Introduction to the Theory of Computation
Introduction to the Theory of Computation
Analytic Combinatorics
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In this paper we approach some questions about quantum contextuality with tools from formal logic. In particular, we consider an experiment associated with the Peres-Mermin square. The language of all possible sequences of outcomes of the experiment is classified in the Chomsky hierarchy and seen to be a regular language. We introduce a very abstract model of machine that simulates nature in a particular sense. A lower-bound on the number of memory states of such machines is proved if they were to simulate the experiment that corresponds to the Peres-Mermin square. Moreover, the proof of this lower bound is seen to scale to a certain generalization of the Peres-Mermin square. For this scaled experiment it is seen that the Holevo bound is violated and that the degree of violation increases uniformly.