Transducers with Set Output

Abstract

We consider transducers with set output, i.e., finite state machines which produce a set of output symbols upon reading any input symbol. When a word consisting of input symbols is read, the union of corresponding output sets is produced. Such transducers are instrumental in some important data classification tasks, such as multi-field packet classification. Two transducers are called equivalent if they produce equal output upon reading any input word. In practical data classification applications, it is important to store in memory only one transducer of every equivalence class, in order to save memory space. This yields the need of finding, in any equivalence class, one transducer, called canonical which is easy to compute, given any transducer from this class. One of the results of this paper is the construction of an algorithm which completes this task. Assuming that the input and output alphabets are of bounded size, for a given n-state transducer T, our algorithm finds the canonical transducer Ψ(T) equivalent to T in time O(nlogn).