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$Π_{2}^{P}$ vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem (2404.03844v2)
Published 5 Apr 2024 in cs.CC, cs.LO, and math.LO
Abstract: The Quantified Constraint Satisfaction Problem is the problem of evaluating a sentence with both quantifiers, over relations from some constraint language, with conjunction as the only connective. We show that for any constraint language on a finite domain the Quantified Constraint Satisfaction Problem is either in $\Pi_{2}{P}$, or PSpace-complete. Additionally, we build a constraint language on a 6-element domain such that the Quantified Constraint Satisfaction Problem over this language is $\Pi_{2}{P}$-complete.
- Computational complexity: a modern approach. Cambridge University Press, 2009.
- Polymorphisms, and how to use them. 2017. Preprint.
- The algebraic dichotomy conjecture for infinite domain constraint satisfaction problems. In Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS ’16, New York, NY, USA, July 5-8, 2016, pages 615–622, 2016.
- The complexity of constraint satisfaction games and QCSP. Inf. Comput., 207(9):923–944, 2009.
- Promise constraint satisfaction: Structure theory and a symmetric boolean dichotomy. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, LA, USA, January 7-10, 2018, pages 1782–1801, 2018.
- Classifying the complexity of constraints using finite algebras. SIAM J. Comput., 34(3):720–742, March 2005.
- Andrei A. Bulatov. A dichotomy theorem for nonuniform CSPs. In 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pages 319–330, 2017.
- Andrei A. Bulatov. A dichotomy theorem for nonuniform CSPs. CoRR, abs/1703.03021, 2017.
- Hubie Chen. A rendezvous of logic, complexity, and algebra. SIGACT News, 37(4):85–114, 2006.
- Hubie Chen. The complexity of quantified constraint satisfaction: Collapsibility, sink algebras, and the three-element case. SIAM J. Comput., 37(5):1674–1701, 2008.
- Hubie Chen. Quantified constraint satisfaction and the polynomially generated powers property. Algebra universalis, 65(3):213–241, 2011. An extended abstract appeared in ICALP B 2008.
- Hubie Chen. Meditations on quantified constraint satisfaction. In Logic and Program Semantics - Essays Dedicated to Dexter Kozen on the Occasion of His 60th Birthday, pages 35–49, 2012.
- Peter Jeavons. On the algebraic structure of combinatorial problems. Theoretical Computer Science, 200(1-2):185–204, 1998.
- The complexity of general-valued CSPs. SIAM J. Comput., 46(3):1087–1110, 2017.
- Barnaby Martin. Quantified Constraints in Twenty Seventeen. In Andrei Krokhin and Stanislav Zivny, editors, The Constraint Satisfaction Problem: Complexity and Approximability, volume 7 of Dagstuhl Follow-Ups, pages 327–346. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2017.
- Thomas J. Schaefer. The complexity of satisfiability problems. In Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, STOC ’78, pages 216–226, New York, NY, USA, 1978. ACM.
- D. Zhuk. A proof of CSP dichotomy conjecture. In 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pages 331–342, Oct 2017.
- Dmitriy Zhuk. The size of generating sets of powers. Journal of Combinatorial Theory, Series A, 167:91–103, 2019.
- Dmitriy Zhuk. A proof of the CSP dichotomy conjecture. Journal of the ACM (JACM), 67(5):1–78, 2020.
- Dmitriy Zhuk. The complexity of the quantified CSP having the polynomially generated powers property, 2021.
- DMITRIY ZHUK. Strong subalgebras and the constraint satisfaction problem. Journal of Multiple-Valued Logic & Soft Computing, 36, 2021.
- QCSP monsters and the demise of the chen conjecture. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, pages 91–104, 2020.
- QCSP monsters and the demise of the chen conjecture. J. ACM, 69(5), oct 2022.