Lower bounds on the computational power of an optical model of computation

Authors:
Damien Woods;J. Paul Gibson
Affiliations:
Department of Computer Science, University College Cork, Cork, Ireland;Département Logiciels-Réseaux, Institut National des Télécommunications, Évry cedex, France 91011
Venue:
Natural Computing: an international journal
Year:
2008

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Abstract

This work is concerned with the computational complexity of a model of computation that is inspired by optical computers. We present lower bounds on the computational power of the model. Parallel time on the model is shown to be at least as powerful as sequential space. This gives one of the two inclusions that are needed to show that the model verifies the parallel computation thesis. As a corollary we find that when the model is restricted to simultaneously use polylogarithmic time and polynomial space, its power is lower bounded by the class NC. By combining these results with the known upper bounds on the model, we find that the model verifies the parallel computation thesis and, when suitably restricted, characterises NC.