hierarchy theorem造句

• The analogous theorems for space are the space hierarchy theorems.
• The second follows simply from the space hierarchy theorem.
• The space hierarchy theorems rely on the concept of space-constructible functions.
• The time and space hierarchy theorems form the basis for most separation results of complexity classes.
• In fact, by the time hierarchy theorem, they cannot be solved in significantly less than exponential time.
• The deterministic and nondeterministic space hierarchy theorems state that for all space-constructible functions " f " ( " n " ),
• The first follows from direct diagonalization ( the space hierarchy theorem, NL ?" NPSPACE ) and the fact that PSPACE NPSPACE via Savitch's theorem.
• For instance, the time hierarchy theorem tells us that P is strictly contained in EXPTIME, and the space hierarchy theorem tells us that L is strictly contained in PSPACE.
• For instance, the time hierarchy theorem tells us that P is strictly contained in EXPTIME, and the space hierarchy theorem tells us that L is strictly contained in PSPACE.
• Because of the time hierarchy theorem, these classes form a strict hierarchy; we know that \ mathrm { P } \ subsetneq \ mathrm { EXPTIME }, and on up.
• The proof is similar to the proof of the space hierarchy theorem, but with two complications : The universal Turing machine has to be space-efficient, and the reversal has to be space-efficient.
• He is best known for his Turing-award winning paper with Richard Stearns, in which he introduced time complexity classes " TIME ( f ( n ) ) " and proved the time hierarchy theorem.
• Proves that ACC 0 does not contain NEXPTIME . The proof uses many results in complexity theory, including the time hierarchy theorem, IP = PSPACE, derandomization, and the representation of ACC 0 via SYM + circuits.
• Indeed, whereas the time hierarchy theorem has seen little remarkable improvement since its inception, the nondeterministic space hierarchy theorem has seen at least one important improvement by Viliam Geffert in his 2003 paper " Space hierarchy theorem revised ".
• Indeed, whereas the time hierarchy theorem has seen little remarkable improvement since its inception, the nondeterministic space hierarchy theorem has seen at least one important improvement by Viliam Geffert in his 2003 paper " Space hierarchy theorem revised ".
• Indeed, whereas the time hierarchy theorem has seen little remarkable improvement since its inception, the nondeterministic space hierarchy theorem has seen at least one important improvement by Viliam Geffert in his 2003 paper " Space hierarchy theorem revised ".
• Because the bound may be very large ( and often will be nonconstructible ) the Gap Theorem does not imply anything interesting for complexity classes such as P or NP, and it does not contradict the time hierarchy theorem or space hierarchy theorem.
• Because the bound may be very large ( and often will be nonconstructible ) the Gap Theorem does not imply anything interesting for complexity classes such as P or NP, and it does not contradict the time hierarchy theorem or space hierarchy theorem.
• The beginning of systematic studies in computational complexity is attributed to the seminal 1965 paper " On the Computational Complexity of Algorithms " by Juris Hartmanis and Richard E . Stearns, which laid out the definitions of time complexity and space complexity, and proved the hierarchy theorems.
• The PSPACE-complete problems are widely suspected to be outside the more famous complexity classes "'NC "'( a class of problems with highly efficient parallel algorithms ), because problems in "'NC "'can be solved in an amount of space polynomial in the logarithm of the input size, and the class of problems solvable in such a small amount of space is strictly contained in "'PSPACE "'by the space hierarchy theorem.