We define a fundamental domain for a linear programming relaxation of a combinatorial integer program which is symmetric under a group action. We then describe a straightforward w...
We study the complexity of computing Boolean functions using AND, OR and NOT gates. We show that a circuit of depth d with S gates can be made to output a constant by setting O(S1...
In their seminal paper, Valiant, Skyum, Berkowitz and Rackoff proved that arithmetic circuits can be balanced [VSBR]. That is, [VSBR] showed that for every arithmetic circuit of ...
Hierarchical graph definitions allow a modular description of graphs using modules for the specification of repeated substructures. Beside this modularity, hierarchical graph de...
We consider random 3CNF formulas with n variables and m clauses. It is well known that when m > cn (for a sufficiently large constant c), most formulas are not satisfiable. How...