Undergraduate Course: Computational Complexity (INFR11102)
Course Outline
| School | School of Informatics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This module studies the problem of classifying computational problems according to their intrinsic difficulty or 'complexity'. We begin by defining a standard computational model, the Turing machine, which is useful for abstracting out complexity aspects of computational problems. We define various complexity resources, such as time, space, non-determinism , randomness and non-uniformity, and learn how to classify computational problems according to their resource requirements. Among other topics, we discuss the central problem of theoretical computer science, the P vs NP problem, and explain its importance using the notions of reductions and completeness. |
| Course description |
* The computational model: Turing machines
* NP and NP completeness
* Space complexity
* Diagonalization
* The polynomial hierarchy and alternations
* Circuits
* Randomized computation
* Hardness of approximation and the PCP theorem
Relevant QAA Computing Curriculum Sections: Concurrency and Parallelism, Data Structures and Algorithms, Theoretical Computing
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | This course is open to all Informatics students including those on joint degrees. For external students where this course is not listed in your DPT, please seek special permission from the course organiser.
Participants should have some facility with mathematical modes of reasoning. |
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Students will be able to formulate computational models with resource constraints, and be able to describe relationships between these models.
- Students will be able to analyse computational problems from a complexity perspective, and so locate them within the complexity landscape.
- Students will be able to apply mathematical skills and knowledge from earlier years (eg., from logic and discrete mathematics) to concrete problems in computational complexity.
- Students will gain an appreciation of the broader importance of fundamental problems in computer science, such as the P vs NP problem.
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Reading List
1. Sanjeev Arora and Boaz Barak, 'Computational Complexity: A Modern Approach', Cambridge University
Press, 2009. Required
2. Michael Sipser, 'Introduction to the Theory of Computation', PWS, 1997. Background reading
3. Christos Papadimitriou, 'Computational Complexity', Addison-Wesley, 1994. Supplementary reading
4. Uwe Schoening, 'Gems of Theoretical Computer Science', Springer Verlag, 1998. Supplementary
reading |
Contacts
| Course organiser | Dr Ilias Diakonikolas
Tel: (0131 6)50 5129
Email: |
Course secretary | Mr Gregor Hall
Tel: (0131 6)50 5194
Email: |
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