The complexity of Boolean functions
The complexity of Boolean functions
Neural networks: a systematic introduction
Neural networks: a systematic introduction
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Linear 0-1 Inequalities and Extended Clauses
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
SATO: An Efficient Propositional Prover
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Generic ILP versus specialized 0-1 ILP: an update
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
A fast pseudo-boolean constraint solver
Proceedings of the 40th annual Design Automation Conference
Combining satisfiability techniques from AI and OR
The Knowledge Engineering Review
HySAT: An efficient proof engine for bounded model checking of hybrid systems
Formal Methods in System Design
BDDs for pseudo-boolean constraints: revisited
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
A new look at BDDs for Pseudo-Boolean constraints
Journal of Artificial Intelligence Research
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A linear pseudo-Boolean constraint(LPB) is an expression of the form a1·驴1+ ... + am·驴m驴 d, where each 驴iis a literal(it assumes the value 1 or 0 depending on whether a propositional variable xiis true or false) and a1,...,am,dare natural numbers. An LPB is a generalisation of a propositional clause, on the other hand it is a restriction of integer linear programming. LPBs can be used to represent Boolean functions more compactly than the well-known conjunctiveor disjunctivenormal forms. In this paper, we address the question: how muchmore compactly? We compare the expressiveness of a single LPB to that of related formalisms, and give an algorithm for computing an LPB representation of a given formula if this is possible.