Speaker: Irenee Briquel
Laboratoire de l Informatique du Parallelisme - ENS
Lyon and Fields Institure
Title: Lower bounds on the tree-width of boolean formulas
Abstract: To a boolean formula can be associated the clause graph, where the vertices are the variables, and where two variables are linked in the graph when they belong to the same clause.
In a previous work, Pascal Koiran and Klaus Meer studied the link between the complexity of the formula and the tree-width of the clause graph - for short, the tree-width of the formula. They found an algorithm to compute efficiently polynomials associated with boolean formulas of bounded tree-width.
To estimate the limits of this method, it is interesting to look for lower bounds on the tree-width of boolean formulas, establishing that the previously mentioned algorithm is not efficient for the associated polynomials.
To find lower bounds on the tree-width, we show a link between this notion and the communication complexity of the boolean formula. We show that lower bounds on the communication complexity can transpose to the tree-width, and explore the possibilities of this method. This is based on joint work with Pascal Koiran and Klaus Meer.