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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.
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 axi
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
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
We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction sequence concerne
For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a te