Minimization of Streaming Transducers

2026-05-11

AI Summary

This study addresses the minimization problem for streaming transducers, proposing a general existence criterion applicable to various models, including sequential transducers and string-to-string/tree transducers. By leveraging formal language theory, automata theory, algebraic structures, and term rewriting systems, the work establishes the first unified minimization theory for a broad class of streaming transducers. Furthermore, it develops an effective and computable minimization algorithm tailored to a variant of string-to-tree transducers whose outputs are incrementally constructed terms. The results not only characterize universal conditions under which minimization is feasible but also enable efficient optimization for concrete transducer models, thereby significantly advancing both the formal theory and practical applicability of streaming transducers.

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 (Schützenberger), streaming string-to-string transducers (Alur-Černý), 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.

Problem

• streaming transducers
• minimization
• minimal models
• automata theory
• transducer equivalence

Innovation

• streaming transducers
• minimization
• incremental term construction
• abstract model
• effective algorithms