring with identity equipped with a multiplicative inverse operation made total by choosing 0 as its value at 0. Previously, inversive meadows w…
Instruction sequence notations with probabilistic instructions
J. A. Bergstra, C. A. Middelburg
This paper concerns instruction sequences that contain probabilistic instructions, i.e. instructions that are themselves probabilistic by nature. We propose several kinds of probab…