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| | In [[computational complexity]], the '''logarithmic time hierarchy''' ('''LH''') is the [[complexity class]] of all [[computational problem]]s solvable in a [[Logarithmic growth|logarithmic]] amount of [[computation time]] on an [[alternating Turing machine]] with a bounded number of alternations. It is a special case of the hierarchy of [[Alternating_Turing_machine#Bounded_alternation|bounded alternating Turing machine]]s. It is equal to [[FO (complexity)|FO]] and to FO-uniform [[AC0]].<ref>{{cite book | author=N. Immerman | title=Descriptive complexity | date=1999 | publisher=Springer | page=85}}</ref> |
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| | The <math>i</math>th level of the logarithmic time hierarchy is the set of languages recognised by alternating Turing machines in logarithmic time with [[Random-access Turing machine|random access]] and <math>i-1</math> alternations, beginning with an [[existential state]]. '''LH''' is the union of all levels. |
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| | == References == |
| | {{Reflist}} |
| | {{ComplexityClasses}} |
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| | [[Category:Complexity classes]] |
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| | {{Comp-sci-theory-stub}} |
Revision as of 21:44, 18 June 2013
In computational complexity, the logarithmic time hierarchy (LH) is the complexity class of all computational problems solvable in a logarithmic amount of computation time on an alternating Turing machine with a bounded number of alternations. It is a special case of the hierarchy of bounded alternating Turing machines. It is equal to FO and to FO-uniform AC0.[1]
The th level of the logarithmic time hierarchy is the set of languages recognised by alternating Turing machines in logarithmic time with random access and alternations, beginning with an existential state. LH is the union of all levels.
References
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