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accepts algorithm analysis applied assignment assume asymptotic attribute binary bounded called complexity component computation configuration consider consists construction contains Corollary correctness corresponding counting database decision defined definition denoted dependencies deterministic distributed elements equal equivalent example execution exists expressions extended fact finite first-order fixed formal formula function given global graph holds Horn implication initial input integer labelled language least lemma length logic machine means messages method natural nodes Note notion obtained operator parallel partial particular permutations polynomial positive predicate presented problem procedure proof properties propositional prove random recursive reduced relation requirements respectively restriction ring rule satisfies schema Science semantics sequence steps strings structures subset Suppose symbol terminate Theorem theory tree tuple Turing universal variables