ICCA2020:P000117

The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics

3 - 7 August, 2020

P000117

The Clifford algebra of $R^{n, n}$ and the Boolean SATisfiability Problem

*Marco Budinich (University of Trieste and INFN, Italy)

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{%Title of Talk	
 The Clifford algebra of $R^{n,n}$ and the Boolean SATisfiability Problem
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{% Name
Marco Budinich
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mbh@ts.infn.it
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University of Trieste and INFN, Trieste, Italy 
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{% Abstract 
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We show that the Boolean SATisfiability Problem with $n$ literals has a simple formulation in the Clifford algebra of neutral space $R^{n,n}$. In this setting there is a natural bijection between the $2^n$ simple spinors forming the Fock basis of the spinor space of the algebra and the possible assignments of the $n$ Boolean literals, the Boolean atoms. Moreover any of these simple spinors is the representative element of a partition of the group O$(n)$ into $2^n$ equivalence classes that, in a nutshell, are the ``fundamental'' involutions of $R^{n}$. In this way the combinatorial Boolean SATisfiability Problem can be attacked in the continuous group O$(n)$ rather that in a discrete set with $2^n$ elements. We argue that, being O$(n)$ a smooth compact manifold of dimension $n (n-1) / 2$, this offers some advantages.
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%% ABSTRACT template %% 12th ICCA, Aveiro
\documentclass[9pt]{amsart} % \usepackage{amsfonts,amsthm,amssymb,amsmath} \usepackage[scale={0.8,0.9}, a4paper, nofoot, bindingoffset=1cm]{geometry} \parindent0mm \parskip0mm \sloppy % \newtheorem*{theorem}{Theorem} % \newcommand{\ICCAabstract}[5]{{\bf #1}\par\medskip{\sc #2}\{#4}\{\tt #3} \par\bigskip {#5}\bigskip\bigskip} % $Unknown environment 'document'$

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The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics

3 - 7 August, 2020

The Clifford algebra of Rn,n and the Boolean SATisfiability Problem

The Clifford algebra of $R^{n, n}$ and the Boolean SATisfiability Problem