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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)
A B S T R A C T Boolean games are a succinct representation of strategic games wherein a player seeks to satisfy a formula of propositional logic by selecting a truth assignment to a set of propositional variables under his control. The difficulty arises because a player does not necessarily control every variable on which his formula depends, hence the(More)
The Duggan-Schwartz theorem [Duggan and Schwartz, 1992] is a famous result concerning strategy-proof social choice correspondences, often stated as " A social choice correspondence that can be manipulated by neither an optimist nor a pessimist has a weak dictator ". However, this formulation is actually due to Taylor [2002], and the original theorem, at(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)