Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior

Turing machine universality of the game of life

This project proves universal computation in the Game of Life cellular automaton by using a Turing machine construction.Existing proofs of universality in the Game of Life rely on a counter machine. These machines require complex encoding and decoding of the input and output and the proof of universality for these machines by the Church Turing thesis is that they can perform the equivalent of a Turing machine. A proof based directly on a Turing machine is much more accessible.The computational power available today allows powerful algorithms such as HashLife to calculate the evolution of cellular automata patterns sufficiently fast that an efficient universal Turing machine can be demonstrated in a conveniently short period of time. Such a universal Turing machine is presented here. It is a direct simulation of a Turing machine and the input and output are easily interpreted.In order to achieve full universal behaviour an infinite storage media is required. The storage media used to represent the Turing machine tape is a pair of stacks. One stack representing the Turing tape to the left of the read/write head and one for the Turing tape to the right. Collision based construction techniques have been used to add stack cells to the ends of the stacks continuously.The continuous construction of the stacks is equivalent to the formatting of blank media. This project demonstrates that large areas of a cellular automata can be formatted in real time to perform complex functions

Computing, Modelling, and Scientific Practice: Foundational Analyses and Limitations

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic computation and to offer foundations for scientific computing. The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal