Minimizing Streaming String Transducers: An algebraic approach

2026-04-13

AI Summary

This study addresses the minimization of states and registers in additive streaming string transducers (aSSTs) while preserving functional equivalence, thereby reducing resource consumption. By establishing a bijection between a subclass of aSSTs and bimachines, and introducing an asynchronous bimachine model that encompasses the entire class of aSSTs, the work reframes aSST minimization as a bimachine parameter optimization problem for the first time. The main contributions are twofold: first, a polynomial-time algorithm for register minimization within the aSST subclass; second, a proof that register minimization for the full class of aSSTs is NP-complete when the underlying automaton structure is fixed. The approach integrates techniques from algebraic automata theory, bimachine models, and rational function representations.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• streaming string transducers
• minimization
• bimachines
• registers
• states

Innovation

• streaming string transducers
• bimachines
• minimization
• asynchronous bimachines
• NP-completeness