Definitions
NL consists of the decision problems that can be solved by a nondeterministic Turing machine with a read-only input tape and a separate read-write tape whose size is limited to be proportional to the logarithm of the input length. Similarly, L consists of the languages that can be solved by a deterministic Turing machine with the same assumptions about tape length. Because there are only a polynomial number of distinct configurations of these machines, both L and NL are subsets of the class P of deterministic polynomial-time decision problems.
Formally, a decision problem is NL-complete when it belongs to NL, and has the additional property that every other decision problem in NL can be reduced to it. Unless otherwise specified, the reductions in this definition are assumed to be many-one reductions by a deterministic logarithmic-space algorithm.
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