LH (complexity)

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 particular case of a bounded alternating Turing machine hierarchy. It is equal to FO and to FO-uniform AC⁰.{{cite book | author=Neil Immerman | title= Descriptive Complexity|title-link= Descriptive Complexity | date=1999 | publisher=Springer | page=[https://archive.org/details/descriptivecompl00imme_115/page/n96 85]}}

The $i$th level of the logarithmic time hierarchy is the set of languages recognised by alternating Turing machines in logarithmic time with random access and $i-1$ alternations, beginning with an existential state. LH is the union of all levels.