Instruction sequence processing operators

Bergstra, Jan A.; Middelburg, Cornelis A.

doi:10.1007/s00236-012-0154-2

Cited by 28 publications

(74 citation statements)

References 47 publications

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“…The extension of BTA described in this section is a simple version of the extension of BTA presented in [9]. We have chosen to use the former extension because it is adequate to the purpose of this paper and it allows a terser survey.…”

Section: Interaction Of Threads With Servicesmentioning

confidence: 99%

Instruction Sequence Based Non-uniform Complexity Classes

Bergstra¹,

Middelburg²

2014

SACS

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Abstract. We present an approach to non-uniform complexity in which single-pass instruction sequences play a key part, and answer various questions that arise from this approach. We introduce several kinds of non-uniform complexity classes. One kind includes a counterpart of the well-known non-uniform complexity class P/poly and another kind includes a counterpart of the well-known non-uniform complexity class NP/poly. Moreover, we introduce a general notion of completeness for the non-uniform complexity classes of the latter kind. We also formulate a counterpart of the well-known complexity theoretic conjecture that NP ⊆ P/poly. We think that the presented approach opens up an additional way of investigating issues concerning non-uniform complexity.

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Section: Interaction Of Threads With Servicesmentioning

confidence: 99%

Instruction Sequence Based Non-uniform Complexity Classes

Bergstra¹,

Middelburg²

2014

SACS

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“…4 The instruction sequence represented by a closed term of the form t ; t is the instruction sequence represented by t concatenated with the instruction sequence represented by t . The instruction sequence represented by a closed term of the form t ω is the instruction sequence represented by t concatenated infinitely many times with itself.…”

Section: Axioms For Behavioural Congruence Of Single-pass Instructionmentioning

confidence: 99%

“…threads without a finite upper bound to the number of basic actions that it can perform, can be defined by means of a set of recursion equations (see e.g. [4]). A regular thread is a finite or infinite thread that can only be in a finite number of states.…”

Section: Basic Thread Algebra For Finite and Infinite Threadsmentioning

confidence: 99%

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2017

SACS

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In program algebra, an algebraic theory of single-pass instruction sequences, three congruences on instruction sequences are paid attention to: instruction sequence congruence, structural congruence, and behavioural congruence. Sound and complete axiom systems for the first two congruences were already given in early papers on program algebra. The current paper is the first one that is concerned with an axiom system for the third congruence. The presented axiom system is especially notable for its axioms that have to do with forward jump instructions.

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“…Program algebra and basic thread algebra were first presented in [4]. 1 The extension of basic thread algebra referred to above, an extension to deal with the interaction between the behaviours produced by instruction sequences under execution and components of an execution environment, was first presented in [5]. The presentation of the extension is rather involved because it is parameterized and owing to this covers a generic set of basic instructions and a generic set of execution environment components.…”

Section: Introductionmentioning

confidence: 99%

Program Algebra for Turing-Machine Programs

Bergstra¹,

Middelburg²

2019

SACS

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This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such behaviours and Turing tapes provided by an execution environment. This theory provides a setting for the development of theory in areas such as computability and computational complexity that distinguishes itself by offering the possibility of equational reasoning and being more general than the setting provided by a known version of the Turing-machine model of computation. The theory is essentially an instantiation of a parameterized algebraic theory which is the basis of a line of research in which issues relating to a wide variety of subjects from computer science have been rigorously investigated thinking in terms of instruction sequences.

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Instruction sequence processing operators

Cited by 28 publications

References 47 publications

Instruction Sequence Based Non-uniform Complexity Classes

Instruction Sequence Based Non-uniform Complexity Classes

Untitled

Program Algebra for Turing-Machine Programs

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