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

Ling Zhang¹, Richard A Williams², Derek Gatherer¹

¹Division of Biomedical & Life Sciences, Faculty of Health & Medicine, Lancaster University, Lancaster LA1 4YW, UK.

|January 3, 2016

Summary

Robert Rosen's (M,R) system, a biological network model, is shown to be computable. Using Unified Modelling Language (UML), this study demonstrates that the (M,R) system can be accurately represented and computed, refuting claims of non-computability.

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

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Area of Science:

Theoretical Biology
Computer Science
Systems Biology

Background:

Robert Rosen's (M,R) system is an abstract biological network architecture.
The computability of the (M,R) system on a Turing machine has been a long-standing debate.
Previous attempts to model the (M,R) system in software have been criticized for altering its properties.

Purpose of the Study:

To formally represent Robert Rosen's (M,R) system using the Unified Modelling Language (UML).
To determine if the (M,R) system is computable by demonstrating its accurate instantiation in UML.
To address the implications of the (M,R) system's computability for biological network modeling.

Main Methods:

Representing the (M,R) system as a UML communication diagram.
Utilizing UML's object-oriented structure to define system attributes, functions, and relations.
Leveraging the formal compatibility of UML with object-oriented programming languages.

Main Results:

The (M,R) system is demonstrated to be implicitly a UML communication diagram.
Instantiation of the (M,R) system in UML preserves its original properties without corruption.
The UML representation strongly implies the computability of the (M,R) system in object-oriented coding languages.

Conclusions:

Robert Rosen's (M,R) system is computable, contrary to previous claims of non-computability.
The use of UML provides a rigorous method for modeling biological networks.
This work has significant implications for the computational modeling of complex biological systems.