T-79.148 Introduction to Theoretical Computer Science (2 cr)

Spring 2003

This introductory course on the theory of computation covers the basic aspects of finite automata and regular languages, context-free grammars and pushdown automata, Turing machines and computability theory.

The spring installation of the course is primarily oriented towards T students. However also students from other degree programmes (e.g. S) are welcome to participate at their own risk, i.e. considering that the selection of topics and the expected background may at times be somewhat T-specific.

[Current] [General] [Lectures] [Tutorials] [Material] [Feedback]

Previous years: [Autumn 2002] [Spring 2002] [Spring 2001] [Spring 2000] [Spring 1999] [Spring 1998]

Current

• Feedback summary available.
• The course exam is on Wednesday 7 May, 9--12 a.m. Remember to register for the exam via TOPI, and note that all your Regis assignments must be completed by the exam date --- otherwise your exam paper will not be graded (really!). Please fill in and return also the computerised course feedback form. (English form here.) If you submit the form by 11 May, you earn an extra exam point that counts towards increasing your grade in case you pass the course. The feedback is processed anonymously, i.e. the computerised feedback system removes the student id's from the forms and provides them as a separate list only for credit assignment purposes.
• A link to the Clay Mathematics Institute Millennium Prize Problems discussed at the lecture on 20 March. (Note specifically the P vs. NP problem.)
• Links to the cellular automata applets presented at the lecture on Thu 6 Feb: general CA (dead?), 1D cellular automata, Conway's Game of Life, self-replicating CA. (These are just for fun & interest, not formally part of the course.)

General Information

• The course consists of:
  • lectures (2 h per week, in Finnish)
  • tutorials (1 h per week, one group in English)
  • an examination (Wed 7 May, 9-12 ABC)

• Registration by TOPI. You must register both for the lectures and for a tutorial group. (Your registration is needed for bookkeeping purposes, even if you were not intending to attend.) One of the tutorial groups (indicated below) will be given in English and the rest in Finnish. Registration for the tutorials opens Monday 13 January at 9:00 and closes Friday 31 January at 18:00.

• In order to pass the course you have to:
  1. complete three compulsory sets of home assignments, and
  2. get a passing grade on the exam, as augmented by credit earned from the tutorials.
  The compulsory assignments are individually computer-generated for each student, and are submitted over the network. Completing these assignments is a mandatory prerequisite for participating in the exam. For more details, see the computerised assignments info page.

• Grading: Exam max 60 points, tutorials max 6 points. Min passing grade approx. 30 points (tolerance 4 p), highest grade (5) approx. 54 points. In the case of "close call" failures (at most 2 points below passing) despite serious study effort (at least 4 tutorial bonus points), there is a possibility of getting a passing grade by solving additional tutorial problems. To discuss this option, please contact the lecturer after the exam has been graded.

• Newsgroup: opinnot.tik.tkt

Lectures

Lecture schedule (tentative; slides partly from 2002):

Week	Date	Topic	Sipser	Lewis-Papadimitriou	Lecture slides (in Finnish)
3.	16 Jan	Administration. Review of basic math (functions, relations, induction).	Pp. 1-13, 23-25	1.1-1.3, 1.5	Kalvot (pdf)
4.	23 Jan	Alphabets, strings and languages. Countable and uncountable sets.	Pp. 13-14, 16, 161-164	1.4, 1.7	Kalvot (pdf)
5.	30 Jan	Finite automata.	Pp. 31-43	2.1	Kalvot (pdf)
6.	6 Feb	Automata minimisation. Nondetermistic finite automata.	Pp. 47-58, 275	2.2, 2.5	Kalvot (pdf)
7.	13 Feb	Regular expressions and finite automata.	Pp. 58-76	1.8, 2.3	Kalvot (pdf)
8.	20 Feb	Nonregular languages and the "pumping lemma". Context-free grammars and languages. Regular grammars.	Pp. 77-97	2.4, 3.1	Kalvot (pdf)
9.	27 Feb	Parse trees and derivations. Recursive-descent parsing of LL(1) grammars.	Pp. 97-98	3.2, 3.7 (partly)	Kalvot (pdf)
10.	6 Mar	Chomsky normal form and the CYK parsing algorithm. Pushdown automata.	Pp. 98-114, 240-241	3.3, 3.4, 3.6	Kalvot (pdf)
11.	13 Mar	The context-free pumping ("uvwxy") lemma. Turing machines.	Pp. 115-135	3.5, 4.1	Kalvot (pdf)
12.	20 Mar	Multitrack and multitape Turing machines. Nondeterministic Turing machines.	Pp. 136-140	4.3, 4.5	Kalvot (pdf)
13.	27 Mar	Recursive and recursively enumerable languages. Turing machine encoding and universal Turing machines.	Pp. 142-145, 159-168	4.2, 5.1, 5.2, 5.7	Kalvot (pdf)
14.	3 Apr	The halting problem. Undecidability. Rice's theorem. Recursive functions. Recursive reductions and RE-completeness.	Pp. 171-174, 190-193, 196	5.3, 5.4	Kalvot (pdf)
15.	10 Apr	General and context-sensitive grammars. Linear bounded automata. The Chomsky hierarchy.	-	4.6, p. 271	Kalvot (pdf)
16.	17 Apr	Easter vacation. No lecture.	-	-	-
17.	24 Apr	Review and discussion of the course material. Exam requirements.	-	-	-

Tutorials

In the tutorials, there will be three home assignments and two or three demonstration problems each week. The tutorials are not compulsory, but bonus exam points (max 6) will be awarded for doing the home assignments and marking them as done at the tutorial sessions. The grading scheme for the tutorials is as follows:

Problems solved	Bonus points
5	1
10	2
15	3
20	4
25	5
30	6

In addition to the voluntary tutorials there are three compulsory computer-generated problem sets. (See the info page.)

The tutorial bonus points awarded expire in one year, i.e. they are valid up to but not including the corresponding course exam in the following year (approx. May 2004). The demonstration problems are likely to be at least 90% the same as in the Autumn 2002 installation of the course. The Autumn 2002 problem sets and their solutions are bundled together with the lecture notes, and can be ordered from Edita. The demonstration problems are discussed at the tutorials to the extent that time permits. Updates to the demonstration problems and their solutions are distributed via this site.

Tutorial problems: Electronic copies downloadable here on the Tuesday of each week. Paper copies available at the lectures, and from the rack outside the theory lab office (TB336).

1. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
2. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
3. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
4. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
5. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
6. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
7. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
8. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
9. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
10. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
11. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
12. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)
13. tehtävät (pdf) ratkaisut (pdf) problems (pdf) solutions (pdf)

Tutorial scores.

Note: The demonstration problems and their solutions are for the most part the same as last Autumn.

Material

• Lecture Notes: Typeset lecture notes (in Finnish) distributed by Edita. Table of contents for the notes available here (pdf).
• Textbook(s): The recommended English textbook for the course is M. Sipser, Introduction to the Theory of Computation (PWS Publishing 1997). The former recommended text, H. Lewis and C. Papadimitriou, Elements of the Theory of Computation (Prentice Hall 1998) is being phased out. Finnish students do not need to purchase the textbook, since the course follows closely the lecture notes. However the Sipser book is very reader-friendly yet insightful, so reading it on the side will help in following the course.
• Supporting material:
  • Demonstration problems and their solutions from the tutorials. Material from Autumn 2003 bundled together with the lecture notes; updates available as the course progresses.
  • Some of the material will be available also via this web page. Please avoid unnecessary printing of this material to save printers, paper and thus nature !!!
  • A short introduction to set theory and relations (by Tommi Syrjänen, in Finnish, ps/ pdf).
  • An example on determinising a finite-state automaton (by Heikki Tauriainen, in Finnish, ps/ pdf).
• Examination requirements.
• Mallitentti vm 2001 (ps/ pdf), vastaukset (ps/ pdf). A sample examination from 2001 (ps/ pdf).
• Tentti/exam 11.2.2002: tehtävät (pdf), problems (pdf), tulokset/results.
• Tentti/exam 8.5.2002: tehtävät (pdf), problems (pdf), tulokset/results.
• Tentti/exam 12.8.2002: tehtävät (pdf), problems (pdf), tulokset/results.
• Tentti/exam 28.10.2002: tehtävät (pdf), problems (pdf), tulokset/results.
• Tentti/exam 17.12.2002: tehtävät (pdf), problems (pdf), tulokset/results.
• Tentti/exam 3.2.2003: tehtävät (pdf), problems (pdf), tulokset/results.
• Tentti/exam 7.5.2003: tehtävät (pdf), problems (pdf), tulokset/results.
• Tentti/exam 18.8.2003: tehtävät (pdf), problems (pdf).

Feedback

Summary of the feedback results for Spring 2003.

Summaries from previous courses: Autumn 2002, Spring 2002.