Computational Paths -- An approach in the $LND_{EQ}-TRS_{2}$ system

Anjolina G. de Oliveira; Arthur F. Ramos; Ruy J. G. B. de Queiroz; Tiago M. L. Veras

Computational Paths -- An approach in the $LND_{EQ}-TRS_{2}$ system

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arxiv 2007.07769 v3 pith:XFIFU54F submitted 2020-07-13 cs.LO

Tiago M. L. Veras , Arthur F. Ramos , Ruy J. G. B. de Queiroz , Anjolina G. de Oliveira This is my paper · ORCID

classification cs.LO

keywords computationalpathssystemapproachconceptallowedcarrydeduction

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abstract

We use a labelled deduction system ( LND$_{ED-}$TRS ) based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type, which allowed us to carry out in homotopic theory an approach using the concept of computational paths. From this, we show that the computational paths can be used to perform the proofs of the $LND_{EQ}-TRS_{2}$ rewriting system.

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Monte-Carlo simulations show that 45-65% of unused spectrum in an 80-channel WDM system can be repurposed for QKD using a stochastic traffic model and key reservoir management with defined reliability metrics.

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