In computational complexity theory, the complexity class FL is the set of function problems that 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. In this way, FL is distinguished from the set L of decision problems that can be solved in deterministic logspace. FL is a subset of FP , the set of function problems that 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 using logspace 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]