Paraconsisted computation : a logic approach to quantum / Computação paraconsistente : uma abordagem logica a computação quantica

AUTOR(ES)
DATA DE PUBLICAÇÃO

2009

RESUMO

This work provides evidences to view computational complexity as logic-relative, by introducing new models of computation through non-classical logics and by studying their features with respect to computational expressivity and efficiency. From this point of view, we suggest a new way to study the efficiency of quantum computational models consisting in the analysis of an underlying logic. The contents of the thesis is structured in the following way: the first chapter presents a conceptual analysis of the notion of computation , showing how this concept evolved since the decade of 1930 and discussing whether it can be considered a pure physical or a pure logic-mathematical concept, or a combination of both paradigms. Chapter 2 introduces two versions of paraconsistent Turing machines , by considering different logic systems and obtaining models with different computational capabilities (with respect to efficiency); such a result constitute a first evidence in favor of the logical relativity of computation that we are defending here. Another evidence in the same direction is presented in Chapter 3 through a generalization of boolean circuits to non-classical logics, particularly for the paraconsistent logic mbC and for the modal logic S5, and by analyzing the computational power of such generalizations. Chapter 4 consists in an introduction to quantum computation. This is used in Chapter 5 to establish some relationships between quantum and paraconsistent models of computation, in order to propose a logic interpretation of quantum models. The final chapter (Chapter 6) describes several connections between quantum mechanics and paraconsistent logic; such relationship suggests highly relevant potentialities in favor of the paraconsistent approach to quantum computation phenomena encouraging to continue exploring this alternative

ASSUNTO(S)

circuitos logicos funções computaveis quantum computation logical circuits turing machines computability theory computação quantica turing - máquinas

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