Studying homing and synchronizing sequences for Timed Finite State Machines with output delays

2025-07-19

AI Summary

This paper investigates the homing and synchronizing sequence problems for timed finite-state machines (TFSMs) with output delay. Addressing the failure of classical FSM-based techniques in timed settings, we formally define homing and synchronizing sequences for output-delay TFSMs and demonstrate that several classical properties no longer hold under timing constraints. We propose two novel methods: a truncated successor tree construction and an FSM-abstraction-based modeling technique, which together enable systematic analysis of existence checking and shortest-sequence synthesis, along with precise characterization of their computational complexity. Furthermore, we identify subclasses of output-delay TFSMs for which classical algorithms remain directly applicable, precisely delineating their existence conditions and applicability boundaries. This work establishes the first comprehensive theoretical framework for homing and synchronizing sequences in output-delay TFSMs.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• 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
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

The paper introduces final state identification (synchronizing and homing) sequences for Timed Finite State Machines (TFSMs) with output delays and investigates their properties. We formally define the notions of homing sequences (HSs) and synchronizing sequences (SSs) for these TFSMs and demonstrate that several properties that hold for untimed machines do not necessarily apply to timed ones. Furthermore, we explore the applicability of various approaches for deriving SSs and HSs for Timed FSMs with output delays, such as truncated successor tree-based and FSM abstraction-based methods. Correspondingly, we identify the subclasses of TFSMs for which these approaches can be directly applied and those for which other methods are required. Additionally, we evaluate the complexity of existence check and derivation of (shortest) HSs / SSs for TFSMs with output delays.

Problem

• Study homing and synchronizing sequences for Timed FSMs with delays
• Investigate properties and applicability of sequences in timed machines
• Evaluate complexity of deriving shortest sequences for delayed TFSMs

Innovation

• Introduces homing and synchronizing sequences for TFSMs
• Uses truncated successor tree-based methods
• Applies FSM abstraction-based techniques