Union-Theorem

Union-Theorem

Das Union-Theorem ist ein Ergebnis aus der Frühzeit der Forschung zur Komplexitätstheorie. Es geht auf eine Veröffentlichung von Ed McCreight und Albert Meyer aus dem Jahr 1969 zurück und sagt Folgendes aus: Ist eine Liste von Zeitschranken t1,t2,... mit t_{i+1} \ge t_i für alle i gegeben, so existiert eine Zeitschranke t, so dass ein Problem genau dann in Zeit t berechenbar ist, wenn es für irgendein ti berechenbar ist. Das Theorem lässt sich insbesondere zur Bildung von Komplexitätsklassen einsetzen und bildet damit eine der Grundlagen zur Formulierung der Hierarchiesätze. Beispielsweise folgt aus dem Theorem, dass Funktionen, die deterministisch in Polynomialzeit berechenbar sind, eine Komplexitätsklasse bilden.


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