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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, there are problems that can be solved with n2 time but not n time, where n is the input length.

Consequences, Overview & Sharper hierarchy theorems

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Overview

Background

Proof overview

Deterministic time hierarchy theorem

Non-deterministic time hierarchy theorem

Consequences

Sharper hierarchy theorems

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Time hierarchy theorem

Nodes42
Edges41
Triples10
Avg. degree1.95
Density0.047619
Components1

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Time hierarchy theorem

Top relations

related to Consequences · 9
Time hierarchy theorem → DTIME, EXP, EXPTIME, For, Indeed, NEXP, NEXPTIME, NP, The

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Important terminology

time hierarchy theorem displaystyle turing machine deterministic mathsf complexity class machines dtime theorems time-constructible problems proof subsetneq left right function

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
2ninstance ofas are exponential functions0.80text
Time hierarchy theoremrelated to ConsequencesThe0.60section
Time hierarchy theoremrelated to ConsequencesEXPTIME0.60section
Time hierarchy theoremrelated to ConsequencesEXP0.60section
Time hierarchy theoremrelated to ConsequencesNP0.60section
Time hierarchy theoremrelated to ConsequencesNEXPTIME0.60section
Time hierarchy theoremrelated to ConsequencesNEXP0.60section
Time hierarchy theoremrelated to ConsequencesFor0.60section
Time hierarchy theoremrelated to ConsequencesDTIME0.60section
Time hierarchy theoremrelated to ConsequencesIndeed0.60section

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