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L is a subclass of NL, which is the class of languages decidable in logarithmic space on a nondeterministic Turing machine.A problem in NL may be transformed into a problem of reachability in a directed graph representing states and state transitions of the nondeterministic machine, and the logarithmic space bound implies that this graph has a polynomial number of vertices and edges, from ...
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In computational complexity theory, a log-space computable function is a function : that requires only () memory to be computed (this restriction does not apply to the size of the output). The computation is generally done by means of a log-space transducer .
The top left graph is linear in the X- and Y-axes, and the Y-axis ranges from 0 to 10. A base-10 log scale is used for the Y-axis of the bottom left graph, and the Y-axis ranges from 0.1 to 1000. The top right graph uses a log-10 scale for just the X-axis, and the bottom right graph uses a log-10 scale for both the X axis and the Y-axis.
In computational complexity theory, a log space transducer (LST) is a type of Turing machine used for log-space reductions. A log space transducer, , has three tapes: A read-only input tape. A read/write work tape (bounded to at most () symbols). A write-only, write-once output tape.
NL is a generalization of L, the class for logspace problems on a deterministic Turing machine. Since any deterministic Turing machine is also a nondeterministic Turing machine, we have that L is contained in NL. NL can be formally defined in terms of the computational resource nondeterministic space (or NSPACE) as NL = NSPACE(log n).
If an NL-complete language X could belong to L, then so would every other language Y in NL.For, suppose (by NL-completeness) that there existed a deterministic logspace reduction r that maps an instance y of problem Y to an instance x of problem X, and also (by the assumption that X is in L) that there exists a deterministic logspace algorithm A for solving problem X.
Probabilistic logspace without a time limit [ edit ] If time is unlimited, the machines can run in expected exponential time — for example, keep a counter and increment it with probability 1 ⁄ 2 and zero it otherwise; halt when the counter overflows.