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Department of Computer Science

Solving non-linear constraints over continuous functions

Primary supervisor

Additional information

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Other projects with the same supervisor


  • Competition Funded Project (Students Worldwide)

This research project is one of a number of projects at this institution. It is in competition for funding with one or more of these projects. Usually the project which receives the best applicant will be awarded the funding. Applications for this project are welcome from suitably qualified candidates worldwide. Funding may only be available to a limited set of nationalities and you should read the full department and project details for further information.

Project description

Solving non-linear constraints over continuous functions is a very challenging problem with many applications ranging from verification of embedded systems and smart contracts to formalization of the proof of the Kepler's conjecture.
The problem is in general undecidable for constraints beyond polynomials, e.g. in the presence of trigonometric functions such as sine, cosine etc. Nevertheless it is possible to solve such constraints using delta-decision procedures with arbitrary specified precision. In particular we recently developed a kSMT procedure which is delta-complete for all computable functions over the reals. kSMT is based on incremental linearisations and combines symbolic methods with methods from computable analysis. kSMT is a starting point for the project. The problem of solving non-linear constraints remains very challenging and there are a number research directions that this project can take.

Person specification

For information


Applicants will be required to evidence the following skills and qualifications.

  • This project requires mathematical engagement and ability substantially greater than for a typical Computer Science PhD. Give evidence for appropriate competence, as relevant to the project description.
  • You must be capable of performing at a very high level.
  • You must have a self-driven interest in uncovering and solving unknown problems and be able to work hard and creatively without constant supervision.


Applicants will be required to evidence the following skills and qualifications.

  • You will have good time management.
  • You will possess determination (which is often more important than qualifications) although you'll need a good amount of both.


Applicants will be required to address the following.

  • Comment on your transcript/predicted degree marks, outlining both strong and weak points.
  • Discuss your final year Undergraduate project work - and if appropriate your MSc project work.
  • How well does your previous study prepare you for undertaking Postgraduate Research?
  • Why do you believe you are suitable for doing Postgraduate Research?