Derived-Term Automata of Multitape Expressions with Composition

Abstract

Rational expressions are powerful tools to define automata, but often restricted to single-tape automata. Our goal is to unleash their expressive power for transducers, and more generally, any multitape automaton; for instance (a + |x+b + |y) * . We generalize the construction of the derived-term automaton by using expansions. This approach generates small automata, and even allows us to support a composition operator.

Derived Terms Without Derivation a Shifted Perspective on the Derived-Term Automaton

“…It is noteworthy that other works that dealt with the derivation of expressions outside from the scope of the free monoid [8,12] have considered entities which are closed to ours. In particular, the differential of an expression is called the linear form in [12], and the sum of the differential and the constant term is the expansion in [8].…”

“…There are also been several attempts to apply the derivation techniques to expressions over non free monoids, namely direct products of free monoids, for dealing with rational relations. In [8], the extension is made through a new operator that represents the direct product of two languages (or relations), while in [12] the atoms of the expression, that are letters in the classical case, are replaced by pairs of letters or special symbols (expressing constraints over letters or pairs). The formalism used in both papers bears some similarities with ours, but they both use it to define an analogue of the derivation to bring the construction of the transducer back to the usual construction of the derived-term automaton.…”