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Boolean satisfiability problem has applications in various fields. Anefficient algorithm to solve satisfiability problem can be used to solve manyother problems efficiently. The input of satisfiability problem is a finite setof clauses. In this paper, properties of clauses have been studied. A type ofclauses have been defined, called fully populated clauses, which contains eachvariable exactly once. A relationship between two unequal fully populatedclauses has been defined, called sibling clauses. It has been found that, ifone fully populated clause is false, for a truth assignment, then all it'ssibling clauses will be true for the same truth assignment. Which leads to thenecessary and sufficient condition for satisfiability of a boolean formula, inCNF. The necessary and sufficient condition has been used to develop a novelalgorithm to solve boolean satisfiability problem in polynomial time, whichimplies, P equals NP. Further, some optimisations have been provided that canbe integrated with the algorithm for better performance.

Necessary and Sufficient Condition for Satisfiability of a Boolean Formula in CNF and its Implications on P versus NP problem