Cylindrical Algebraic Decomposition is a powerful technique for reasoning with polynomial problems over the real numbers. As such, it would be an obvious candidate for a “theory” in the sense of Satisfiability Modulo Theories (SMT). In practice, the two do not mesh so easily, as outlined in Ábrahám,E., Building Bridges between Symbolic Computation and Satisfiability Checking. Proc. ISSAC 2015 (ed. D. Robertz), ACM, New York, pp. 1-6. Professors Davenport and Ábrahám have recently launched a collaboration to bridge this gap, and have identified several specific research channels, which the student could work on. The student would build on past work of the supervisor in Cylindrical Algebraic Decomposition, e.g. in Bradford,R.J., Davenport,J.H., England,M., McCallum,S. & Wilson,D.J., Truth Table Invariant Cylindrical Algebraic Decomposition. To appear in J. Symbolic Computation. http://dx.doi.org/10.1016/j.jsc.2015.11.002. http://arxiv.org/abs/1401.0645.
We welcome all year round applications from self-funded candidates and candidates who can source their own funding.