Theoretische Modellen - Capita Games and Computer Science
Course  Fall  2002

dr. Peter van Emde Boas

hours:
Monday  13.15 -- 15.--   Zaal P017

Thursday 13.15 -- 15.--   Zaal A303
 

THE  EXCERCISES PAGE NOW HAS BEEN OPENED !
 

Scheme of classes:

Week   Monday                                             Thursday

37        Sep 09 General Introduction                Sep 12  Games and Computation
38        Sep 16  Tiling Game reduction             Sep 19  Endgame analysis in PSPACE
39        Sep 23   Characterization of PSPACE  Sep 26   PSPACE, Games and Parallellism
40        Sep 30   Alternation Model                  Oct 03   Direct reductions PSPACE to games
41        Oct 07   The pebbling Game                 Oct 10  Lowerbound Pebbling Game - Hopcroft Paul Valiant
42       Oct 14   No Class: Schoolweek OZSL    Oct 17  No Class: Schoolweek OZSL
43        Oct 21  (No class: midterm exams)      Oct 24  (No class: midterm exams)
44        Oct 28   Hopcroft Paul Valiant            Oct 31  Gilbert Tarjan & Lengauer
45        Nov 04  (No class: OOPSLA, Seattle)  Nov 07 (No class: OOPSLA, Seattle)
46        Nov 11  (No class: OOPSLA, Seattle)  Nov 14  Interactive models
47        Nov 18  Shamir Theorem IP = PSPACE   Nov 21   Nisan & Ronen:  Agents on the Internet
48        Nov 25 (Exam weeks)                           Nov 28 (Exam weeks)
49        Dec 02  (Exam weeks)                           Dec 05 (Exam weeks)
50        Dec 09   (Exam weeks)                          Dec 12 (Exam weeks)

This course belongs to the by now obsolete 4 year curriculum of the computer scxience program.
It is presented this year for the last time as a service to remaining students from this program and
other interested students who can select this course as a choice item in their program.
The course must be completed before the end of this academic year, I.E. no later than August 31 2003.

Course Contents:

Game theory originates from Economical Sciences; it
treates theories about strategic interaction and
related rationality concepts. The subject is currently attracting researchers from
Computer Science and Technology, particularly  involving
themes about controling behavior of unrelyable agents on the
Internet.

Fact is that concepts from game theory have been used in
Computer Science already much longer. Several of the models
used in theoretical Computer Science for analysing problems with regards to
effectivity and efficiency can be quite reasonably be described and analysed
in terms of games.

This link will be illustrated in this course on the basis of a number
of models which originally date from the 70-ies and 80-ies.
The main target is to illustrate that games represent a computational
model in the same way nondeterministic computations do.

Interesting in this regards is to investigate which computational
models seem to be unrelated to games and which game models
seem not to relate well with computational models.

Examples of models connecting games and computation theory are:

The theory of Traub and Wozniakowski on the solution of numerical
problems.

Deciding Graph properties from Adjacency Matrices ("Twenty Questions");
theory of Evasiveness.

The pebling game, used as a model both for register allocation
and in the context of machine model theory.

The Tiling game and its use in Reduction Theory

The Alternating Machine model and its connection to
logic description languages and games.

Interactive protocols for convincing opponents about the presence of
information, without leaking more information than
necessary: (Interactive proofs, Arthur Merlin games, Zero Knowledge
proofs, ...)

The design of mechanisms for tweaking agents on the internet to behave
in a truthful manner.

Except for the latter problem the game theory involved deals combinatorial
games rather than the more stochasitic real valued games studied in
Econmical Sciences. The game theory involved therefore is rather
elementary.
 
 

Sheets available:    (for the larger part unchanged from the previous edition of this course)

Part 1:      Topics:  Introduction, Games and Tilings:
                Available in  Powerpoint98 format and  pdf format

Part 2:      Topics:  Endgame Analysis, PSPACE and Parallellism:
                Available in  Powerpoint98 format  and pdf format

Part 3:      Topics:  PSPACE, Alternation, Games:
                Available in  Powerpoint98 format and  pdf format

Part 4:      Topics:  the Pebble Game:
                Available in Powerpoint98 Formatand pdf format

Part 5:      Topics:  Diagonalization and Compression:  (version 2000)
                Available in  Powerpoint98 format  and  pdf format

Part 6:       Topics:  Interactive Proof Systems:
                Available in Powerpoint98 formatand pdf format

Part 7:    Controling Selfish Agents on the Internet:
                Available in Powerpoint00 format and pdf format

Extra:      Topics:  Games in the Classroom:
                Available in  Powerpoint98 format and pdf format

Extra:      Topics:  The connection between Games and Computer Science,
                Talks prepared for a trip to China, April 2000:
                Available in  Powerpoint98 format and pdf format

Extra:      Topics:  The Games of Computer Science,
                Talk at TU Delft, Feb 23 2001:
                Available in  Powerpoint98 format and pdf format

Extra:      Topics:  Playing Savage:
                Available in  Powerpoint98 format and pdf format
           Manuscript available in Postscript

Extra:      Topics: Imperfect Information Games, looking for the right model.
                 Talk at Algemeen Wiskunde Colloquium, Feb 27 2002:
                  Available in  Powerpoint2000 format

Extra:      Topics: Imperfect Information Games, what makes them hard to decide.
                 Talk at Amsterdam Aachen Exchange Feb 15, 2002:
                  Available in  Powerpoint2000 format

Literature:  (will be extended during the course).

Game Theory.

Ken Binmore, Fun and Games, Houghton Mifflin Company, 1992;
this is the textbook used in the course  Intelligent Database - Game Theory

Elwyn R. Berlekamp, John H. Conway & Richard K. Guy,
Winning Ways (Vol 1 and Vol. 2), Academic Press, 1982.

John H. Conway, On Numbers and Games, Academic Press 1976.

the above two references develop the mathematics of combinatorial games in great depth.

V.W. Gijlswijk, G.A.P. Kindervater, G.J. van Tubergen & J.J.O.O Wiegerinck,
Computer Analysis of E. de Bono's L-Game, Rep. Math, Inst. UvA 76-18
(an early computerized backward analysis of a non-trivial game; also an early
student project in our department...)

M.J. Osborne & A. Rubinstein, A Course in Game Theory, MIT Press 1994.

Alexander Mehlman, The Game's Afoot!, Game Theory in Mythand Paradox,
Amer. Math. Soc. Student Math. Library 5, 2000
Introduction, with many examples drawn from the literature and
mythology; however, in final sections rather difficult.

Steven J. Brams, Superior Beings, Springer Verlag 1983;
Game theory applied to Theology.

Computation Theory.

John E. Hopcroft & Jeffrey D. Ullman, Intorduction to Automata Theory,
Languages and Computation, Addison Wesley, 1979.

David Harel, Algorithmics; the Spirit of Computing, (second Edition),
Addison Wesley 1992.

Thomas A. Sudkamp, Languages and Machines; An Introduction to the
Theory of Computer Science, (second Edition), Addison Wesley 1997.
a formerly used textbook for the course  Automata and Complexity Theory

Harry R. Lewis & Christos H. Papadimitriou,
Elements of the Theory of Computation, Prentice Hall 1981.

Christos H. Papadimitriou, Computational Complexity,
Addison Wesley 1995.
Chapter 19  covers many of the subjects dealt with in this course!

Cees Slot & Peter van Emde Boas, The Problem of Space Invariance for
Sequential Machines, Inf. and Comp. 77 (1988) 93--122.

Peter van Emde Boas, Space Measures for Storage Modification Machines,
Inf. Proc. Letters  30 (1989) 103--110.

Peter van Emde Boas, Machine Models and Simulations, in
J. van Leeuwen, Handbook of Theoretical Computer Science vol A,
Algorithms and Complexity,  Elsevier, 1990, pp 3--66;
preprint:  ITLC-CT-89-02.

The last three papers concern the Invariance Thesis.

The pebling game, used as a model both for register allocation
and in the context of machine model theory.

J.E. Hopcroft, W. Paul & L. Valiant, On Time versus Space,
J. Assoc. Comput. Mach., 24 (1977) 332--337.

A. Lingas, A PSPACE Complete Problem related to a Pebble Game,
G. Ausiello & C Böhm eds., Proc. ICALP'78,
Springer LNCS 62, 1978, pp. 300--321.

P. van Emde Boas & Jan Van Leeuwen, Move Rules and
Trade-Offs in the Pebble Game, in K. Weihrauch ed.,
Proc. 4th GI Theoretical Computer Science Conference,
Springer LNCS 67 1979, pp. 101--112.

John R. Gilbert, Thomas Lengauer & Robert E. Tarjan,
The Pebbling Problem is Complete in Polynomial Space,
SIAM J. Comput. 9 (1980) 513--524.

Hiroaki Tohyama & Akeo Adachi,
Complexity of path discovery game problems,
Theor. Comp. Sci.. 237, 2000, 381--406.
another PSPACE-hard solitaire game.
 

Tiling Game and its use in Reduction Theory

Bogdan S. Chlebus, Domino-Tiling Games, J. Comput. Syst. Sci. 32
(1986), 374--392.

Martin. P.W. Savelsberg & Peter van Emde Boas, BOUNDED TILING,
an alternative to SATISFIABILITY?, in G.Wechsung ed., proc. 2nd
Frege Memorial Conference, Schwerin, Sep 1984, Akademie Verlag,
Mathematische Forschung vol. 20, 1984, pp. 401--407.
preprint: rep. CWI-OS-R8405.

Peter van Emde Boas, The Convenience of Tilings, in:  Andrea Sorbi, ed.,
Complexity, Logic and Recursion Theory, lecture notes in pure and
applied mathetaics vol 187, 1997, pp. 331--363. (for ps. version of  preprint ).
The sheets of this lecture are available at  sheets in postscript . However
beware: on behalf of its origin as a (by now obsolete MacWrite document)
the Postscript pages are sorted in reverse order.

Peter van Emde Boas, Is elf plus één twaalf?; over rekenen en puzzelen.
Explanation of the construction of the tiling puzzle demonstration
model for precollege students (in Dutch). Text available in  Postscript .
The corresponding figures are available in Postscript also:  pict1pict2pict3pict4 .

David Harel, Recurring Dominos: making the Highly Undecidable
Highly Understandable, Ann. Discrete Math. 24 (1985) 51--72.

David Harel, Dynamic Logic, in D. Gabbay & F. Guenthner (eds.)
Handbook of PhilosophicalLogic, Vol II, D. Reidel 1984, pp. 497--604.
Background information on Dynamic Logic for the reduction to
PDL-Satisfiability from the two person tiling game as invented by
Chlebus.
 

The Alternating Machine model and its connection to
logic description languages and games.

A.K. Chandra, D. Kozen & L.J. Stockmeyer, Alternation,
J.Assoc. Comput. Mach. 28 (1981) 114--133.

Christos H. Papadimitriou, Computational Complexity,
Addison Wesley 1995. See chapter 19 in particular.

L.J. Stockmeyer & A.R. Meyer, Word problems requiring exponential time,
Proc STOC 5 (1973), pp 1--9.
An important early paper and the source of the QBF problem.

T.J. Schäfer, Complexity of some two-person perfect-information games,
J.Comput. Syst. Science, 16 (1978) 185--225.
The first PSPACE complete game: Geography.

D. Lichtenstein & M. Sipser, GO is polynomial-space hard,
J. Assoc. Comput. Mach, 27 (1980) 393--401.

S. Even & R.E. Tarjan, A combinatorial game which is complete for polynomial
space, J. Assoc. Comput. Mach, 23 (1976) 710--719.

S. Reisch, HEX ist PSPACE-volständig, Acta Informatica 15 (1981) 167--191.

A.S. Fraenkel, M.R. Garey, D.S. Johnson, T. Schäfer & Y. Yesha,
The complexity of checkers on an N X N board - preliminary report,
Proc IEEE FOCS 19 (1978) pp. 55--64.

A.S. Fraenkel & D. Lichtenstein, Computing a perfect strategy for n x n chess
requires time exponential in n, J. Combin. Theory series A 31 (1981) 119--213.

G.W. Flake & E.B. Baum, Rush Hour is PSPACE-complete, or "Why you should generously tip
parking lot attendants", Theoretical Computer Science, 270 (2002) 895--911.
A very simple combinatorial solitaire game which is PSPACE-complete. For a yet simpler version
see this note by John Tromp.

Erik D. Demaine,  Playing Games with Algorithms: Algorithmic Combinatorial Game Theory ,
MFCS 2001, Springel LNCS 2136, pp. 18-32 .
Much more information is available from  his impressive  website .

The above five papers involve games played by real people.

P. van Emde Boas, The Second Machine Class 2, an Encyclopedic View on the
Parallel Computation Thesis. in: H. Rasiowa ed.,  Mathe,atical Problems in
Computation Theory, Banach Center Publications, vol 20, PWN Warsaw 1988,
pp. 235--256.
An older version of sections 3 and 4 in my Handbook Chapter.
Slides about this subject are available in Postscript
(but again in reverse order...).

Robert A. Stegwee, Leen Torenvliet & Peter van Emde Boas,
The Power of your Editor, Rep. IBM RJ 4711 (50179) 5/21/85;
also: Report FVI-UvA-85-03.
Sheets have been placed on the Web; once more in reverse order Postscript

Interactive Proof systems and other models of interaction and/or randomized computation

Carsten Lund, Lance Fortnow & Howard Karloff, Algebraic Methods for Interactive Proof Systems,
J. ACM. 39 (1992) 859-868.

Adi Shamir,  IP = PSPACE, J.ACM. 93 (1992) 869-877.

A. Shen, IP= PSPACE: Simplified Proof, J.ACM. 93 (1992) 878-880.

L. Babai,  E-mail and the unexpected power of interaction, Proc. IEEE Symp. Structure in
Complexity Theory 5, Barcelona, July 08-11 1990, pp. 30--44.

Shafi Goldwasser, Silvio Micali & Charles Rackoff, The Knowledge Complexity of
Interactive Proof Systems, SIAM, J. Comput. 18 (1989), 186-208.

Christos H. Papadimitriou, Games against Nature, Proc. IEEE FOCS 1983, pp. 446-450

L. Babai &S. Moran, Arthur-Merlin Games: a Randomized Proof System and a Hierarchy
of Complexity Classes, J. Comput. Syst. Sci. 36 (1988) 254-276.
 

The design of mechanisms for tweaking agents on the internet to behave
in a truthful manner.

Noam Nissan & Amir Ronen, Algorithmic Mechanism Design,
proc. ACM STOC 31 (1999).

Noam Nisan, Algorithms for Selfish Agents,
in C. Meinel & S. Tison, eds., Proc. STACS'99,
Springer LNCS 1563, 1999, pp. 1--15.

Amir Ronen, Algorithms for Rational Agents,
proc. SOFSEM 2000, Springer LNCS 1963, 56--70.

Evasiveness problem ("twenty questions")

M.R. Best, P. van Emde Boas and H.W. Lenstra, jr.,
A Sharpened version of the Aandera-Rosenberg Conjecture,
rep. MC-ZW-30-74, October 1974.

Ronald L. Rivest & Jean Vuillemin,
On recognizing Graph properties from Adjacency Matrices,
Theor. Comp. Sci. 3 (1976) 371-384.

J.Kahn, M. Saks, D. Sturtevant, A topological Approach to Evasiveness,
Combinatorica 4 (1984) 297-306.

N. Illies, A counterexample to the Generalized Aanderaa-Rosenberg Conjecture,
Inf. Proc. Letters, 7 (1978) 154-155.

Unrelated but still about Games and Computer Science.

Peter van Emde Boas, Games in the Classroom,
position paper at OOPSLA'99 Workshop #2, Quest for Effective Classroom Examples.
Postscript version Available .
 

Course Evaluation:

Except for specific student contributions (with previous arrangements
with the teacher) the students will be graded on their solutions of
homework exercises  which will be made public on the website gradually
during the course. Answers should be returned within the deadline as listed with
the exercise, only on paper. Even when the answers are prepared electronically
the solution must be submitted on paper.

Related courses:

prof. dr. J.F.A.K. van Benthem:  Caput Logic and Languages:  Logic and Games

dr. Peter van Emde Boas:  Intelligent Databases (3rd trimester): game theory

dr. Peter van Emde Boas:  Complexity and Computation Theory (2nd trimester): complexity theory