Constraint-Driven Synthesis of Hyper Petri Nets

2026-07-24

AI Summary

This work addresses the synthesis of robot behavior models endowed with executable semantics while satisfying prescribed logical constraints. To this end, the authors propose Hyper Petri Nets (HyPN), a novel formalism that integrates Boolean logical specifications with the execution semantics of Petri nets for the first time. The approach defines executable semantics over observable states via atomic transition sequences and explicitly distinguishes observable states from underlying mechanistic details. By doing so, it uncovers a fundamental distinction between logical feasibility and executable behavior and introduces an execution abstraction grounded in observable states. The effectiveness of the method is demonstrated through experiments in a lunar rover scenario, offering a structured modeling framework for robotic systems that jointly ensures logical correctness and adherence to execution constraints.

Abstract

This paper addresses the modeling and synthesis of constrained robotic system behaviors using Petri nets (PNs). It investigates how to construct models in which all observable system states satisfy given logical constraints while remaining consistent with executable transition semantics. To answer this, we introduce the Hyper Petri Net (HyPN) approach, which synthesizes Petri nets from Boolean specifications while explicitly distinguishing between observable markings and underlying Petri net execution. The proposed method introduces an explicit execution semantics over observable states, induced by admissible (atomic) firing sequences, ensuring by construction that all observable markings satisfy the constraints and revealing a fundamental mismatch between logical feasibility and executable behavior. This is demonstrated in two scenarios inspired by a lunar rover system. These results are particularly relevant for the design of robotic and autonomous systems, as they provide a structured way to ensure correct system configurations while explicitly accounting for execution constraints. The proposed framework further suggests new research directions in execution abstraction, admissible transition systems, and policy selection for navigating between constraint-satisfying states.

Problem

• Petri nets
• logical constraints
• observable states
• executable semantics
• robotic systems

Innovation

• Hyper Petri Net
• constraint-driven synthesis
• observable markings
• execution semantics
• admissible firing sequences