On the behaviours produced by instruction sequences under execution

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 describe the behaviours produced by instruction sequences under execution and to describe two protocols implementing these behaviours in the case where the processing of instructions takes place remotely. We also show that all finite-state behaviours considered in ACP can be produced by instruction sequences under execution.Comment: 36 pages, consolidates material from arXiv:0811.0436 [cs.PL], arXiv:0902.2859 [cs.PL], and arXiv:0905.2257 [cs.PL]; abstract and introduction rewritten, examples and proofs adde

Instruction sequence processing operators

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 behaviours produced by them under execution, the interaction between these behaviours and components of the execution environment, and two issues relating to computability theory. Positioning Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines, and taking instruction sequences as programs, we analyse the autosolvability requirement that a program of a certain kind must solve the halting problem for all programs of that kind. We present novel results concerning this autosolvability requirement. The analysis is streamlined by using the notion of a functional unit, which is an abstract state-based model of a machine. In the case where the behaviours exhibited by a component of an execution environment can be viewed as the behaviours of a machine in its different states, the behaviours concerned are completely determined by a functional unit. The above-mentioned analysis involves functional units whose possible states represent the possible contents of the tapes of Turing machines with a particular tape alphabet. We also investigate functional units whose possible states are the natural numbers. This investigation yields a novel computability result, viz. the existence of a universal computable functional unit for natural numbers.Comment: 37 pages; missing equations in table 3 added; combined with arXiv:0911.1851 [cs.PL] and arXiv:0911.5018 [cs.LO]; introduction and concluding remarks rewritten; remarks and examples added; minor error in proof of theorem 4 correcte