  This paper presents a complete algorithmic study of the decision Boolean
Satisfiability Problem under the classical computation and quantum computation
theories. The paper depicts deterministic and probabilistic algorithms,
propositions of their properties and the main result is that the problem has
not an efficient algorithm (NP is not P). Novel quantum algorithms and
propositions depict that the complexity by quantum computation approach for
solving the Boolean Satisfiability Problem or any NP problem is lineal time.
