An Introduction to Program and Thread Algebra

Ponse, Alban; Zwaag, Mark B. van der

doi:10.1007/11780342_46

Cited by 23 publications

(44 citation statements)

References 10 publications

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“…All regular threads in which tau does not occur represent behaviours of instruction sequences that can be denoted by closed PGA terms (see Proposition 2 in [21]). Closed PGA terms in which the repetition operator does not occur correspond to finite threads.…”

Section: Program Algebra and Basic Thread Algebramentioning

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: Program Algebra and Basic Thread Algebramentioning

confidence: 99%

Instruction Sequence Based Non-uniform Complexity Classes

Bergstra¹,

Middelburg²

2014

SACS

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“…We have also shown that a bound to the number of labels restricts the expressiveness of this variant. Earlier expressiveness results on single-pass instruction sequences as considered in program algebra are collected in [23].…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, it is known that, for each k ∈ N, there exists a closed PGA term for which there does not exist a closed PGA term not containing jump instructions #l with l > k + 3 that denotes the same thread (see e.g. [23], Proposition 3). Hence, we also have the following corollary: Corollary 3 For each k ∈ N, there exists a closed PGA term P for which there does not exist a closed PGA k g term P such that |P | = |pgag2pga(P )|.…”

Section: Theorem 2 For Each Closedmentioning

confidence: 99%

“…As part of the research program of which the work presented in this paper is part, issues concerning the following subjects from the theory of computation have been investigated from the viewpoint that a program is an instruction sequence: semantics of programming languages [4,12], expressiveness of programming languages [9,23], computability [10,13], and computational complexity [7]. Performance related matters of instruction sequences have also been investigated in the spirit of the theory of computation [11,12].…”

Section: Introductionmentioning

confidence: 99%

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On the Expressiveness of Single-Pass Instruction Sequences

Bergstra

Middelburg

2010

Theory Comput Syst

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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 execution environment. Threads as considered in basic thread algebra model such behaviours. We show that all regular threads, i.e. threads that can only be in a finite number of states, can be produced by single-pass instruction sequences without jump instructions if use can be made of Boolean registers. We also show that, in the case where goto instructions are used instead of jump instructions, a bound to the number of labels restricts the expressiveness.

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“…[BBP07,BM07a,PvdZ06]). In this line of research, the view is taken that the behaviour exhibited by a sequential program on execution takes the form of a thread as considered in basic thread algebra [BL02].…”

Section: Introductionmentioning

confidence: 99%

Thread algebra for poly-threading

Bergstra

Middelburg

2011

Form. Asp. Comput.

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Abstract.It is a fact of life that sequential programs are often fragmented. Consequently, fragmented program behaviours are frequently found. We consider this phenomenon in the setting of thread algebra. We extend basic thread algebra with poly-threading, the barest mechanism for sequencing of threads that are taken for program fragment behaviours. This mechanism is the counterpart of program overlaying at the level of program behaviours. We relate the resulting theory to the process theory known as ACP and use it to describe analytic execution architectures suited for fragmented programs. We also consider the case where the steps of fragmented program behaviours are interleaved in the ways of non-distributed and distributed multi-threading.

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An Introduction to Program and Thread Algebra

Cited by 23 publications

References 10 publications

Instruction Sequence Based Non-uniform Complexity Classes

Instruction Sequence Based Non-uniform Complexity Classes

On the Expressiveness of Single-Pass Instruction Sequences

Thread algebra for poly-threading

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