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MAU11602 Computation theory and logic

Module Code MAU11602
Module Title Computation theory and logic
Semester taught Semester 2
ECTS Credits 5
Module Lecturer Prof. John Stalker
Module Prerequisites MAU11201 Single-variable calculus

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 2.
  • Continuous assessment contributes 30% towards the overall mark.
  • The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows: 
    1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session; 
    2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam; 
    3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session..

Contact Hours

11 weeks of teaching with 3 lectures per week.

Tutorials will be held during the lecture time slots and a revision will take place at the end of the semester.

Learning Outcomes

On successful completion of this module, students will be able to

  • check the validity of statements in zeroeth and first order logic.
  • convert informal statements to formal statements in elementary arithmetic.
  • give semiformal proofs in zeroeth and first order logic, elementary arithmetic and set theory.
  • verify the correctness of formal proofs in zeroeth and first order logic, elementary arithmetic and set theory.
  • convert informal descriptions of languages into phrase structure grammars.
  • convert among regular grammars, deterministic and non-deterministic finite state automata and regular expressions.
  • apply the Myhill-Nerode theorem to check whether languages are regular.
  • apply the pumping lemmas to show languages are not regular or context free.
  • apply the various closure properties of regular and context free languages.

Module Content

  • Formal languages and phrase structure grammars.
  • Zeroeth order logic, also known as the propositional calculus.
  • First order logic.
  • Elementary arithmetic.
  • Gödel's and Tarski's theorems.
  • Axiomatic set theory, and finite, countable and uncountable sets.
  • Finite state automata, regular expressions and regular languages.
  • Pushdown automata and context-free languages.
  • Turing machines and recursively enumerable languages.