Encodings of Turing machines in linear logic

We give several different encodings of the step function of a Turing machine in intuitionistic linear logic, and calculate the denotations of these encodings in the Sweedler semantics.

[1]  Valeria C V de Paiva,et al.  Term Assignment for Intuitionistic Linear Logic , 1992 .

[2]  Luca Roversi.  A P-Time Completeness Proof for Light Logics , 1999, CSL.

[3]  Lionel Vaux,et al.  The differential ? -calculus , 2007 .

[4]  C. Papadimitriou,et al.  Introduction to the Theory of Computation , 2018 .

[5]  Martin Hyland,et al.  Glueing and orthogonality for models of linear logic , 2003, Theor. Comput. Sci..

[6]  James Clift,et al.  Derivatives of Turing machines in Linear Logic , 2018, 1805.11813.

[7]  Laurent Regnier,et al.  The differential lambda-calculus , 2003, Theor. Comput. Sci..

[8]  Li Jin-q,et al.  Hopf algebras , 2019, Graduate Studies in Mathematics.

[9]  Nick Benton,et al.  A Term Calculus for Intuitionistic Linear Logic , 1993, TLCA.

[10]  Eitan M. Gurari,et al.  Introduction to the theory of computation , 1989 .

[11]  Jean-Yves Girard,et al.  Light Linear Logic , 1998, Inf. Comput..

[12]  James Clift,et al.  Cofree coalgebras and differential linear logic , 2017, Mathematical Structures in Computer Science.

[13]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[14]  Gerd Folkers,et al.  On computable numbers , 2016 .

[15]  Kazushige Terui,et al.  On the Computational Complexity of Cut-Elimination in Linear Logic , 2003, ICTCS.

[16]  Yurii Rogozhin,et al.  Small Universal Turing Machines , 1996, Theor. Comput. Sci..

[17]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[18]  Daniel Murfet,et al.  Logic and linear algebra: an introduction , 2014, ArXiv.

[19]  Vesselin Drensky,et al.  Polynomial Identity Rings , 2004 .

[20]  Paul-André Melliès.  CATEGORICAL SEMANTICS OF LINEAR LOGIC , 2009 .

[21]  SAMEER KAILASA,et al.  TOPICS IN GEOMETRIC GROUP THEORY , 2015 .

[22]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[23]  Daniel Murfet.  On Sweedler's cofree cocommutative coalgebra , 2014, 1406.5749.