We study graphical games where the payoff function of each player satisfies one of four types of symmetries in the actions of his neighbors. We establish that deciding the existence of a pure Nash equilibrium is NP-hard in graphical games with each of the four types of symmetry. Using a ... more >>>

We introduce the notion of a Canonical Tester for a class of properties, that is, a tester strong and
general enough that ``a property is testable if and only if the
Canonical Tester tests it''. We construct a Canonical Tester
for the class of symmetric properties of one or two
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We prove space hierarchy and separation results for randomized and other semantic models of computation with advice. Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems are the following.

Let <i>s</i>(<i>n</i>) ... more >>>