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New Model Characterizes Finite-State Symbolic Controllers with Dwell

Reda Belaiche· July 2, 2026 View original

Summary

This research introduces Destination-Labeled Self-Looping (DLSL) systems with dwell, a finite-state symbolic controller model for systems where visible transitions are fixed and states have minimum dwell requirements. It characterizes the deterministic transducers that arise from these systems, determines their realization cost, and provides an efficient recognition procedure.

This paper delves into the theoretical underpinnings of finite-state symbolic controllers, specifically focusing on systems where visible transitions are predetermined and each visible state mandates a minimum "dwell" time. This model, termed a Destination-Labeled Self-Looping (DLSL) system with dwell, captures the visible graph and local decision logic, with dwell memory manifesting after phase expansion. A core challenge addressed is that the current visible state alone doesn't dictate whether a departure is permitted once dwell is imposed. The research identifies precisely which deterministic transducers can be realized as phase-expanded versions of DLSL systems over a fixed visible graph, characterizing them as fiber-linear graph-respecting transducers. The study also establishes that equivalent accessible realizations over the same visible graph are isomorphic, meaning the visible transduction uniquely determines the dwell vector and local decision maps. Furthermore, it proves that any graph-preserving deterministic realization enforcing specific dwell values requires a number of control states equal to the sum of those dwell values, and provides an efficient algorithm for recognizing and reconstructing such systems.

Why it matters

This theoretical work provides a deeper understanding of control systems with timing constraints, which is fundamental for designing reliable and predictable autonomous systems, robotics, and embedded software where precise timing and state management are critical.

How to implement this in your domain

  1. 1Apply the theoretical characterizations to analyze the intrinsic properties of existing control systems with dwell requirements.
  2. 2Utilize the recognition procedure to identify if a given deterministic transducer can be realized as a DLSL system.
  3. 3Optimize the design of finite-state controllers by understanding the minimal control state requirements for specific dwell values.
  4. 4Inform the development of formal verification tools for systems where timing and state transitions are critical.

Who benefits

RoboticsAerospaceIndustrial AutomationEmbedded SystemsAutomotive

Key takeaways

  • DLSL systems model controllers with fixed visible transitions and minimum dwell times.
  • The research characterizes deterministic transducers arising from these systems.
  • It quantifies the realization cost, showing control states equal the sum of dwell values.
  • An efficient recognition and reconstruction procedure is provided for DLSL systems.

Original post by Reda Belaiche

"arXiv:2607.00044v1 Announce Type: cross Abstract: We study a finite-state symbolic controller for systems in which the admissible visible transitions are fixed in advance and each visible state carries a minimum dwell requirement. The resulting model, which we call a destination-…"

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