https://hal.inria.fr/inria-00360101Marx, DánielDánielMarxDCSIT - Department of Computer Science and Information Theory - BME - Budapest University of Technology and Economics [Budapest]Tractable Structures for Constraint Satisfaction with Truth TablesHAL CCSD2009computational complexityconstraint satisfactiontreewidthadaptive width[INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC]Loria, PublicationsSusanne Albers and Jean-Yves Marion2009-02-10 11:45:402017-12-08 18:04:012009-02-11 21:16:34enConference papersapplication/pdf1The way the graph structure of the constraints influences the complexity of constraint satisfaction problems (CSP) is well understood for bounded-arity constraints. The situation is less clear if there is no bound on the arities. In this case the answer depends also on how the constraints are represented in the input. We study this question for the truth table representation of constraints. We introduce a new hypergraph measure adaptive width and show that CSP with truth tables is polynomial-time solvable if restricted to a class of hypergraphs with bounded adaptive width. Conversely, assuming a conjecture on the complexity of binary CSP, there is no other polynomial-time solvable case.