Computational intelligence, novelty generation and undecidability


The research will involve theoretical work in computational intelligence as well as computer simulations with cellular automata and other dynamical systems. It will aim to answer fundamental questions on the nature of universal computation, manifested across several classes of complex computational systems.    The PhD will be supervised by Prof. Mikhail Prokopenko. The applicant will join the Complex Systems Research Group (CSRG) at The School of Civil Engineering – The University of Sydney. The CSRG group comprises ten academics, and has wide collaborations across the University, Australia, and internationally. It is a vibrant, world-leading group in the fields of guided self-organisation and critical phenomena forecasting.


Professor Mikhail Prokopenko

Research Location

Research Cluster on Complex Systems

Program Type



One feature of intelligent behaviour is complexity in creating innovations: a mechanism producing computational novelty needs to exceed some threshold of complexity. Furthermore, in order to be truly impressive in generating endogenous innovation, it needs to be capable of universal computation. In other words, computational novelty may be fundamentally related to undecidability. Serious advances have been made in identifying deeper interconnections between dynamical systems, Turing Machines, and formal logic systems: in particular, the complex, class IV, cellular automata were related to formal systems with undecidable statements (Gödel’s incompleteness theorem) and the Halting Problem. Nevertheless, the question whether universal computation is the ultimate innovation-generator is still unresolved, offering a challenging question: how computational intelligence, including mechanisms producing novelty, is related to undecidability?

Additional Information

Applicants need to satisfy the eligibility criteria for PhD enrolment at The University of Sydney.  Backgrounds in applied mathematics, physics, computer science, and specifically in information theory, complex networks and statistical mechanics will be beneficial.   The successful applicant will demonstrate a strong commitment to academic research in the proposed field. He/she will have excellent written and oral communication skills, as well as demonstrated ability to program in MATLAB, Java, or C++, and will be willing to create and develop original approaches to tackle open questions.   Applications should be sent by email to Prof. Mikhail Prokopenko:   They should include a Resume and a Cover Letter. In their Cover Letter, applicants are invited to include a short (about 250 words) research statement explaining how they understand the issues related to the topic of research.

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complex systems, computational intelligence, novelty, undecidability, dynamical systems, Turing Machines, logic systems, class IV complexity, cellular automata, Gödel’s theorem, Halting Problem.

Opportunity ID

The opportunity ID for this research opportunity is: 1948

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