On Streaming String Transducers and HDT0L Systems

TL;DR

This paper proves that streaming string transducers (SST) without the copyless restriction still have a decidable equivalence problem by reducing it to the HDT0L sequence equivalence problem, which is also decidable.

Contribution

It extends the decidability of the SST equivalence problem to the non-copyless case by linking it to the HDT0L sequence equivalence problem.

Findings

Decidable equivalence problem for non-copyless SSTs.

Reduction of SST equivalence to HDT0L sequence equivalence.

Equivalence complexity is linearly related between SSTs and HDT0L systems.

Abstract

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Cerny in 2010 as a one-way deterministic automata model to define transformations of finite strings. Copyless SST extend deterministic finite state automata with a set of registers in which to store intermediate output strings, and those registers can be combined and updated all along the run, in a linear manner, i.e., no register content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transformations, as defined by B. Courcelle, and are equi-expressive to deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace). In this paper, we show that they still have decidable equivalence problem even without the copyless restriction. The proof reduces to the HDT0L sequence equivalence problem, which is known to be decidable. We also show that this latter problem is as difficult as the SST equivalence problem, modulo linear time reduction.