We apply the inductive counting technique to nondetermin-istic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound s(n), the class of languages accepted by nonuniform nondeterministic O(s(n)) space bounded Turing machines is closed under complementation. As a con...

This paper deals with balanced leaf language complexity classes, introduced independently in [1] and [14]. We propose the seed concept for leaf languages, which allows us to give “short” representations for leaf words. We then use seeds to show that leaf languages A with NP ⊆ BLeaf (A) cannot be polylog-sparse (i.e. censusA ∈ O(log )), unless PH collapses. We also generalize balanced ≤ m -reduc...

For a particular class of integral operators K we show that the quantity φ := log det (I + K)log det (/ K) satisfies both the integrated mKdV hierarchy and the Sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.

We establish hardness versus randomness trade-oos for Arthur-Merlin games. We create eecient nondeterministic simulations of bounded round Arthur-Merlin games, using a language in exponential time which small circuits cannot decide given access to an oracle for satissability. Our results yield subexponential size proofs for graph nonisomorphism at innnitely many lengths unless the polynomial-ti...

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation...

In this lecture we first discuss bounded-round interactive proof systems and its relationship with other complexity classes. Along the way we prove an interesting result that coNP is not in AM unless the polynomial time hierarchy collapses to its second level. Given GNI has an AM protocol, this gives strong evidence that GI is not NP-complete. As it is unlikely that coNP has bounded round inter...

We study higher Arthur-Merlin classes de ned via several natural probabilistic operators BP;R and co-R. We investigate the complexity classes they de ne, and a number of interactions between these operators and the standard polynomial time hierarchy. We prove a hierarchy theorem for these higher Arthur-Merlin classes involving interleaving operators, and a theorem giving non-trivial upper bound...

In this paper, we show how a multi-level class hierarchy can be used to better estimate the likelihood of an unseen event. In classical backoff n-gram models, the (n-1)-gram model is used to estimate the probability of an unseen n-gram. In the approach we propose, we use a class hierarchy to define an appropriate context which is more general than the unseen n-gram but more specific than the (n...