30516  THEORETICAL COMPUTER SCIENCE
Department of Computing Sciences
ALON ROSEN
Conoscenze pregresse consigliate
Mission e Programma sintetico
MISSION
PROGRAMMA SINTETICO
Unit 1 (Computability  introduction)
· Course overview
· Introduction
· Turing Machine (TM)
Unit 2 (Computability – more on TM)
· More on the definition of TM
· Decidable and Recognizable languages
· Variants of TM
· Simulation
Unit 3 (Computability – undecidability)
· The ChurchTuring Thesis
· Examples of decidable languages
· The Halting problem
Unit 4 (Computability – undecidability contd.)
· More nondecidable problems
· Reductions
Unit 5 (Computability – Rice’s theorem)
· Rice’s Theorem
· Post Correspondence Problem
· Wrap up computability
Unit 6 (Complexity  Introduction)
· Definition of time complexity
· Complexity of single vs Multiple Tape TM’s
· PTIME, PATH
Unit 7 (Complexity – The class NP)
· Nondeterministic TM
· Polytime verifiability
· The classes NP and coNP
Unit8 (Complexity – NP completeness)
· Polytime reducibility
· NP completeness
· Existence of NPcomplete problems
Unit 9 (Complexity – CookLevin)
· CookLevin Theorem
· More NPcomplete problems
· Decision vs. Search
Unit 10 (Complexity – The class PSPACE)
· Cook/Karp/Levin reductions
· Coping with NPhardness
· Space complexity
Unit 11 (Cryptography  Encryption)
· Perfect secrecy
· Computational secrecy
Unit 12 (Cryptography  Authentication)
· Message authentication
· Digital signatures
Risultati di Apprendimento Attesi (RAA)
CONOSCENZA E COMPRENSIONE
The most important skill that the students are expected to pick up during this course is the ability to recognize and interpret computational intractability in case it is encountered. The course aims to develop a solid conceptual understanding of notions related to computation:
· The concept of universal models of computation (such as Turing machines), that capture our intuitive notion of computation and allow us to reason about the capabilities of computers in a technologyindependent manner.
· The existence of intrinsic limits to computation. Computational problems that cannot be solved by any algorithm whatsoever (undecidability), and problems that are solvable but require unreasonable computational resources (computational complexity).
· The notion of nondeterminism and in particular the conceptual difference between finding a solution and verifying that a given solution is correct.
· The representation of computational problems, and the distinction/relationships between decision and search problems.
· The notion of a reduction between computational problems and its implications on the relative complexity of the problems.
CAPACITA' DI APPLICARE CONOSCENZA E COMPRENSIONE
 Recognize problems that are NPcomplete, and be able to devise simple NPcompleteness proofs
 Recognize problems that are undecidable, and be able to devise simple undecidability proofs
 Apply the idea of a reduction among computational problems
 Apply definitions of security in encryption and authentication
 Be able to spot potential problems in proposed cryptographic protocols
Modalità didattiche
 Lezioni frontali
 Lezioni online
 Testimonianze (in aula o a distanza)
DETTAGLI
Biweekly homework assignments (45 questions each) will give you feedback on how you are doing and will help you internalize the material studied.
Metodi di valutazione dell'apprendimento
Accertamento in itinere  Prove parziali  Prova generale  


x  

x 
STUDENTI FREQUENTANTI E NON FREQUENTANTI
Assessment will be the same for attending and nonattending students. The final exam is written (90% of the grade) and consists of openended questions, some of which will test the student's understanding of the concepts developed during the course and some of which will test the student's ability to apply such concepts to new contexts, for example to prove the NPcompleteness of a new problem, to prove the undecidability of a new problem, or to prove/assess the security of a new cryptographic construction. It will also test knowledge of complexity and computability classes and the relations between them, and the definition of languages and their interrelations.
Materiali didattici
STUDENTI FREQUENTANTI E NON FREQUENTANTI
There is no required textbook. Recommended textbooks will be communicated to the students at the start of classes. Lecture slides and notes will be provided for selected topics.