Axioms for behavioural congruence of single-pass instruction sequences

In program algebra, an algebraic theory of single-pass instruction sequences, three congruences on instruction sequences are paid attention to: instruction sequence congruence, structural congruence, and behavioural congruence. Sound and complete axiom systems for the first two congruences were already given in early papers on program algebra. The current paper is the first one that is concerned with an axiom system for the third congruence. The presented axiom system is especially notable for its axioms that have to do with forward jump instructions.Comment: 19 pages, this paper draws somewhat from the preliminaries of arXiv:1502.00238 [cs.PL] and some earlier papers; some remarks added and some remarks reformulate

A short introduction to program algebra with instructions for Boolean registers

A parameterized algebraic theory of instruction sequences, objects that represent the behaviours produced by instruction sequences under execution, and objects that represent the behaviours exhibited by the components of the execution environment of instruction sequences is the basis of a line of research in which issues relating to a wide variety of subjects from computer science have been rigorously investigated thinking in terms of instruction sequences. In various papers that belong to this line of research, use is made of an instantiation of this theory in which the basic instructions are instructions to read out and alter the content of Boolean registers and the components of the execution environment are Boolean registers. In this paper, we give a simplified presentation of the most general such instantiated theory.Comment: 21 pages, this paper is to a large extent a compilation of material from several earlier publications; 23 pages, presentation improved and section on uses for the theory added. arXiv admin note: text overlap with arXiv:1702.0351

On the complexity of the correctness problem for non-zeroness test instruction sequences

This paper concerns the question to what extent it can be efficiently determined whether an arbitrary program correctly solves a given problem. This question is investigated with programs of a very simple form, namely instruction sequences, and a very simple problem, namely the non-zeroness test on natural numbers. The instruction sequences concerned are of a kind by which, for each $n > 0$, each function from $\{0,1\}^n$ to $\{0,1\}$ can be computed. The established results include the time complexities of the problem of determining whether an arbitrary instruction sequence correctly implements the restriction to $\{0,1\}^n$ of the function from $\{0,1\}^*$ to $\{0,1\}$ that models the non-zeroness test function, for $n > 0$, under several restrictions on the arbitrary instruction sequence.Comment: 32 pages, minor revision with several obscurities made clea

Axioms for behavioural congruence of single-pass instruction sequences

In program algebra, an algebraic theory of single-pass instruction sequences, three congruences on instruction sequences are paid attention to: instruction sequence congruence, structural congruence, and behavioural congruence. Sound and complete axiom systems for the first two congruences were already given in early papers on program algebra. The current paper is the first one that is concerned with an axiom system for the third congruence