Faculty of Computer Science

Master of Science in Computer Science

European Master in Computational Logic

Theory of Computing

**8/10/2016**: The results of the final Theory of Computing exam of 26/9/2016 are available.

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**Course presentation form**

- for the Principles of Computation Course (Theory of Computing module) within the European Master in Computational Logic
- for the Theory of Computing Course within the Data and Knowledge Engineering stream of the MSc in Computer Science

**Objectives.** The objective of the Theory of Computing course is to
introduce and study abstract, mathematical models of computation (such as
Turing machines, formal grammars, recursive functions), and to use the abstract
computation models to study the ability to solve computational problems, by
identifying both the intrinsic limitations of computing devices, and the
practical limitations due to limited availability of resources (time and
space). A second objective is to show how to reason and prove properties about
computations in a precise, formal, abstract way.

**Prerequisites.** There are no prerequisites in terms of courses to
attend. Students should be familiar with notions of mathematics and set theory,
and with basic proof techniques, as taught in the mathematics courses of a
bachelor in computer science.

**Teaching material**

[M1]Introduction to Automata Theory, Languages, and Computation (3rd edition).J.E. Hopcroft, R. Motwani, J.D. Ullman. Addison Wesley, 2007.

[M2]Lecture Notes for Theory of Computing. Diego Calvanese. 2013. Available as scanned pages in pdf.

[M3]Languages and Machines (3rd edition).Thomas A. Sudkamp. Addison Wesley, 2005. Only Chapter 13.

[M4]The Convenience of Tilings.Peter van Emde Boas. InComplexity, Logic, and Recursion Theory, volume 187 of Lecture Notes in Pure and Applied Mathematics, pages 331-363, 1997.

[M5]Exercises on Theory of Computing. Available as scanned pages in pdf.

*Elements of the Theory of Computation (2nd edition).*H.R. Lewis, C.H. Papadimitriou. Prentice Hall. 1998.*Introduction to the Theory of Computation.*M. Sipser. PWS Publishing Company. 1997.*Computational Complexity.*C.H. Papadimitriou. Addison Wesley. 1995.*The Universal Computer: The Road from Leibniz to Turing.*M. Davis. A K Peters/CRC Press. 2011. Full text accessible to all unibz users at Safari Books Online.*The Church-Turing Thesis.*Copeland, B. Jack. The Stanford Encyclopedia of Philosophy. Fall 2008 Edition.*The Status of the P versus NP Problem.*Lance Fortnow. Communications of the ACM. Vol. 52 No. 9, Pages 78-86, September 2009. pdf*On P, NP, and Computational Complexity.*Moshe Y. Vardi. Communications of the ACM. Vol. 53 No. 11, Page 5, November 2010. pdf*Solving the Unsolvable.*Moshe Y. Vardi. Communications of the ACM. Vol. 54 No. 7, Page 5, July 2011. pdf*An Interview with Stephen A. Cook.*Philip L. Frana. Communications of the ACM. Vol. 55 No. 1, Pages 41-46, January 2012. pdf

- Andrew Hodges Alan Turing Home Page.
- For info on simple Turing Machines with complex behaviour, consult the web pages on Busy Beavers by the following people: Heiner Marxen, Michael Somos, and Pascal Michel.
- A Universal Turing Machine with just 2 states and 3 symbols. Read more at http://www.wolframprize.org/.
- Lego Turing Machines: a version built in 2009 and one built in 2012.
- A Turing Machine in the classic style.
- The original 1971 paper by Steve Cook showing NP-completeness of SAT and 3SAT (put into TeX format by Tim Rohlfs).
- The P-versus-NP page, collecting links around papers that try to settle the "P versus NP" question (in either way).
- Video of a talk on What's all this about P not equaling NP?.

**Office hours**- Teaching assistant: there is no teaching assistant for this course. The exercise hours are taught by the lecturer.
- Schedule: The course is taught in the 1st semester: from October 19,
2015 to January 21, 2016.
**Lectures**(Lecture Room E411, Sernesi E):- Tuesday 8:30-10:30
- Thursday 8:30-10:30

**Exercises**(Lecture Room F0.03, Sernesi F): Monday 14:00-16:00

**Additional teaching material**- Lecture notes (made available during the course)
- Esercises solved in class (made available during the course)
- Course program
- Exam esercises from the last years (in
part with solutions).

Note that Part 1 of the exams up to June 2007 deals with topics that are not covered anymore in this course.

**Exam dates**- Winter session: Tuesday, 16/2/2016, 14:00-18:00
- Summer session: Monday, 20/6/2016, 14:00-18:00
- Autumn session: Tuesday, 20/9/2016, 8:30-12:30

**Rules for the exam**- At the exam, the student has to solve exercises and/or answer questions on the course topics in written or oral form.
- The exam is divided into two parts:
- Part 1 covers topics 1-4 of the course program;
- Part 2 covers topics 5-7 of the course program.

- The two parts of the exam can be taken together in the same exam session, or separately in different exam sessions.
- Even when the two parts of the exam are taken together, they can be passed separately.
- For a part to be passed, a minimum of 18/30 points is required (half marks are rounded upwards).
- A passed part of the exam (or the passed midterm) is valid until the end of the academic year (i.e., exam session of September). If the other part is not passed by then, the passed part is lost and cannot be carried over to the next academic year.
- For the written exam, each part has a duration of 90 minutes, with 15
minutes break between the two parts. During the exam, it
will
**not**be possible to consult any kind of material, to use laptops, smartphones, or tablets, or to leave the exam room before the break/end of the exam.

teaching page of Diego Calvanese