Program algebra with unit instruction operators

AbstractIn the setting of program algebra (PGA), a projection from PGAu, i.e., PGA extended with a unit instruction operator, into PGA is defined. This is done via a composition that employs backward jumps and (labeled) goto's

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

Functional units for natural numbers

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 interaction in question have been proposed in the setting of thread algebra. Like thread, service is an abstract behavioural concept. The concept of a functional unit is similar to the concept of a service, but more concrete. A state space is inherent in the concept of a functional unit, whereas it is not inherent in the concept of a service. In this paper, we establish the existence of a universal computable functional unit for natural numbers and related results.Comment: 17 pages; notational mistakes in tables 5 and 6 corrected; erroneous definition at bottom of page 9 correcte

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

Turing Impossibility Properties for Stack Machine Programming

The strong, intermediate, and weak Turing impossibility properties are introduced. Some facts concerning Turing impossibility for stack machine programming are trivially adapted from previous work. Several intriguing questions are raised about the Turing impossibility properties concerning different method interfaces for stack machine programming.Comment: arXiv admin note: substantial text overlap with arXiv:0910.556

Instruction sequences with indirect jumps

We study sequential programs that are instruction sequences with direct and indirect jump instructions. The intuition is that indirect jump instructions are jump instructions where the position of the instruction to jump to is the content of some memory cell. We consider several kinds of indirect jump instructions. For each kind, we define the meaning of programs with indirect jump instructions of that kind by means of a translation into programs without indirect jump instructions. For each kind, the intended behaviour of a program with indirect jump instructions of that kind under execution is the behaviour of the translated program under execution on interaction with some memory device.Comment: 23 pages; typos corrected, phrasing improved, reference replace

Mechanistic Behavior of Single-Pass Instruction Sequences

Earlier work on program and thread algebra detailed the functional, observable behavior of programs under execution. In this article we add the modeling of unobservable, mechanistic processing, in particular processing due to jump instructions. We model mechanistic processing preceding some further behavior as a delay of that behavior; we borrow a unary delay operator from discrete time process algebra. We define a mechanistic improvement ordering on threads and observe that some threads do not have an optimal implementation.Comment: 12 page