A cycle cover of a graph is a set of cycles such that every vertex is
part of exactly one cycle. An L-cycle cover is a cycle cover in which
the length of every cycle is in the set L. The weight of a cycle cover
of an edge-weighted graph ... more >>>

We continue a study initiated by Krajicek of
a Resolution-like proof system working with clauses of linear
inequalities, R(CP). For all proof systems of this kind
Krajicek proved an exponential lower bound that depends
on the maximal absolute value of coefficients in the given proof and
the maximal clause width.

... more >>>

We demonstrate a family of propositional formulas in conjunctive normal form
so that a formula of size $N$ requires size $2^{\Omega(\sqrt[7]{N/logN})}$
to refute using the tree-like OBDD refutation system of
Atserias, Kolaitis and Vardi
with respect to all variable orderings.
All known symbolic quantifier elimination algorithms for satisfiability
generate ... more >>>