Incomputational complexity theory, thecomplexity classFL is the set offunction problems that can be solved by adeterministic Turing machine in alogarithmic amount ofmemory space.[1] As in the definition ofL, the machine reads its input from a read-only tape and writes its output to a write-only tape; the logarithmic space restriction applies only to the read/write working tape.
Loosely speaking, a function problem takes a complicated input and produces a (perhaps equally) complicated output. Function problems are distinguished fromdecision problems, which produce only Yes or No answers. In this way,FL is distinguished from the setL ofdecision problems that can be solved in deterministic logspace.FL is a subset ofFP, the set of function problems that can be solved in deterministicpolynomial time.[1]
FL is known to contain several natural problems, including arithmetic on numbers. Addition, subtraction and multiplication of two numbers using logspace are fairly simple, but achieving division is a far deeper problem which was open for decades.[2][3]
Similarly one may defineFNL, which has the same relation withNL asFNP has withNP.[1]
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