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28, 2008. il Abstract. Simple Stochastic Games (SSGs), Mean Payoff Games (MPGs), and Parity Games (PGs) are three closely related families of infinite-duration games played on finite graphs. The best known algorithms for the solution of these games run in subexponential time and it is a major open problem whether they can be solved in polynomial time. In the talk, I plan to define these games, describe what is known about them and present many intriguing open problems. A. Hirsch et al. ): CSR 2008, LNCS 5010, p.

Thus, we obtain logspace canonization algorithms for these graph classes. Furthermore, partial 2-trees are planar graphs. However, we do not know if planar graph isomorphism is in logspace (or in NL). In that direction, recently Thierauf and Wagner gave a UL ∩ co-UL upper bound for planar 3-connected graph isomorphism [20]. They also provide an NL algorithm for oriented graphs. We note that Arnborg and Proskurowski gave a linear time and quadratic space2 canonization algorithm for both partial 2-trees and partial 3-trees [5].

A switching lemma primer. Technical Report UW-CSE-95-07-01, Department of Computer Science and Engineering, University of Washington (November 1994) 4. : Lower Bounds for Lov´ asz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity. , Yung, M. ) ICALP 2005. LNCS, vol. 3580, pp. 1176–1188. Springer, Heidelberg (2005) 5. : No feasible interpolation for T C 0 -Frege proofs. In: Proc. 38-th FOCS, pp. 254–263 (1997) 6. : Bounded Arithmetic. Bibliopolis (1986) 7. : Proof complexity in algebraic systems and constant depth Frege systems with modular counting.

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