Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Academic calendar
The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period | From | To |
---|---|---|
I semestre | Oct 3, 2011 | Jan 31, 2012 |
II semestre | Mar 1, 2012 | Jun 15, 2012 |
Session | From | To |
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Sessione straordinaria | Feb 1, 2012 | Feb 29, 2012 |
Sessione estiva | Jun 18, 2012 | Jul 31, 2012 |
Sessione autunnale | Sep 3, 2012 | Sep 28, 2012 |
Session | From | To |
---|---|---|
Sessione autunnale | Oct 20, 2011 | Oct 20, 2011 |
Sessione straordinaria | Dec 14, 2011 | Dec 14, 2011 |
Sessione invernale | Mar 22, 2012 | Mar 22, 2012 |
Sessione estiva | Jul 17, 2012 | Jul 17, 2012 |
Period | From | To |
---|---|---|
Festa di Ognissanti | Nov 1, 2011 | Nov 1, 2011 |
Festa dell'Immacolata Concezione | Dec 8, 2011 | Dec 8, 2011 |
Vacanze Natalizie | Dec 22, 2011 | Jan 6, 2012 |
Vacanze Pasquali | Apr 5, 2012 | Apr 10, 2012 |
Festa della Liberazione | Apr 25, 2012 | Apr 25, 2012 |
Festa del Lavoro | May 1, 2012 | May 1, 2012 |
Festa del Patrono di Verona S. Zeno | May 21, 2012 | May 21, 2012 |
Festa della Repubblica | Jun 2, 2012 | Jun 2, 2012 |
Vacanze estive | Aug 8, 2012 | Aug 15, 2012 |
Exam calendar
Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.
Academic staff
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2012/2013
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Algorithms - COMPLESSITÀ (2011/2012)
Teaching code
4S02709
Teacher
Credits
6
Language
Italian
Scientific Disciplinary Sector (SSD)
ING-INF/05 - INFORMATION PROCESSING SYSTEMS
Period
I semestre dal Oct 3, 2011 al Jan 31, 2012.
Learning outcomes
The goal of this module is to introduce students to computational complexity theory in general, to the NP-completeness theory in detail and to computational analysis of problems with respect to their approximability.
Program
Introduction.
Computational model concept, computational resource, efficient algorithm and tractable problem.
Computational models
Turing Machine (MdT): definition, behavior, configuration, production and computation concepts. MdT examples. MdT and languages: the difference between accepting and deciding a language. MdT extension: multi-tape MdT (k-MdT)
Time Complexity
Time computational resource. Computational class TIME(). Theorem about polynomial relation between k-MdT computations and MdT ones (sketch of proof).
Introduction to Random Access Machine (RAM) computational model: configuration, program and computation concepts. RAM: computation time by uniform cost criterion and by logarithmic cost one. Example of a RAM program that determines the product of two integers.
Theorem about simulation cost of a MdT by a RAM.
Theorem about simulation cost of a RAM program by a MdT.
Sequential Computation Thesis and its consequences.
Linear Speed-up Theorem and its consequences.
P Computational Class.
Problems in P: PATH, MAX FLOW, PERFECT MATCHING.
Extension of MdT: non-deterministic MdT (NMdT).
Time resource for k-NMdT. NTIME() computational class.
Example of non-deterministic algorithm computable by a NMdT: algorithm for Satisfiability (SAT).
Relation between MdT and NMdT.
NP Computational Class.
Relation between P and NP. Example of a problem into NP: Travel-salesman Problem (TSP).
An alternative characterization of NP: polynomial verifiers.
EXP Computation Class.
Space Complexity.
Space complexity concept. MdT with I/O. Computational Classes: SPACE() and NSPACE().
Compression Theorem.
Computational Classes: L and NL.
Example of problems: PALINDROME ∈ L and PATH ∈ NL.
Theorems about relations between space and time for a MdT with I/O.
Relations betwee complexity classes.
Proper function concept and example of proper functions.
Borodin Gap Theorem.
Reachability method. Theorem about space-time classes: NTIME(f(n)) ⊆ SPACE(f(n)), NSPACE(f(n)) ⊆ TIME(k(log n+f(n))).
Universal MdT.
The Hf set.
Lemma 1 and 2 for time hierarchy theorem.
Time Hierarchy Theorem: strict and no-strict versions.
P ⊂ EXP Corollary.
Space Hierarchy Theorem. L ⊂ PSPACE Corollary.
Savitch Theorem. SPACE(f(n))=SPACE(f(n)^2) corollary. PSPACE=NPSPACE Corollary.
Reductions and completeness.
Reduction concept and logarithmic space reduction. HAMILTON PATH ≤log SAT, PATH ≤log CIRCUIT VALUE, CIRCUIT SAT ≤log SAT.
Language completeness concept.
Closure concept with respect to reduction.
Class reduction of L, NL, P, NP, PSPACE and EXP.
Computation Table concept.
Theorem about P-completeness of CIRCUIT VALUE problem.
Cook Theorem: an alternative proof.
Gadget concept and completeness proof of: INDEPENDENT SET, CLIQUE, VERTEX COVER and others.
Randomized computational complexity.
Probabilistic Turing machines.
Computational classes: BPP, RP, coRP e ZPP. Relationship between BPP and other classes.
Randomized reductions.
Approximation algorithms and approximate complexity classes.
Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|
Christos H. Papadimitriou | Computational complexity | Addison Wesley | 1994 | 0201530821 | |
S. Arora, B. Barak | Computational Complexity. A modern approach (Edizione 1) | Cambridge University Press | 2009 | 9780521424264 | principale |
Examination Methods
The examination consists of a written test. The grade in this module is worth 1/3 of the grade in the Algorithms examination.
Type D and Type F activities
Documents and news
- SE1 - Curriculum Sistemi Embedded: presentazione (Embedded systems: curriculum presentation) (pdf, en, 873 KB, 25/01/12)
- SE2 - Curriculum Sistemi Embedded: formazione (Embedded Systems: programme) (pdf, it, 212 KB, 25/01/12)
- SE3 - Curriculum Sistemi Embedded: ricerca avanzata (Embedded Systems: research) (pdf, it, 641 KB, 25/01/12)
- SE4 - Curriculum Sistemi Embedded: esempi reali (Embedded Systems: practical cases) (pdf, it, 1046 KB, 25/01/12)
- SE5 - Curriculum Sistemi Embedded: relazioni aziendali (Embedded Systems: cooperations with companies) (pdf, it, 1941 KB, 25/01/12)
- SWE&S1 - Curriculum Ingegneria del Software e sicurezza: presentazione (Ingegneria del Software e sicurezza: curriculum presentation) (pdf, it, 11261 KB, 11/04/12)
- SWE&S2 - Curriculum Ingegneria del Software e sicurezza: ricerca avanzata (Ingegneria del Software e sicurezza: research)) (pdf, it, 4044 KB, 11/04/12)
- SWE&S3 - Curriculum Ingegneria del Software e sicurezza: relazioni aziendali (Ingegneria del Software e sicurezza: collaborations with companies) (pdf, it, 2764 KB, 11/04/12)
- VC1 - Curriculum Visual Computing: didattica (pdf, it, 1979 KB, 08/03/12)
- VC2 - Curriculum Visual Computing: ricerca (pdf, it, 3299 KB, 08/03/12)
- VC3 - Curriculum Visual Computing: aziende (pdf, it, 1907 KB, 08/03/12)
Modules not yet included
Career prospects
Module/Programme news
News for students
There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and also via the Univr app.
Graduation
Deadlines and administrative fulfilments
For deadlines, administrative fulfilments and notices on graduation sessions, please refer to the Graduation Sessions - Science and Engineering service.
Need to activate a thesis internship
For thesis-related internships, it is not always necessary to activate an internship through the Internship Office. For further information, please consult the dedicated document, which can be found in the 'Documents' section of the Internships and work orientation - Science e Engineering service.
Final examination regulations
List of thesis proposals
Attendance modes and venues
As stated in the Teaching Regulations, attendance at the course of study is not mandatory.
Part-time enrolment is permitted. Find out more on the Part-time enrolment possibilities page.
The course's teaching activities take place in the Science and Engineering area, which consists of the buildings of Ca‘ Vignal 1, Ca’ Vignal 2, Ca' Vignal 3 and Piramide, located in the Borgo Roma campus.
Lectures are held in the classrooms of Ca‘ Vignal 1, Ca’ Vignal 2 and Ca' Vignal 3, while practical exercises take place in the teaching laboratories dedicated to the various activities.