In computational complexity theory, the complexity class FL is the set of function problems which can be solved by a deterministic Turing machine in a logarithmic amount of memory space.^[1] As in the definition of L, 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 from decision problems, which produce only Yes or No answers and corresponds to the set L of decision problems which can be solved in deterministic logspace. FL is a subset of FP, the set of function problems which can be solved in deterministic polynomial time.^[1]

FL is known to contain several natural problems, including arithmetic on numbers. Addition, subtraction and multiplication of two numbers are fairly simple, but achieving division is a far deeper problem which was open for decades.^[2][3]

Similarly one may define FNL, which has the same relation with NL as FNP has with NP.^[1]

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