In computational complexity theory, a leaf language is a method of characterizing a complexity class by formalizing what it means for a machine to "accept" an input.
Several complexity classes are typically defined in terms of a polynomial-time nondeterministic Turing machine, where each branch can either accept or reject, and the entire machine accepts or rejects as some function of the branches' conditions. For example, a non-deterministic Turing machine accepts if at least one branch accepts, and rejects only if all branches reject. A co-non-deterministic Turing machine, on the other hand, accepts only if all branches accept, and rejects if any branch rejects. Many classes can be defined in this fashion.
We can then formalize this by examining the formal language associated with each acceptance condition. We assume that the tree is ordered, and read the accept/reject strings off the leaves of the computation tree. For example, the nondeterministic machine will accept iff the leaf string is in the language {0, 1}*1{0, 1}*, and will reject iff the leaf string is in the language 0*.
Famous quotes containing the words leaf and/or language:
“The type of fig leaf which each culture employs to cover its social taboos offers a twofold description of its morality. It reveals that certain unacknowledged behavior exists and it suggests the form that such behavior takes.”
—Freda Adler (b. 1934)
“Both the Moral Majority, who are recycling medieval language to explain AIDS, and those ultra-leftists who attribute AIDS to some sort of conspiracy, have a clearly political analysis of the epidemic. But even if one attributes its cause to a microorganism rather than the wrath of God, or the workings of the CIA, it is clear that the way in which AIDS has been perceived, conceptualized, imagined, researched and financed makes this the most political of diseases.”
—Dennis Altman (b. 1943)