Transmission protocols for instruction streams

Threads as considered in thread algebra model behaviours to be controlled by some execution environment: upon each action performed by a thread, a reply from its execution environment -- which takes the action as an instruction to be processed -- determines how the thread proceeds. In this paper, we are concerned with the case where the execution environment is remote: we describe and analyse some transmission protocols for passing instructions from a thread to a remote execution environment.Comment: 13 page

Periodic Single-Pass Instruction Sequences

A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and so-called repeat instructions, a particular type of control instructions. The resulting mathematical structure is a semigroup. We relate this set of programs to program algebra (PGA) and show that a particular subsemigroup is a carrier for PGA by providing axioms for single-pass congruence, structural congruence, and thread extraction. This subsemigroup characterizes periodic single-pass instruction sequences and provides a direct basis for PGA's toolset.Comment: 16 pages, 3 tables, New titl

On the expressiveness of single-pass instruction sequences

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.Comment: 14 pages; error corrected, acknowledgement added; another error corrected, another acknowledgement adde

Straight-line instruction sequence completeness for total calculation on cancellation meadows

A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the instruction set $\{x \Leftarrow 0, x \Leftarrow 1, x\Leftarrow -x, x\Leftarrow x^{-1}, x\Leftarrow x+y, x\Leftarrow x\cdot y\}$. It is proven that total functions on cancellation meadows can be computed by straight-line programs using at most 5 auxiliary variables. A similar result is obtained for signed meadows.Comment: 24 page

Instruction sequences for the production of processes

Single-pass instruction sequences under execution are considered to produce behaviours to be controlled by some execution environment. Threads as considered in thread algebra model such behaviours: upon each action performed by a thread, a reply from its execution environment determines how the thread proceeds. Threads in turn can be looked upon as producing processes as considered in process algebra. We show that, by apposite choice of basic instructions, all processes that can only be in a finite number of states can be produced by single-pass instruction sequences.Comment: 23 pages; acknowledgement corrected, reference update

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

Thread extraction for polyadic instruction sequences

In this paper, we study the phenomenon that instruction sequences are split into fragments which somehow produce a joint behaviour. In order to bring this phenomenon better into the picture, we formalize a simple mechanism by which several instruction sequence fragments can produce a joint behaviour. We also show that, even in the case of this simple mechanism, it is a non-trivial matter to explain by means of a translation into a single instruction sequence what takes place on execution of a collection of instruction sequence fragments.Comment: 21 pages; error corrected; presentation improve

Instruction sequences with dynamically instantiated instructions

We study sequential programs that are instruction sequences with dynamically instantiated instructions. We define the meaning of such programs in two different ways. In either case, we give a translation by which each program with dynamically instantiated instructions is turned into a program without them that exhibits on execution the same behaviour by interaction with some service. The complexity of the translations differ considerably, whereas the services concerned are equally simple. However, the service concerned in the case of the simpler translation is far more powerful than the service concerned in the other case.Comment: 25 pages; phrasing improve