Rosen's (M,R) system in Unified Modelling Language

Abstract

Robert Rosen's (M,R) system is an abstract biological network architecture that is allegedly non-computable on a Turing machine. If (M,R) is truly non-computable, there are serious implications for the modelling of large biological networks in computer software. A body of work has now accumulated addressing Rosen's claim concerning (M,R) by attempting to instantiate it in various software systems. However, a conclusive refutation has remained elusive, principally since none of the attempts to date have unambiguously avoided the critique that they have altered the properties of (M,R) in the coding process, producing merely approximate simulations of (M,R) rather than true computational models. In this paper, we use the Unified Modelling Language (UML), a diagrammatic notation standard, to express (M,R) as a system of objects having attributes, functions and relations. We believe that this instantiates (M,R) in such a way than none of the original properties of the system are corrupted in the process. Crucially, we demonstrate that (M,R) as classically represented in the relational biology literature is implicitly a UML communication diagram. Furthermore, since UML is formally compatible with object-oriented computing languages, instantiation of (M,R) in UML strongly implies its computability in object-oriented coding languages.

Keywords: (M,R); Computability; Entailment; Entscheidungsproblem; Halting problem; Modelling; Networks; OOP; Object-orientation; Reduction; Reductionism; Relational biology; Rosen; Simulation; Systems biology; UML; Unified Modelling Language.