Limits of Computation (G5029)

15 credits, Level 6

Spring teaching

This module addresses fundamental questions of computing like 'what is computable?' and 'what is feasibly computable?' The problems are discussed using a particular choice of 'effective procedure' that you can program in easily. This allows one to view all problems and solutions in this course as programming-related.

The importance of understanding the reasons for the existence of non-computable and intractable problems is discussed, techniques for recognising them are presented and real-world examples of non-computable or intractable problems are given.

The following topics are covered to answer the fundamental questions above:

  • Interpreters, compilers, specializers, in particular self-interpreters.
  • Definition of an unsolvable problem (Halting problem) and generalisation (Rice's Theorem).
  • Examples of unsolvable problems.
  • What does feasible mean? How can one measure resource-usage of (time, space, non-determinism) of programs?
  • Definition of unfeasible problems. Examples of such problems.
  • Definition of asymptotic complexity classes and their relationships.

Teaching

69%: Lecture
31%: Seminar

Assessment

50%: Coursework (Problem Set, Test)
50%: Examination (Unseen examination)

Contact hours and workload

This module is 150 hours of work. This breaks down into 32 hours of contact time and 118 hours of independent study.

This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.