Rosen's (M, R) system as an X-machine. (7th November 2016)

• Record Type: Journal Article
• Authors: Palmer, Michael L.; Williams, Richard A.; Gatherer, Derek
• Is Part Of: Journal of theoretical biology. Volume 408(2016)
• Page Start: 97
• Page End: 104
• Publication Date: 2016-11-07
• Subjects: Systems biology -- Computability -- Reductionism -- Mechanism -- Self-reference -- Turing machine -- UML -- Unified Modelling Language -- Finite state machine -- Stream X-machine -- Communicating X-machine; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2016.08.007
• Languages: English
• ISSNs: 0022-5193

Abstract

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. Highlights: Finite state machines and stream X-machines fail to model the self-referential (M, R) system. Communicating X-machines can evade the self-referential problem. Communicating X-machines require parallel processing. Communicating X-machines can have object-oriented components. We produce an object-oriented communicating X-machine architecture for (M, R) .