Derived-Term Automata of Multitape Rational Expressions

Abstract

We consider (weighted) rational expressions to denote series over Cartesian products of monoids. We define an operator | to build multitape expressions such as (a + | x + b + | y) * . We introduce expansions, which generalize the concept of derivative of a rational expression, but relieved from the need of a free monoid. We propose an algorithm based on expansions to build multitape automata from multitape expressions. Changes:2016-07-25 Appendix A.4 was added, showing how to compute the constant term and the derivatives for the tuple operator. Sect. 5 was adapted accordingly.

Regular Expressions and Transducers over Alphabet-Invariant and User-Defined Labels

“…Champarnaud and Ziadi [10] proved that the two formulations are equivalent. Lombardy and Sakarovitch [16] generalised these constructions to weighted regular expressions, and recently Demaille [12] defined derivative automata for multitape weighted regular expressions.…”

“…Not only they are in general more succinct than other equivalent constructions but also for several operators they are easily defined (e.g. for intersection [4] or tuples [12]). The partial derivative automaton of a regular expression over Σ ⋆ was introduced independently by Mirkin [18] and Antimirov [3].…”

Derived-Term Automata of Multitape Expressions with Composition

“…To compute the edit-distance between words and/or (rational) languages, Mohri [20, Figure 4] introduces the following two-tape automaton (aka transducer) A, whose weights, written in angle brackets, are in N, min, + : 0 0 0 a|a, 0 b|b, 1 ε|a, 1 ε|b, 1 a|ε, 1 b|ε Ng [21, Figure 2] focuses on the prefix distance and introduces A : * Extended version of Derived-term automata of multitape rational expressions, presented at CIAA'16 [9].…”