The Matiyasevich/MRDP Theorem relates two notions:one from computability theory, the other from number theory, thus Turing Machine and algorithms finding integral solution to algebraic equations can be regarded as equal. Therefore, the hardness for finding integral solution to algebraic equations and computational complexity are related, we can charactorize computational complexity based on finding solution to algebraic equations, any reference for this idea?
closed as unclear what you're asking by D.W., Jan Johannsen, Kaveh, András Salamon, Emil Jeřábek Feb 7 '18 at 16:59
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