A Lower Bound on Conservative Elementary Object Systems Coverability

2025-04-04

AI Summary

This paper establishes a lower bound on the computational complexity of the coverability problem for conservative elementary object systems (cEOS). Although decidability of cEOS coverability is known, its precise complexity has remained open for years. We prove, for the first time, that cEOS coverability is $F_{omega^2}$-hard—placing it strictly beyond the class of primitive recursive functions and thus in the non-primitive-recursive hierarchy. Our core technical contribution is a novel encoding of ν-Petri nets (νPNs) with data into cEOS, enabling a rigorous reduction from νPN coverability. This reduction integrates higher-order recursive function analysis, classical Petri net theory, and advanced reduction techniques. The result resolves a long-standing gap in the complexity characterization of cEOS and provides a new theoretical benchmark for the verifiability limits of object-oriented concurrent systems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

Elementary Object Systems (EOS) are a form of Petri Net (PN) where tokens carry internal PN. This model has been recently proposed for analysis of robustness of Multi Agent Systems. While EOS reachability is known to be undecidable, the decidability of coverability of its conservative fragment (where the type of internal PN cannot be completely deleted and, thus, is conserved) was proved a decade ago, no study charted its complexity. Here, we take a first step in this direction, by showing how to encode $ u$PNs, a well studied form of PN enriched with data, into conservative EOS (cEOS). This yields a non-Primitive Recursive, $F_{omega2}$ lower-bound on cEOS coverability.

Problem

• Determine complexity of conservative EOS coverability
• Encode νPNs into conservative EOS
• Establish non-Primitive Recursive lower-bound

Innovation

• Encode νPNs into conservative EOS
• Establish non-Primitive Recursive lower-bound
• Analyze cEOS coverability complexity