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arXiv · 1512.04964

Horn Linear Logic and Minsky Machines

Max Kanovich
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Abstract

Here we give a detailed proof for the crucial point in our Minsky machine simulation - that any linear logic derivation for a specific Horn sequent can be transformed into a Minsky computation leading from an initial configuration to the halting configuration. Among other things, the presentation advantage of the 3-step program is that the non-trivial tricky points are distributed between the independent parts each of which we justify following its own intrinsic methodology (to say nothing of the induction used in the opposite directions): (1) From LL to HLL - we use purely proof-theoretic arguments. (2) From HLL to Horn programs - we translate trees (HLL derivations) into another trees (Horn programs)of the same shape, almost. (3) From Horn programs to Minsky computations - we use purely computational arguments.

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Max Kanovich. 2015-12-15. Horn Linear Logic and Minsky Machines. https://arxiv.org/abs/1512.04964

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