In computational complexity theory, a log space transducer (LST) is a type of Turing machine used for log-space reductions. A log space transducer, M, has three tapes: M will be designed to compute a log-space computable function (where \Sigma is the alphabet of both the input and output tapes). If M is executed with w on its input tape, when the machine halts, it will have f(w) remaining on its output tape. A language is said to be log-space reducible to a language if there exists a log-space computable function f that will convert an input from problem A into an input to problem B in such a way that. This seems like a rather convoluted idea, but it has two useful properties that are desirable for a reduction: Transitivity holds because it is possible to feed the output tape of one reducer (A→B) to another (B→C). At first glance, this seems incorrect because the A→C reducer needs to store the output tape from the A→B reducer onto the work tape in order to feed it into the B→C reducer, but this is not true. Each time the B→C reducer needs to access its input tape, the A→C reducer can re-run the A→B reducer, and so the output of the A→B reducer never needs to be stored entirely at once.