Computability and Complexity

Code:

CC3004

Acronym:

CC3004

Level:

300

Keywords
Classification	Keyword
OFICIAL	Computer Science

Instance: 2021/2022 - 2S

Active?	Yes
Web Page:	http://https://moodle.up.pt/enrol/index.php?id=3670
Responsible unit:	Department of Computer Science
Course/CS Responsible:	Bachelor in Computer Science

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	77	study plan from 2021/22	3	-	6	56	162
L:F	0	Official Study Plan	2	-	6	56	162
			3
L:G	0	study plan from 2017/18	2	-	6	56	162
			3
L:IACD	0	study plan from 2021/22	3	-	6	56	162
L:M	3	Official Study Plan	2	-	6	56	162
			3
L:Q	0	study plan from 2016/17	3	-	6	56	162

Teaching language

Portuguese

Objectives

Study and comparison of different (Turing-complete) models of computation, their computational power and limitations. Study of the various complexity classes of problems.

After completing this course students are expected to

- know the classical models of computation;
- be able to prove the equivalence of several Turing-complete models;
- know the fundamental results and methods used in the study of computability and complexity;
- be able to classify concrete examples of problems and prove their (un)decidability within several classes of computability;
- be able to classify concrete problems about their time complessity, and understand the consequences of that classification.

Learning outcomes and competences

Students are exposed to different standard Turing-complete models of computation, such as register machines, Turing machines e recursive functions. Besides proving the equivalence of those models, they also are used to identify different undecidable problems. For this, different techniques, such as the diagonalization method and the reduction between languages are used. In order to gain experience identifying the computational complexity of concrete problems, students are introduced to the classes P and NP, the notion of NP-completeness and Cook’s theorem, revisiting again the reduction technique.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Knowledge of some models of computation such as Finite Automata, Regular Expressions and Context-free Grammars. Basic notions of Logic.

Program

Notion of (semi-)decidable language/problem. Revision of some models of computation (DFA, NFA, CFG and PDA) and their power of computation. Register machines. Turing machines. Recursion theory. Lambda Calculus. Church-Turing thesis. Chomsky hierarchy. Kleene's Recursion Theorem. The diagonalization method and the indecidability of the halting-problem. Reduction “many to one” between languages. Introduction to complexity theory: P and NP classes, NP-completeness, Cook’s theorem and other NP-complete problems. Class co_NP, etc. 
The PSPACE class. 

Mandatory literature

Introduction to Automata Theory, Languages and Computation, Hopcroft, Motwani and Ullmann.
Recursion theory, Phillips, in Handbook of logic in computer science (vol. 1), Oxford University Press.

Complementary Bibliography

Introduction to the Theory of Computation, Michael Sipser.
Models of Computation - An Introduction to Computability Theory, Maribel Fernández.
Oded Goldreich; P, NP, and NP-Completeness - The Basics of Computational Complexity, Cambridge University Press, 2010

Teaching methods and learning activities

Lectures: exposition of the elements in the syllabus.
Lab classes: resolution of exercises proposed each week.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

No specific requirements to attend exams.

Calculation formula of final grade

First test (50% of the final mark).
Second test (50% of the final mark).
If FT is the mark obtained in the first test and ST the mark obtained in second test, then the final mark is given by:
F = FT*(0.5) + ST*(0.5)  
FT,ST >= 6 and F >= 9.5
To get approval in the distributed evaluation, students must obtain a minimum of 6 points (in a total of 20) in each test and a minimum of 9.5 as final mark.
The students not obtaining approval, can take a resit exam, with a weight of 100% of the final mark. 

Additionally there could be lab projects proposed in each module, with the weight of these projects in the final mark to be determined by the teacher.