Minimizing Streaming String Transducers: An algebraic approach

TL;DR

This paper presents an algebraic approach to minimize streaming string transducers by leveraging bimachines, providing polynomial-time algorithms for certain subclasses and proving NP-completeness for general cases.

Contribution

It introduces a novel algebraic framework connecting aSST and bimachines, enabling efficient minimization and establishing complexity results.

Findings

Polynomial-time minimization for a subclass of aSST

Introduction of asynchronous bimachines for full aSST class

NP-completeness of register minimization with fixed automaton

Abstract

In this work, we study minimization of rational functions given as appending streaming string transducers (aSST for short). We rely on an algebraic presentation of these functions, known as bimachines, to address the minimization of both states and registers of aSST. First, we show a bijection between a subclass of aSST and bimachines, which maps the numbers of states and registers of the aSST to two natural parameters of the bimachine. Using known results on the minimization of bimachines, this yields a Ptime (resp. NP) procedure to minimize this subclass of aSST with respect to registers (resp. both states and registers). In a second step, we introduce a new model of bimachines, named asynchronous bimachines, which allows to lift the bijection to the whole class of aSST. Based on this, we prove that register minimization with a fixed underlying automaton is NP-complete.