Related papers: Instruction sequence processing operators
We position Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that…
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…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
We study several aspects of the behaviours produced by instruction sequences under execution in the setting of the algebraic theory of processes known as ACP. We use ACP to describe the behaviours produced by instruction sequences under…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
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,…
The behaviour produced by an instruction sequence under execution is a behaviour to be controlled by some execution environment: each step performed actuates the processing of an instruction by the execution environment and a reply returned…
Termination property of functions is an important issue in computability theory. In this paper, we show that repeated iterations of a function can induce an order amongst the elements of its domain set. Hasse diagram of the poset, thus…
Interaction with services provided by an execution environment forms part of the behaviours exhibited by instruction sequences under execution. Mechanisms related to the kind of interaction in question have been proposed in the setting of…
The present work determines the exact nature of {\em linear time computable} notions which characterise automatic functions (those whose graphs are recognised by a finite automaton). The paper also determines which type of linear time…
This paper presents an algebraic theory of instruction sequences with instructions for a random access machine (RAM) as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction…
Software testing is presented as a so-called theme within which different authors and groups have defined different subjects each of these subjects having a different focus on testing. A uniform concept of software testing is non-existent…
Even as machine learning exceeds human-level performance on many applications, the generality, robustness, and rapidity of the brain's learning capabilities remain unmatched. How cognition arises from neural activity is a central open…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
An attempt is made to define the concept of execution of an instruction sequence. It is found to be a special case of directly putting into effect of an instruction sequence. Directly putting into effect of an instruction sequences…
There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their…
What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…
The Apperception Engine is an unsupervised learning system. Given a sequence of sensory inputs, it constructs a symbolic causal theory that both explains the sensory sequence and also satisfies a set of unity conditions. The unity…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…