Related papers: Program algebra for Turing-machine programs

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…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

We introduce a new type of generalized Turing machines (GTMs), which are intended as a tool for the mathematician who studies computability in Analysis. In a single tape cell a GTM can store a symbol, a real number, a continuous real…

We study sequential programs that are instruction sequences with jump-shift instructions in the setting of PGA (ProGram Algebra). Jump-shift instructions preceding a jump instruction increase the position to jump to. The jump-shift…

We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…

We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.

We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…

The general acceptance of sequence diagrams can be attributed to their relatively intuitive nature and ability to describe partial behaviors (as opposed to such diagrams as state charts). However, studies have shown that over 80 percent of…

Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…

Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…

We develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…

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…

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…

An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…

We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…

The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…

There are countless reasons cited in scientific studies to explain the difficulties in programming learning. The reasons range from the subject's complexity, the ineffective teaching and study methods, to psychological aspects such as…

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length $\omega$ to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite…

We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…

The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…