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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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A language is said to be log-space reducible to a language if there exists a log-space computable function that will convert an input from problem into an input to problem in such a way that (). This seems like a rather convoluted idea, but it has two useful properties that are desirable for a reduction:
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 constant 1/3 is arbitrary; any x with 0 ≤ x < 1/2 would suffice. It turns out that C = NL . Notice that C , unlike its deterministic counterpart L , is not limited to polynomial time, because although it has a polynomial number of configurations it can use randomness to escape an infinite loop.
[1] Comparing the number of accepting and rejecting paths can be done in PL as follows. Modify the graph to make all paths the same length and for each node to have at most two successors. Take a random path. For each node with just one successor, fail (output random answer) with probability 1 ⁄ 2. At the end, accept if we reached Accept node ...
In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means it can keep a constant number of pointers into the input, along with a logarithmic number of fixed-size integers . [ 1 ]
Specifically, a straight line on a log–log plot containing points (x 0, F 0) and (x 1, F 1) will have the function: = (/) (/), Of course, the inverse is true too: any function of the form = will have a straight line as its log–log graph representation, where the slope of the line is m.