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However, log-space reductions are probably weaker than polynomial-time reductions; while any non-empty, non-full language in P is polynomial-time reducible to any other non-empty, non-full language in P, a log-space reduction from an NL-complete language to a language in L, both of which would be languages in P, would imply the unlikely L = NL.
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:
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 ...
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 .
Semi-log plot of the Internet host count over time shown on a logarithmic scale. A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved.
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Together with its modest O(log n) space usage, quicksort is one of the most popular sorting algorithms and is available in many standard programming libraries. The important caveat about quicksort is that its worst-case performance is O( n 2 ); while this is rare, in naive implementations (choosing the first or last element as pivot) this ...
New details about a study that warned against black plastic spatulas and other kitchen tools have come out. (Getty Creative) (Анатолий Тушенцов via Getty Images)