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We study the computational complexity of a perfect-information two-player game proposed by Aigner and Fromme in [AF–84]. The game takes place on an undirected graph where n simultaneously moving cops attempt to capture a single robber, all moving at the same speed. The players are allowed to pick their starting positions at the first move. The question of(More)
We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence is the " infini-tesimal subgroup " of G and G/G 00 is a compact real Lie group. We show that given a connected open subset U of G/G 00 there is a canonical isomorphism between the fundamental(More)
We consider groups definable in an o-minimal expansion of a real closed field. To each definable group G is associated in a canonical way a real Lie group G/G 00 which, in the definably compact case, captures many of the algebraic and topological features of G. In particular, if G is definably compact and definably connected, the definable fundamental group(More)
A semilinear relation S ⊆ ℚ n $S \subseteq {\mathbb {Q}}^{n}$ is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to(More)
We prove that to find optimal positional strategies for stochastic mean payoff games when the value of every state of the game is known, in general, is as hard as solving such games tout court. This answers a question posed by Daniel Andersson and Peter Bro Miltersen. In this note, we consider perfect information 0-sum stochastic games, which, for short, we(More)
Modify the Blum-Shub-Smale model of computation replacing the permitted computational primitives (the real field operations) with any finite set <i>B</i> of real functions semialgebraic over the rationals. Consider the class of Boolean decision problems that can be solved in polynomial time in the new model by machines with no machine constants. How does(More)
—Modify the Blum-Shub-Smale model of computation replacing the permitted computational primitives (the real field operations) with any finite set B of real functions semialgebraic over the rationals. Consider the class of Boolean decision problems that can be solved in polynomial time in the new model by machines with no machine constants. How does this(More)