Model theory is a branch of mathematical logic that investigates the
logical properties of mathematical structures. It has been quite
successfully applied to computational complexity resulting in an
area of research called descriptive complexity theory. Descriptive
complexity is essentially a syntactical characterization of
complexity classes using logical formalisms. However, there ... more >>>

Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms operate.

First, we show that for any problem that ... more >>>

Following Hastad, Pass, Pietrzak, and Wikstrom (2008), we study parallel repetition theorems for public-coin interactive arguments and their generalization. We obtain the following results:

1. We show that the reduction of Hastad et al. actually gives a tight direct product theorem for public-coin interactive arguments. That is, $n$-fold parallel repetition ... more >>>