BSc Computer Science and Mathematics / Course details

This is a unique course developed at the University of Manchester. It explains how implementations of logic can be used to solve a number a number of problems, such as solving hardest Sudoku puzzles in no time, analysing two-player games, or finding serious errors in computer systems

Students who are not from the Department of Computer Science must have permission from both Computer Science and their home School to enrol. Students must have taken either COMP11120 or MATH11121 and MATH11022.

Pre-requisites

To enrol students are required to have taken COMP11120 or one of the following: MATH10111, MATH10131 , MATH10212, MATH10232.

This course intends to build an understanding of fundamentals of (mathematical) logic as well as some of the applications of logic in modern computer science, including hardware verification, finite domain constraint satisfaction and verification of concurrent systems.

• Have a knowledge about basic reasoning (or satisfiability-checking) algorithms for propositional logic.

• Have a knowledge of quantified boolean formulas and basic understanding of bound variables and quantifiers.

• To understand BDDS (binary decision diagrams) as a data structure for compact representation of propositional formulas.

• Have a knowledge about applications of propositional logic (such as finite domain constraint satisfaction and planning) and be able to apply it for solving hard combinatorial problems.

• Have a knowledge of simple temporal logics.

• Be able to formally specify finite-state concurrent systems as transition systems.

• Be able to specify properties of simple transition systems in temporal logics.

• Propositional logic
• Conjunctive normal form (CNF)
• DPLL satisfiability algorithm
• Randomized satisfiability algorithms
• Compact representations of Boolean functions using BDTs/BDDs/OBDDs
• Quantified Boolean Logic (QBF) Splitting and DPLL algorithms for QBF 
• Propositional logic of finite domains
• State-changing systems 
• Linear temporal logic (LTL)
• Model checking

Lectures

22 in total, 2 per week, including some feedback sessions on exercises

My Website of this course will contain a lot of material, including solutions to exercises

COMP21111 reading list can be found on the Department of Computer Science website for current students.

Course unit materials

Links to course unit teaching materials can be found on the School of Computer Science website for current students.