Linear Programming Formulation of Boolean Satisfiability Problem

Conference paper

DOI: 10.1007/978-94-007-7684-5_22

Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 275)
Cite this paper as:
Maknickas A.A. (2014) Linear Programming Formulation of Boolean Satisfiability Problem. In: Yang GC., Ao SI., Huang X., Castillo O. (eds) Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 275. Springer, Dordrecht


It was investigated the Boolean satisfiability (SAT) problem defined as follows: given a Boolean formula, check whether an assignment of Boolean values to the propositional variables in the formula exists, such that the formula evaluates to true. If such an assignment exists, the formula is said to be satisfiable; otherwise, it is unsatisfiable. With using of analytical expressions of multi-valued logic 2SAT boolean satisfiability was formulated as linear programming optimization problem. The same linear programming formulation was extended to find 3SAT and kSAT boolean satisfiability for k greater than 3. So, using new analytic multi-valued logic expressions and linear programming formulation of boolean satisfiability proposition that kSAT is in P and could be solved in linear time was proved.


Boolean satisfiability Conjunctive normal form Convex function Linear programming Multi-valued logic NP problem Time complexity. 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Vilnius Gediminas Technical UniversityVilniusLithuania

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