Combinatorial problems for Horn clauses

Generalising submodularity and horn clauses: Tractable optimization problems defined by tournament pair multimorphisms

The submodular function minimization problem (SFM) is a fundamental problem in combinatorial optimization and several fully combinatorial polynomial-time algorithms have recently been discovered to solve this problem. The most general versions of these algorithms are able to minimize any submodular function whose domain is a set of tuples over any totally-ordered nite set and whose range includ...

Cryptographic Protocol Verification Using Tractable Classes of Horn Clauses

We consider secrecy problems for cryptographic protocols modeled using Horn clauses and present general classes of Horn clauses which can be efficiently decided. Besides simplifying the methods for the class of flat and onevariable clauses introduced for modeling of protocols with single blind copying [7,25], we also generalize this class by considering k-variable clauses instead of one-variabl...

From Horn Strong Backdoor Sets to Ordered Strong Backdoor Sets

Identifying and exploiting hidden problem structures is recognized as a fundamental way to deal with the intractability of combinatorial problems. Recently, a particular structure called (strong) backdoor has been identified in the context of the satisfiability problem. Connections has been established between backdoors and problem hardness leading to a better approximation of the worst case ti...

Horn Clause Solvers for Program Verification

Automatic program verification and symbolic model checking tools interface with theorem proving technologies that check satisfiability of formulas. A theme pursued in the past years by the authors of this paper has been to encode symbolic model problems directly as Horn clauses and develop dedicated solvers for Horn clauses. Our solvers are called Duality, HSF, SeaHorn, and μZ and we have devot...

Submodularity and Horn Clauses : Tractable Optimization Problems Defined Bytournament Pair