Program algebra for Turing-machine programs

01/25/2019

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by   J. A. Bergstra, et al.

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This note 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 the Turing tapes provided by an execution environment. This theory provides a setting for investigating issues relating to computability and computational complexity that is more general than the closely related Turing-machine models 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.