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hierarchy theorem

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  • Space hierarchy theorem — In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more space, subject to certain conditions. For… …   Wikipedia

  • Time hierarchy theorem — In computational complexity theory, the time hierarchy theorems are important statements about time bounded computation on Turing machines. Informally, these theorems say that given more time, a Turing machine can solve more problems. For example …   Wikipedia

  • Hierarchy problem — In theoretical physics, a hierarchy problem occurs when the fundamental parameters (couplings or masses) of some Lagrangian are vastly different (usually larger) than the parameters measured by experiment. This can happen because measured… …   Wikipedia

  • Exponential hierarchy — In computational complexity theory, the exponential hierarchy is a hierarchy of complexity classes, starting with EXP:: m{EXP} = igcup {kinmathbb{N mbox{DTIME}left(2^{n^k} ight)and continuing with: m{2EXP} = igcup {kinmathbb{N… …   Wikipedia

  • Post's theorem — In computability theory Post s theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. Background The statement of Post s theorem requires several concepts relating to definability and… …   Wikipedia

  • Tarski's undefinability theorem — Tarski s undefinability theorem, stated and proved by Alfred Tarski in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that arithmetical truth… …   Wikipedia

  • Borel determinacy theorem — In descriptive set theory, the Borel determinacy theorem shows that any Gale Stewart game whose winning set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. It was proved by Donald A.… …   Wikipedia

  • Sipser-Lautemann theorem — In computational complexity theory, the Sipser Lautemann theorem or Sipser Gács Lautemann theorem states that BPP (Bounded error Probablistic Polynomial) time, is contained in the polynomial time hierarchy, and more specifically Sigma;2 cap; Pi;2 …   Wikipedia

  • Prime number theorem — PNT redirects here. For other uses, see PNT (disambiguation). In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are… …   Wikipedia

  • Toda's theorem — The Toda s Theorem was proven by Seinosuke Toda in his paper PP is as Hard as the Polynomial Time Hierarchy (1991) and was given 1998 Gödel Prize. The theorem considers solution counting for polynomial problem class PP and polynomial hierarchy PH …   Wikipedia

  • Arithmetical hierarchy — In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical. The… …   Wikipedia

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