# Program algebra for Turing-machine programs

## TL;DR

This paper develops an algebraic framework for Turing-machine programs that enables equational reasoning and generalizes traditional models, facilitating rigorous analysis in computability and complexity.

## Contribution

It introduces a parameterized algebraic theory of instruction sequences for Turing tapes, expanding the theoretical tools for computer science research.

## Key findings

- Provides an algebraic setting for instruction sequences with Turing tapes.
- Enables equational reasoning in the analysis of Turing-machine programs.
- Offers a more general framework than classical Turing-machine models.

## Abstract

This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such behaviours and Turing tapes provided by an execution environment. This theory provides a setting for the development of theory in areas such as computability and computational complexity that distinguishes itself by offering the possibility of equational reasoning and being more general than the setting provided by a known version of the Turing-machine model of computation. The theory is essentially an instantiation of a parameterized algebraic theory which 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.