We consider worst case time bounds for NP-complete problems
including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring.
Our algorithms are based on a common generalization of these problems,
called symbol-system satisfiability or, briefly, SSS [R. Floyd &
R. Beigel, The Language of Machines]. 3-SAT is equivalent to
(2,3)-SSS while the other problems ... more >>>

Let $p(x_1,...,x_n) = p(X) , X \in R^{n}$ be a homogeneous polynomial of degree $n$ in $n$ real variables ,
$e = (1,1,..,1) \in R^n$ be a vector of all ones . Such polynomial $p$ is
called $e$-hyperbolic if for all real vectors $X \in R^{n}$ the univariate polynomial
equation ... more >>>

We give a polynomial time algorithm that computes a
decomposition of a finite group G given in the form of its
multiplication table. That is, given G, the algorithm outputs two
subgroups A and B of G such that G is the direct product
of A ... more >>>