Minimization of Streaming Transducers

TL;DR

This paper establishes criteria for minimal models of streaming transducers, unifying various models and providing effective minimization results for specific variants.

Contribution

It introduces general criteria for minimality in streaming transducers and applies them to obtain minimization results for models with incremental output construction.

Findings

Criteria for minimal models of streaming transducers are provided.

Effective minimization algorithms are developed for certain output-constructing variants.

The framework unifies classical and modern streaming transducer models.

Abstract

We provide general criteria for the existence of minimal models of streaming transducers, namely devices that read an input word and produce an output value by iteratively updating an internal memory. This abstract model subsumes classical (sub)sequential transducers (Sch\"utzenberger), streaming string-to-string transducers (Alur-\v{C}ern\'y), polynomial automata (Benedikt et al.), and variants of streaming string-to-tree transducers (Alur-D'Antoni). We then instantiate these criteria to obtain effective minimization results for variants of the latter model, where outputs are terms constructed incrementally by extending (tuples of) terms either at the leaves or at the roots.