On the Expressiveness of Single-Pass Instruction Sequences

Abstract

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.

Instruction Sequence Based Non-uniform Complexity Classes

“…This led among other things to expressiveness results about the instruction sequences considered and variations of the instruction sequences considered (see e.g. [11,12]). As another continuation of the work on the above-mentioned approach to programming language semantics, selected issues relating to well-known subjects from the theory of computation and the area of computer architecture were rigorously investigated thinking in terms of instruction sequences (see e.g.…”

A short introduction to program algebra with instructions for Boolean registers

“…the binary use operator / : T × BRF → T; -the binary apply operator • : T × BRF → BRF; -the unary abstraction operator τ tau : T → T; and the axioms given in Tables 6. 6 In these tables, f stands for an arbitrary focus from F , p and q stand for arbitrary Boolean functions from B → B, b stands for an arbitrary Boolean value from B, n stands for an arbitrary natural number from N, and t and s stand for arbitrary terms of sort BRF. We use infix notation for the use and apply operators.…”

“…We remark that Boolean registers cannot only be used to compute partial functions from B n to B m . For example, it is shown in [6] that jump instruction are not necessary if use can be made of Boolean registers.…”

Untitled

“…In that way, the behaviour of PGLC ij programs on execution is described indirectly: the behaviour of the programs denoted by closed terms of program algebra on execution is formally described in several papers, including [2], using basic thread algebra [1]. 4 Because PGLB ij is a minor variant of PGLC ij , we refrain from describing the behaviour of PGLB ij programs on execution formally in the current paper.…”