Computer Science

ECM3422 - Computability and Complexity (2019)

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MODULE TITLEComputability and Complexity CREDIT VALUE15
MODULE CODEECM3422 MODULE CONVENERDr Enrico Malizia (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
Number of Students Taking Module (anticipated) 13
DESCRIPTION - summary of the module content

It is popularly supposed that there is no limit to the power of computers to perform any task, so long as it is sufficiently well defined, and to do so quickly and efficiently. In fact this is not so, and it can be proved mathematically that there are well-defined computational tasks which cannot, in principle, be performed by computers as we know them; and other tasks which, while they can be performed, cannot be completed in a feasible amount of time. This module will introduce you to the Turing Machine model of computation which underpins the fundamental theories of computability (concerned with what can be computed at all) and complexity (concerned with how efficiently things which can be computed can be computed). These theories will be introduced in a precise and formal way, and the main results and theorems will be stated and proven.

Pre-requisites: ECM1414, ECM2418

AIMS - intentions of the module

To introduce the Mathematical basis and practical implications of the classical theory of computability and complexity and to consider the extent to which this is still relevant to modern developments in computing.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 explain what is meant by a general model of computation and work with some specific examples of such models;

2 describe the mathematical basis of the theory of computability and complexity;

3 appreciate the relationship between the theory of computation and complexity and practical computing.

Discipline Specific Skills and Knowledge:

4 appreciate the power of abstraction to support a general understanding of some subject matter;

5 appreciate the role of theoretical understanding in underpinning disciplined and responsible practice.

Personal and Key Transferable / Employment Skills and Knowledge:

6 approach problems analytically at an appropriate level of abstraction.

SYLLABUS PLAN - summary of the structure and academic content of the module

- Turing machines, and the universal Turing machine;

- recursive and recursively enumerable languages;

- undecidability of the halting problem for Turing machines; variants of the halting problem; other undecidable languages;

- the Church-Turing thesis;

- properties of languages and Rice’s theorem;

- time complexity;

- Complexity classes P and NP, and the P vs NP problem;

- NP-complete problems;

- Cook’s theorem;

- Space complexity classes and their relationships with the other complexity classes seen in the module.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 46.00 Guided Independent Study 104.00 Placement / Study Abroad
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching 22 Lectures
Scheduled learning and teaching 24 Tutorials
Guided Independent Study 24 Coursework
Guided Independent Study 80 Independent study

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
       
       
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 20 Written Exams 80 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 2 hours - Summer Exam Period 1, 2, 3, 4, 5, 6 None
Coursework assignment 20 20 hours 1, 2, 4, 5, 6 Written
         
         
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def
       
       

 

RE-ASSESSMENT NOTES

Referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.


 

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE-https://vle.exeter.ac.uk

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Hopcroft, J. E.; Motwani, R. and Ullman, J. D. Introduction to Automata Theory, Languages, and Computation 3 Addison-Wesley 2007 978-0321476173 [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES ECM1414, ECM2418
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 3 (NQF level 6) AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 06 July 2017 LAST REVISION DATE Tuesday 16 July 2019
KEY WORDS SEARCH Turing machine; computability; computational complexity.