Mathematical Foundations of Computer Science
 Lecturers:
 Professor Cristian S. Calude,
room 303S571, Science Building, course coordinator.
 Professor Bakhadyr Khoussainov,
room 303581, Science Building.

Tutor:
To be announced. Office hours:
By appointment. Any problem
related to marking should be addressed to the tutor.

Class representative:
To be announced.
Course Facebook group.
 Taught: First semester 2015, three hours of lectures and a tutorial a week (see 2016 Academic Dates).

Timetable: Lectures: Monday 1314, Tuesday 1314, Thursday 1415. Tutorial: Thursday 1112, starting the second
week. Check updates at UoA Timetables 2016.
 Short Description:
The aim of this paper is to present mathematical models for computers and
computation, and derive results about what can and cannot be computed. It
deals with idealised computers (automata) which operate on idealised input
and output (formal languages). For example, we prove that it is impossible
to write a computer program that takes as input any computer program and
tells us whether or not that program will end up in an endless loop (the
halting problem).
Quantum computing will also be briefly described and the ChurchTuring Thesis will be critically discussed. In addition we will discuss some problems in algorithmic complexity.
We assume you are comfortable with formal mathematical proofs and can write them
properly.
 Content:
 Automata and regular languages
 Contextfree languages
 Computability and decidability
 Algorithmic complexity
 ChurchTuring Thesis
 Expected learning outcomes: On completion, students will be able to
 explain the theoretical limits on computational solutions of undecidable and inherently complex problems
 describe concrete examples of computationally undecidable or inherently infeasible problems from different fields
 understand formal definitions of machine models, classical and quantum
 prove the undecidability or complexity of a variety of problems
 understand the issue of whether there are limits of computability
 Textbook:
M. Sipser.
Introduction to the Theory of
Computation,
PWS Publishing Company, Boston, 2013, third edition.
 Software: Register machine simulation
 Tutorials: Materials will be available on the Tutorial page.
 Assessment: Two assignments worth 20% in total, Test: 30%, Exam: 50%.
 Assignments (the assignment dropbox will be outside the room 303S571): Assignment 1:
due Wednesday, 23 March, before 4.00pm,
worth 10%;
assignment 2:
due Thursday 2 June, before 4.00pm,
worth 10%.

Test:
To be announced.
 Handouts:
 Policy on
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