On Computational Complexity of Clifford Algebra

After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl 2m that simplifies greatly the actual calculations and, without resorting to the conventional matrix isomorphism formulation, obtains the same complexity. In the last part we apply these results to the Clifford algebra formulation of the NP-complete problem of the maximum clique of a graph introduced by Budinich and Budinich “A spinorial formulation of the maximum clique problem of a graph,” J. Math. Phys. 47, 043502 2006 . © 2009 American Institute of Physics. DOI: 10.1063/1.3133042