Scaling GR(1) Synthesis via a Compositional Framework for LTL Discrete Event Control

2025-06-19

AI Summary

To address the state-explosion problem in Linear Temporal Logic (LTL) controller synthesis for discrete-event systems, this paper proposes a compositional control synthesis method based on modular plant structure. The approach innovatively integrates observation-equivalence abstraction with an iterative weak-control solving framework, decomposing a global GR(1) specification into distributed safety subproblems solvable in parallel. These subproblems are modeled as labeled transition systems (LTS) and implemented using the MTSA tool. Compared to monolithic synthesis, the proposed method scales up problem size by up to three orders of magnitude while guaranteeing maximally permissive safe controllers. Key contributions include: (1) a modular divide-and-conquer mechanism mitigating state explosion; (2) an abstraction-refinement workflow driven by observation equivalence; and (3) a distributed controller construction paradigm supporting parallel execution, significantly enhancing scalability and engineering applicability.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Distributed Problem Solving

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We present a compositional approach to controller synthesis of discrete event system controllers with linear temporal logic (LTL) goals. We exploit the modular structure of the plant to be controlled, given as a set of labelled transition systems (LTS), to mitigate state explosion that monolithic approaches to synthesis are prone to. Maximally permissive safe controllers are iteratively built for subsets of the plant LTSs by solving weaker control problems. Observational synthesis equivalence is used to reduce the size of the controlled subset of the plant by abstracting away local events. The result of synthesis is also compositional, a set of controllers that when run in parallel ensure the LTL goal. We implement synthesis in the MTSA tool for an expressive subset of LTL, GR(1), and show it computes solutions to that can be up to 1000 times larger than those that the monolithic approach can solve.

Problem

• Mitigate state explosion in discrete event control synthesis
• Compositionally build safe controllers for LTL goals
• Scale GR(1) synthesis via modular plant structure

Innovation

• Compositional approach for LTL control synthesis
• Modular structure mitigates state explosion
• Observational synthesis equivalence reduces plant size