Building on Barak's work (Random'02),
Fortnow and Santhanam (FOCS'04) proved a time hierarchy
for probabilistic machines with one bit of advice.
Their argument is based on an implicit translation technique,
which allow to translate separation results for short (say logarithmic)
advice (as shown by Barak) into separations for ... more >>>

A string $\alpha\in\Sigma^n$ is called {\it p-periodic},
if for every $i,j \in \{1,\dots,n\}$, such that $i\equiv j \bmod p$,
$\alpha_i = \alpha_{j}$, where $\alpha_i$ is the $i$-th place of $\alpha$.
A string $\alpha\in\Sigma^n$ is said to be $period(\leq g)$,
if there exists $p\in \{1,\dots,g\}$ such that $\alpha$ ... more >>>

We consider the problem of testing whether a given system of equations
over a fixed finite semigroup S has a solution. For the case where
S is a monoid, we prove that the problem is computable in polynomial
time when S is commutative and is the union of its subgroups
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