Efficient Construction of Reversible Transducers from Regular Transducer Expressions

The class of regular transformations has several equivalent characterizations such as functional MSO transductions, deterministic two-way transducers, streaming string transducers, as well as regular transducer expressions (RTE). For algorithmic applications, it is very common and useful to transform a specification, here, an RTE, to a machine, here, a transducer. In this paper, we give an efficient construction of a two-way reversible transducer (2RFT) equivalent to a given RTE. 2RFTs form a well behaved class of transducers which are deterministic and co-deterministic (hence allows evaluation in linear time w.r.t. the input word), and where composition has only polynomial complexity. As a significant complexity improvement over existing techniques, we give the first elementary procedure for translating RTEs to machines. For full RTE, the constructed 2RFT has size doubly exponential in the size of the expression. If the RTE does not use Hadamard product or chained-star, the constructed 2RFT has size exponential in the size of the RTE.