Derivatives of Turing machines in Linear Logic

James Clift; Daniel Murfet

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arXiv · 1805.11813

Derivatives of Turing machines in Linear Logic

James Clift·Daniel Murfet

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Abstract

We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier derivatives of various encodings of Turing machines into linear logic. We show that these derivatives calculate the rate of change of probabilities naturally arising in the Sweedler semantics of linear logic proofs. The resulting theory is applied to the problem of synthesising Turing machines by gradient descent.

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BibTeX RIS

James Clift, Daniel Murfet. 2018-05-30. Derivatives of Turing machines in Linear Logic. https://arxiv.org/abs/1805.11813

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