On the Contribution of Backward Jumps to Instruction Sequence Expressiveness

Abstract

We investigate the expressiveness of backward jumps in a framework of formalized sequential programming called program algebra. We show that-if expressiveness is measured in terms of the computability of partial Boolean functions-then backward jumps are superfluous. If we, however, want to prevent explosion of the length of programs, then backward jumps are essential.6.-7. the termination instructions !t, !f which prescribe successful termination and in doing so deliver the Boolean value t and f, respectively.Complex instruction sequences are obtained from primitive instructions using concatenation: if I and J are instruction sequences, then so is I; J which is the instruction sequence that lists J's primitive instructions right after those of I. We denote by IS(A) the set of PGLB bt (A) instruction sequences.Thread algebra is the behavioural semantics for PGA and was introduced in e.g. [1,3] under the name Polarized Process Algebra.

A Survey of Testing for Instruction Sequence Theory

“…There are several differences however: (i) a run can get into a loop while interacting with the auxiliary services only. To decide whether or not that will happen is NP-hard (see [13]); it is the task of A to determine how long to wait before a run is aborted. (ii) Because the system is deterministic once X is known as a text, a test case suffices for computational path reconstruction.…”

Long multiplication by instruction sequences with backward jump instructions

“…It is among other things shown that a function on bit strings whose result is a bit string of length 1 belongs to P/poly iff it can be computed by polynomial-length instruction sequences of this kind. In [1], instruction sequences are considered which contain backward jump instructions in addition to the above-mentioned instructions. It is among other things shown that a function on bit strings whose result is a bit string of length 1 belongs to PSPACE/poly iff it can be computed by polynomial-length instruction sequences of this latter kind.…”

“…The groundwork for the approach is an algebraic theory of single-pass instruction sequences, called program algebra, and an algebraic theory of mathematical objects that represent the behaviours produced by instruction sequences under execution, called basic thread algebra. 1 As a continuation of this work on an approach to programming language semantics, (a) the notion of an instruction sequence was subjected to systematic and precise analysis using the groundwork laid earlier and (b) 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. [4]).…”

Four Conceptions of Instruction Sequence Faults

“…A degree of freedom is obtained concerning the determination of meaning of terms and phrases which is unavailable when writing on program faults. If needed, the scope of claims concerning instruction sequence faults (or instruction sequence testing) can be limited by making the implicit assumption that instruction sequence theory is meant to refer specifically to a theory in the style of [11,15,12,13,9]. 2.…”

“…The notion of a computer program not only lacks any common definition, definitions of the concept of a computer program that have not gained wide acceptance are also hard to find. For instruction sequences matters of definition have been settled in [11,15,12,9]. Defining program faults is made much harder in the absence of a definition of program.…”