SBP is a probabilistic promise class located
between MA and AM \cap BPPpath. The first
part of the paper studies the question of whether
SBP has many-one complete sets. We relate
this question to the existence of uniform
enumerations. We construct an oracle relative to
which SBP and AM do ... more >>>

A polynomial time hierarchy for ZPTime with one bit of advice is proved. That is for any constants a and b such that 1 < a < b, ZPTime[n^a]/1 \subsetneq ZPTime[n^b]/1.

The technique introduced in this paper is very general and gives the same hierarchy for NTime \cap coNTime, UTime, ... more >>>

We show that for any reasonable semantic model of computation and for
any positive integer $a$ and rationals $1 \leq c < d$, there exists a language
computable in time $n^d$ with $a$ bits of advice but not in time $n^c$
with $a$ bits of advice. A semantic ... more >>>

We prove space hierarchy and separation results for randomized and other semantic models of computation with advice. Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems are the following.

Let <i>s</i>(<i>n</i>) ... more >>>

We investigate the connection between optimal propositional
proof systems and complete languages for promise classes.
We prove that an optimal propositional proof system exists
if and only if there exists a propositional proof system
in which every promise class with the test set in co-NP
... more >>>

In this paper we investigate the following two questions:

Q1: Do there exist optimal proof systems for a given language L?
Q2: Do there exist complete problems for a given promise class C?

For concrete languages L (such as TAUT or SAT and concrete promise classes C (such as NP ... more >>>