Home page of the course
Theory of Computing

News

• 9/2/2014: The results of the final Theory of Computing exam of 28/1/2014 are available.
  At the office hour of Friday 14/2/2014 at 15:00 in my office in piazza Domenicani 3 (2nd floor), students can get an insight in their exam and discuss the corrections.
  

Course presentation form

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. Will be made available on the course web page 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. In Complexity, Logic, and Recursion Theory, volume 187 of Lecture Notes in Pure and Applied Mathematics, pages 331-363, 1997.

• 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 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 2nd 2013 to January 15th 2014, in Seminar Room E411, fourth floor, Sernesi E (typically)
  • Lectures:
    • Monday 10:30-12:30
    • Wednesday 10:30-12:30
  • Exercises: Monday 14:00-16:00

  An updated schedule of the lectures and exercises is available (changes with respect to the regular schedule are marked in yellow).
  See also the on-line timetable page for changes.
  

• 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, 28/1/2014, 8:30-12:30
  • Summer session: Friday, 4/7/2014, 8:30-12:30
  • Autumn session: Thursday, 18/9/2014, 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 5-8 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.