## Department of Computer Science, Unit Catalogue 2008/09 |

## CM20217 Foundations of computation 1 |

Credits: 6 |

Level: Intermediate |

Semester: 1 |

Assessment: EX75CW25 |

Requisites: |

Before taking this unit you must take CM10192 and (take CM10196 or take MA10001) |

Aims: To introduce formal models of computation. To give students an appreciation of the complexity of different algorithms and problems and the limits of computation. To provide students with a basic understanding of formal computational models such as finite state automata and Turing machines.
Learning Outcomes : On completion of this unit, students will be able to: 1. demonstrate an understanding of the fundamental models of computation. 2. explain the notion of complexity class, and establish what classes a range of well-known problems belong to. 3. demonstrate that some computational problems are undecidable. Skills: Use of IT (A), Application of Number (T/F, A), Problem Solving (T/F, A). Content: * Models of computation: for example, basic notions of finite state automata, Turing Machines, register machines. * Decidability. The undecidability of the Halting Problem. Reduction of other problems to the halting problem. * Complexity. Big-O notation and complexity of algorithms. The notion of complexity class as a measure of the difficulty of a problem. Reduction between problems. Hardness and completeness of a problem with respect to a complexity class. The hierarchy of complexity classes. The question of whether P=NP and its importance for computer science. |