title: Rosen's (M,R) system as an X-machine.
abstract: Robert Rosen's (M,R) system is an abstract biological network architecture that is allegedly both irreducible to sub-models of its component states and non-computable on a Turing machine. (M,R) stands as an obstacle to both reductionist and mechanistic presentations of systems biology, principally due to its self-referential structure. If (M,R) has the properties claimed for it, computational systems biology will not be possible, or at best will be a science of approximate simulations rather than accurate models. Several attempts have been made, at both empirical and theoretical levels, to disprove this assertion by instantiating (M,R) in software architectures. So far, these efforts have been inconclusive. In this paper, we attempt to demonstrate why - by showing how both finite state machine and stream X-machine formal architectures fail to capture the self-referential requirements of (M,R). We then show that a solution may be found in communicating X-machines, which remove self-reference using parallel computation, and then synthesise such machine architectures with object-orientation to create a formal basis for future software instantiations of (M,R) systems.
authors: Division of Biomedical & Life Sciences, Faculty of Health & Medicine, Lancaster University, Lancaster LA14YW, UK.
authors: Michael L
authors: ML
authors: Palmer
authors: Department of Management Science, Management School, Lancaster University, Lancaster LA1 4YW, UK.
authors: Richard A
authors: RA
authors: Williams
authors: Division of Biomedical & Life Sciences, Faculty of Health & Medicine, Lancaster University, Lancaster LA14YW, UK. Electronic address: d.gatherer@lancaster.ac.uk.
authors: Derek
authors: D
authors: Gatherer
mesh_terms: D003198:Computer Simulation; D007802:Language; D008962:Models, Theoretical; D049490:Systems Biology
keywords: Communicating X-machine; Computability; Finite state machine; Mechanism; Reductionism; Self-reference; Stream X-machine; Systems biology; Turing machine; UML; Unified Modelling Language