Almost everywhere elimination of probability quantifiers

Almost everywhere elimination of probability quantifiers

We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [10]. This logic has quantifiers like ∃≥3/4y, which says that “for at least 3/4 of all y”. These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifi...

Almost Everywhere Elimination of Probability Quantifiers H. Jerome Keisler and Wafik Boulos Lotfallah

We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [9]. This logic has quantifiers like ∃≥3/4y, which says that “for at least 3/4 of all y”. These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifie...

On almost sure elimination of generalized quantifiers

Incentive Compatibility: Everywhere vs. Almost Everywhere∗

A risk neutral buyer observes a private signal s ∈ [a, b], which informs her that the mean and variance of a normally distributed risky asset are s and σ s respectively. She then sets a price at which to acquire the asset owned by risk averse “outsiders”. Assume σ s ∈ { 0, σ } for some σ > 0 and let B = { s ∈ [a, b] | σ s = 0 } . If B = ∅, then there exists a fully revealing equilibrium in whic...

Almost-Everywhere Secure Computation

Secure multi-party computation (MPC) is a central problem in cryptography. Unfortunately, it is well known that MPC is possible if and only if the underlying communication network has very large connectivity — in fact, , where is the number of potential corruptions in the network. This impossibility result renders existing MPC results far less applicable in practice, since many deployed network...