Two Parsing Algorithms by Means of Finite State Transducers

We present a new approach, illustrated by two algorithms, for parsing not only Finite State Grammars but also Context Free Grammars and their extension, by means of finite state machines. The basis is the computation of a fixed point of a finite-state function, i.e. a finite-state transducer. Using these techniques, we have built a program that parses French sentences with a grammar of more than 200,000 lexical rules with a typical response time of less than a second. The first algorithm computes a fixed point of a non-deterministic finite-state transducer and the second computes a fixed point of a deterministic bidirectional device called a bimachine. These two algorithms point out a new connection between the theory of parsing and the theory of representation of rational transductions.