Course: 2020/2021

Advanced theory of computation

(15763)

Students are expected to have completed

Automata and Formal Language Theory
Discrete Mathematics

ObjectivesFurther information on this link

The aim of this course is that students acquire the following skills:
1.Transverse (Generic) competences
- Ability to analyze and synthesize.
PO: a,e,g
- Problem Solving
PO: a,e
- Critical Reasoning.
PO: b,g
- Teamwork
PO: b,e,g
- Written communication.
PO: g
- CB4 Students can communicate information, ideas, problems and solutions
to both specialist and non-specialist audiences.
2.Specific competences for Learning
a.- Cognitive (To Know).
PO: a
- To Understand the formal definition of computation.
- To understand the limits of computation
- To know the methods to calculate the computational complexity.
- To know what could be efficiently computed
- To Understand what reducing one problem to another is.
b.- Procedural
PO: a,b,e,g,h,i
- To fix what can be efficiently computed
- To fix if a problam can be efficiently computed
- To fix which algorithm is the most efficient
- To select the most efficent data structure and the most suitable
programming technique for designing an efficient algorithm
- To fix the simplest model of computation for a problem
- Ability to transform a formal statement into a informal statement
and vice versa
- CB5 Students have developed those learning skills needed
to undertake a further study with a high degree of autonomy.
- CECRI6 Students must learn about basic algorithmic procedures, and its application, for computing technologies to design solutions to problems, analyzing the appropriateness and complexity of the proposed algorithms.
- CECC1 Students must achieve the knowledge of the fundamental principles
and models of computers, and know how to apply them to interpret, select,
estimate, model, and create new concepts, theories, uses and developments
computer-related technology.
- CECC3 Students must achieve the ability to evaluate the computational complexity of a problem,
to know algorithmic strategies that can lead to its resolution and
to recommend, develop and implement them to ensure that
the best performance according to the requirements.
c.- Attitude
PO: a,b,e,g,h,i
- Ability to analize computational problems and its solutions.
- Concern on quality
- Interest for finding new alternatives

Description of contents: programme

1. Cost of Algorithms.
1.1 Computational Complexity.
1.2 Computational Cost: Structured Programming
1.3 Recursive Algorithms
1.4 Probabilistic Analysis
2. Introduction to Computability Theory
2.1 Problem: definition
2.2 Turing Machine: decidability
2.3 Class of Problems (Computability)
3. Introduction to Complexity Theory
3.1 Problem Reducction
3.2 Classes P, NP y NP-Complete.
3.3 Classes PSpace, NPSpace.
3.3 Classes NP-Hard,Exp,CoP, CoNP.
4. Other Models of Computation
4.1 Lambda-Calculus
4.2 RAM Model
4.2 Cellular Automata
4.3 Lindenmayer Systems
4.4 Randomized Algorithms

Learning activities and methodology

Theoretical lectures: 1.5 ECTS.
These classes constitute a guide for students to achieve cognitive skills, and acquire
the basic elements to develop procedural skills. A part of the ECTS corresponds to the
load of autonomous work carried out by the students.
PO: a,b,e,h,i
Practical Lectures and Labs: 1.5 ECTS
They contribute to the development of the generic competences and the application
of the attitude ones. These classes consist on developing and solving practical
cases (exercises, problems and practices) which are aimed at achieving the
procedural competences. An important part of the ECTS corresponds to the autonomous
work of the student.
PO: a,b,e,g,h,i
Realización de Actividades Académicas
Other academic activities
Present teacher: 1.0 ECTS.
Resolution of small questions and exercises.
Practical Work
PO: a,e,g,
Absent teacher: 1.5 ECTS.
Readings about the field as well as exercises, problems and practices related to the
theoretical lectures and practical classes.
PO: a,b,e,g,h,i
Exam: 0.5 ECTS.
Preparation and realization of the examination, in which the level achieved by the
student in relation to the established competences is assessed.
PO: a,b,e,g

Assessment System

- % end-of-term-examination 35
- % of continuous assessment (assigments, laboratory, practicals...) 65

Basic Bibliography

- John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman.. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley 3rd Edition.
- Michael Sipser.. Introduction to the Theory of Computation. 2nd ed.. Boston, MA: Course Technology, 2005. ISBN: 0534950973..
- S. Wolfram.. Cellular Automata and Complexity.. Addison-Wesley, (1996).

Additional Bibliography

- C. Papadimitriou. Computational Complexity.. Addison-Wesley, 1995.
- H. S. Wilf. Algorithms and Complexity.. Prentice-Hall, 1986.
- Jeffrey Shallit.. A Second Course in Formal Languages and Automata Theory.. Cambridge University Press..