The constraint satisfaction problem (CSP) provides a framework in which it is possible to express, in a natural way, many
combinatorial problems encountered in artificial intelligence and computer science. In many cases effective algorithms exist
to solve such a problem, and in others (such as 3SAT) we can show it to be NP-complete. It is conjectured that every CSP
is either in P or NP-complete, which is the so called dichotomy conjecture. In the course, we will study the mathematics of
CSP and focus on algebraic methods.
Last update: T_KA (19.05.2009)
Problém splnitelnosti omezení (the Constraint Satisfaction Problem, CSP) poskytuje společný rámec pro studium mnoha
kombinatorických problémů v umělé inteligenci a informatice. V mnoha případech existují efektivní algoritmy pro řešení
tohoto problému, v jiných (například 3SAT) lze ukázat jeho NP-úplnost. Takzvaná dichotomická hypotéza říká, že každý
CSP je buď polynomiálně řešitelný, nebo NP-úplný. V přednášce se zaměříme na matematické aspekty CSP, zejména na
algebraický přístup k řešení dichotomické hypotézy.
Literature -
Last update: T_KA (19.05.2009)
[1] A. Bulatov, A. Krokhin, P. Jeavons: Constraint satisfaction problems and finite algebras. In: Proc. 27th International Colloquium on Automata, Languages and Programming, ICALP'00. Volume 1853 of LNCS, Springer-Verlag (2000) 272-282.
[2] V. Dalmau: Generalized majority-minority operations are tractable. In Proceedings 20th IEEE Symposium on Logic in Computer Science, (LICS 2005),438-447.
[3] T. Feder, M.Y. Vardi: The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory. SIAM J. Computing, 28 (1), 1998, 57-104.
[4] B. Larose, L. Zádori: Bounded width problems and algebras. Algebra Universalis 56 (3-4), 2007, 439-466.
[5] T. J. Schaefer: The complexity of satisfiability problems, in Proc. 10th ACM Symp. on Theory of Computing, ACM, New York, 1978, 216-226.
Last update: T_KA (19.05.2009)
[1] A. Bulatov, A. Krokhin, P. Jeavons: Constraint satisfaction problems and finite algebras. In: Proc. 27th International Colloquium on Automata, Languages and Programming, ICALP'00. Volume 1853 of LNCS, Springer-Verlag (2000) 272-282.
[2] V. Dalmau: Generalized majority-minority operations are tractable. In Proceedings 20th IEEE Symposium on Logic in Computer Science, (LICS 2005),438-447.
[3] T. Feder, M.Y. Vardi: The computational structure of monotone monadic SNP and constraint satisfaction: a study through Datalog and group theory. SIAM J. Computing, 28 (1), 1998, 57-104.
[4] B. Larose, L. Zádori: Bounded width problems and algebras. Algebra Universalis 56 (3-4), 2007, 439-466.
[5] T. J. Schaefer: The complexity of satisfiability problems, in Proc. 10th ACM Symp. on Theory of Computing, ACM, New York, 1978, 216-226.
Syllabus -
Last update: T_KA (19.05.2009)
1. Definition of CSP, its equivalent forms, basic notions and properties
2. Polymorphisms, algebraic reductions
3. Bounded width problems
4. Schaefer's dichotomy theorem for boolean CSPs
5. Maltsev CSPs
Last update: T_KA (19.05.2009)
1. Definice CSP, ekvivalentní přístupy, základní pojmy a vlastnosti
2. Polymorfismy, algebraické redukce
3. Problémy konečné šířky
4. Schaeferova věta o dichotomii pro booleovská CSP
