This paper proves that there is, in every direction in Euclidean space, a line that misses every computably random point. Our proof of this fact shows that a famous set constructed by Besicovitch in 1964 has computable measure 0.

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Circumscription is one of the main formalisms for non-monotonic reasoning. It uses reasoning with minimal models, the key idea being that minimal models have as few exceptions as possible. In this contribution we provide the first comprehensive proof-complexity analysis of different proof systems for propositional circumscription. In particular, we investigate ... more >>>

It is generally assumed that you can make a financial asset out of any underlying event or combination thereof, and then sell a security. We show that while this is theoretically true from the financial engineering perspective, compound securities might be intractable to price. Even given no information asymmetries, or ... more >>>