Instruction sequence notations with probabilistic instructions

Abstract

This paper concerns instruction sequences that contain probabilistic instructions, i.e. instructions that are themselves probabilistic by nature. We propose several kinds of probabilistic instructions, provide an informal operational meaning for each of them, and discuss related work. On purpose, we refrain from providing an ad hoc formal meaning for the proposed kinds of instructions. We also discuss the approach of projection semantics, which was introduced in earlier work on instruction sequences, in the light of probabilistic instruction sequences.

Probabilistic Thread Algebra

“…Thus, we have paved the way for rigorous investigation of issues related to probabilistic computation thinking in terms of instruction sequences and rigorous investigation of probabilistic interleaving strategies. As an example of the use of prTA tsi , the probabilistic version of the extension of BTA with thread-service interaction, we have added the most basic kind of probabilistic instructions proposed in [12] to a program notation rooted in PGA and have given a formal definition of the behaviours produced by the instruction sequences from the resulting program notation under excution with the help of prTA tsi .…”

“…In [12], we proposed several kinds of probabilistic jump instructions (bounded and unbounded, according to uniform probability distributions and geometric probability distributions). The meaning of instruction sequences from extensions of prPGLB with these kinds of probabilistic instructions can be given by a translation to instruction sequences from prPGLB.…”

“…In [12], we gave an enumeration of kinds of probabilistic instructions that were chosen on the basis of direct intuitions and therefore not necessarily the best kinds in any sense. We only gave an informal explanation for each of the enumerated kinds because we considered it premature at the time to add probabilistic features to BTA that would make it possible to give a formal explanation.…”

“…Later, we have found that the ramification of semantic options with the addition of probabilistic features to BTA is well surveyable because of (a) the limitation of the scope to behaviours produced by instruction sequences under execution and (b) the semantic constraints brought about by the informal explanations of the kinds of probabilistic instructions enumerated in [12] and the desired elimination property of all but one kind. In the case of a general process algebra, such as ACP [3], CCS [27] or CSP [24], the ramification becomes much more complex, particularly because a limitation of the scope to behaviours of a special kind is lacking.…”

“…The probabilistic features added to the extension of BTA with thread-service interaction make it possible to give a formal explanation for each of the kinds of probabilistic instructions enumerated in [12] in terms of non-probabilistic in-structions and probabilistic services. To demonstrate this, we add the kind of probabilistic instructions that cannot be eliminated to PGLB (ProGramming Language B), a program notation rooted in PGA and close to existing assembly languages, and give a formal definition of the behaviours produced by the instruction sequences from the resulting program notation.…”