Stefan Szeider

Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference

A formula (in conjunctive normal form) is said to be minimal unsatisfiable if it is unsatisfiable and deleting any clause makes it satisfiable. The deficiency of a formula is the difference of the number of clauses and the number of variables. It is known that every minimal unsatisfiable formula has positive deficiency. Until recently, polynomial-time algorithms were known to recognize minimal unsatisfiable formulas with deficiency 1 and 2. We state an algorithm which recognizes minimal unsatisfiable formulas with any fixed deficiency in polynomial time.

Clique-Width is NP-Complete

Clique-width is a graph parameter that measures in a certain sense the complexity of a graph. Hard graph problems (e.g., problems expressible in monadic second-order logic with second-order quantification on vertex sets, which includes NP-hard problems such as 3-colorability) can be solved in polynomial time for graphs of bounded clique-width. We show that the clique-width of a given graph cannot be absolutely approximated in polynomial time unless

Algorithms for propositional model counting

P = NP

On Fixed-Parameter Tractable Parameterizations of SAT

. We also show that, given a graph

Fixed-Parameter Algorithms For Artificial Intelligence, Constraint Satisfaction and Database Problems

G

Constraint satisfaction with bounded treewidth revisited

and an integer

Backdoor Sets of Quantified Boolean Formulas

k

Backdoors to satisfaction

, deciding whether the clique-width of

The Added Value of Argumentation

G

Editing graphs to satisfy degree constraints: A parameterized approach

is at most