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Turing universality of the Biochemical Ground Form

Published online by Cambridge University Press:  26 February 2010

LUCA CARDELLI  and
GIANLUIGI ZAVATTARO
LUCA CARDELLI
Affiliation:
Microsoft Research, Cambridge, United Kingdom Email: luca@microsoft.com
GIANLUIGI ZAVATTARO
Affiliation:
Dip. Scienze dell'Informazione, Università di Bologna, Italy Email: zavattar@cs.unibo.it
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Abstract

We explore the expressive power of languages that naturally model biochemical interactions relative to languages that only naturally model basic chemical reactions, identifying molecular association as the basic mechanism that distinguishes the former from the latter. We use a process algebra, the Biochemical Ground Form (BGF), that adds primitives for molecular association to CGF, which is a process algebra that has been proved to be equivalent to the traditional notations for describing basic chemical reactions. We first observe that, unlike CGF, BGF is Turing universal as it supports a finite precise encoding of Random Access Machines, which comprise a well-known Turing powerful formalism. Then we prove that the Turing universality of BGF derives from the interplay between the molecular primitives of association and dissociation. In fact, the elimination from BGF of the primitives already present in CGF does not reduce the computational strength of the process algebra, but if either association or dissociation is removed, BGF ceases to be Turing complete.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Special Issue 1: Expressiveness in Concurrency 2008 , February 2010 , pp. 45 - 73
Copyright
Copyright © Cambridge University Press 2010

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