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We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations R, S, a componentwise reducibility is defined by R ≤ S ⇐⇒ ∃f ∀x, y [xRy ↔ f (x)Sf (y)]. Here f is taken from a suitable class of effective functions. For us the relations will be on natural numbers, and f must be(More)
[Slinko and White, 2008] have recently introduced a new model of coalitional manipulation of voting rules under limited communication, which they call safe strategic voting. The computational aspects of this model were first studied by [Hazon and Elkind, 2010], who provide polynomial-time algorithms for finding a safe strategic vote under k-approval and the(More)
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal operator [a] comes with a converse [a] −1. Extending previous works on nested sequent systems for tense logics, we show all(More)
Buchi's theorem, in establishing the equivalence between languages definable in S1S over element and<and the omega-regular languages also demonstrated that S1S over element and<is no more expressive than its existential fragment. It is also easy to see that S1S over element and<is equi-expressive with S1S over element and successor. However, it is not(More)
Boolean games are an expressive and natural formalism through which to investigate problems of strategic interaction in multiagent systems. Although they have been widely studied , almost all previous work on Nash equilibria in Boolean games has focused on the restricted setting of pure strategies. This is a shortcoming as finite games are guaranteed to(More)
We show that the following problem is EXP-complete: given a rational v and a two player, zero-sum Boolean game G determine whether the value of G is at least v. The proof is via a translation of the proof of the same result for Boolean circuit games in [1]. 1 Preliminaries We will be using the encoding of [2] to replicate the proof of [1]. A familiarity(More)