Hastings’s Additivity Counterexample via Dvoretzky’s Theorem

Hastings’s Additivity Counterexample via Dvoretzky’s Theorem

The goal of this note is to show that Hastings’s counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky’s theorem.

First-Order Logic Theorem Proving via Counterexample-Guided Abstraction Refinement

Counterexample-guided abstraction refinement is a well-established technique in verification. In this paper we instantiate the idea for firstorder logic theorem proving. Given a clause set N we propose its abstraction into a clause set N ′ belonging to a decidable first-order fragment. The abstraction preserves satisfiability: if N ′ is satisfiable, so is N . A refutation in N ′ can then either...

The additivity theorem in algebraic K-theory

The additivity theorem in algebraic K-theory, due to Quillen and Waldhausen, is a basic tool. In this paper we present a new proof, which proceeds by constructing an explicit homotopy combinatorially.

A counterexample to the a-‘theorem’

We exhibit a renormalization group flow for a four-dimensional gauge theory along which the conformal central charge a increases. The flow connects the maximally superconformal point of an N = 2 gauge theory with gauge group SU(N+1) and Nf = 2N flavors in the ultraviolet, to a strongly-coupled superconformal point of the SU(N) gauge theory with Nf = 2N massless flavors in the infrared. Our exam...

A Counterexample to a Theorem of Chase