We strengthen the non-deterministic time hierarchy theorem of
\cite{Cook72, Seiferas-Fischer-Meyer78, Zak83} to show that the lower bound
holds against sublinear advice. More formally, we show that for any constants
$c$ and $d$ such that $1 \leq c < d$, there is a language in $\NTIME(n^d)$
which is not in $\NTIME(n^c)/n^{1/d}$. ... more >>>

The notion of online space complexity, introduced by Karp in 1967, quantifies the amount of states required to solve a given problem using an online algorithm,
represented by a machine which scans the input exactly once from left to right.
In this paper, we study alternating machines as introduced by ... more >>>

In this work we study oblivious complexity classes. Among our results:
1) For each $k \in \mathbb{N}$, we construct an explicit language $L_k \in O_2P$ that cannot be computed by circuits of size $n^k$.
2) We prove a hierarchy theorem for $O_2TIME$. In particular, for any function $t:\mathbb{N} \rightarrow \mathbb{N}$ ... more >>>

We prove a time hierarchy theorem for the promise-BPTIME. This is considered to be a folklore problem and was thought to follow from the existence of complete problems or through direct diagonalization. We observe that neither argument carries through in some immediate way in the promise version. However, the hierarchy ... more >>>