Monash University Handbook 2011 Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Synopsis

This unit gives an introduction to formal languages using logic programming and looks at what a computer can compute and what problems are intractable. Examples include why it is so difficult to design timetables, get computers to play Go, or crack a code. Topics include computable functions, finite state automata, regular expressions, grammars, Turing computability, polynomial-time reductions, and NP-completeness.

Objectives

At the completion of this unit, students will have -

A knowledge and understanding of:

• propositional and predicate logic;
• how to describe languages using Regular Expressions, Finite Automata, Nondeterministic Finite Automata, Context Free Grammars, Pushdown Automata, and Turing Machines;
• the relationship between Regular Languages, Context Free Languages, Recursive Languages, and Recursive-Enumerable (or Computable) Languages;
• how to use Turing Machines to represent computable functions;
• how a Universal Turing machine can simulate any Turing Machine on any input;
• basic computational complexity theory, including verifiers, polynomial-time reductions and NP-completeness.

• appreciate the limitations of Regular Languages, Context Free Languages, Recursive Languages, and Computable Languages;
• comprehend the limitations of computers in terms of the problems they can solve;
• appreciate that there are many solvable problems which cannot be solved in polynomial time.

• use propositional logic to represent and analysis problems in the theory of computation;
• construct Finite Automata, Nondeterministic Automata, and Turing Machines to describe languages;
• convert Regular Expressions into a Finite Automata;
• convert Finite Automata into Regular Expressions;
• find a Regular Grammar for a Regular Language;
• find a parse tree, leftmost derivation and rightmost derivation for a word in a Context Free Language;
• know how to show a Context Free Grammar is ambiguous;
• show a problem is NP-complete.

Assessment

Examination (3 hours): 70%; In-semester assessment: 30%

Chief examiner(s)

Dr David Dowe

Contact hours

2 hrs lectures/wk, 3 hrs laboratory/fortnight, 2 hrs tutorial/fortnight

Prerequisites

FIT1029 and 6 points of level 1 (or above) mathematics

For students in courses 2380, 2770, 0050, 2672, 3517, 3282 and 0085 who commenced prior to 2011: FIT1008/FIT1015 and 6 points of approved mathematics

Co-requisites

6 points of level 1 (or above) mathematics

Prohibitions

CSE2303

Additional information on this unit is available from the faculty at:

http://www.infotech.monash.edu.au/units/fit2014