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Abstract: This article discusses completeness of Boolean Algebra as First Order Theoryin Goedels meaning. If Theory is complete then any possible transformation isequivalent to some transformation using axioms, predicates etc. defined forthis theory. If formula is to be proved or disproved then it has to bereduced to axioms. If every transformation is deducible then also optimaltransformation is deducible. If every transformation is exponential thenoptimal one is too, what allows to define lower bound for discussed problem tobe exponential outside P. Then we show algorithm for NDTM solving the sameproblem in On^c so problem is in NP, what proves that P eq NP.Article proves also that result of relativisation of P=NP question and oracleshown by Baker-Gill-Solovay distinguish between deterministic andnon-deterministic calculation models. If there exists oracle A for whichP^A=NP^A then A consists of infinite number of algorithms, DTMs, axioms andpredicates, or like NDTM infinite number of simultaneous states.

Author: Radoslaw Hofman


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