Petri Net Reachability Mapping for Real-Time State Analysis
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The complexity of reachability analysis in Petri Nets (PNs) leads to the state explosion problem, making it difficult to derive real-time reachability information for large systems, which limits the size of systems that can be modeled and hinders efficient resource allocation and deadlock avoidance in concurrent systems.
Innovation Solution
The Topological Reverse Mirroring (TRM) methodology allows for the derivation of closed-form formulas for Control-Related states in PNs by establishing a reversible one-to-one mapping between Gen-Right and Gen-Left networks, reducing the need for whole net structure analysis and enabling real-time reachability information based on current states.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional reachability analysis methods are used for Petri Nets, then system properties can be verified, but the state explosion problem occurs and computation time becomes prohibitively long for large systems
Solution Approach 1:
The patent segments the Petri net into two parts: a controlled part and a free-choice part. By dividing the net structure, the reachability analysis can be performed more efficiently on each segment separately, avoiding the need to analyze the entire state space of the large system at once. This segmentation reduces the computational complexity and time required while still verifying system properties.
Solution Approach 2:
The patent extracts and analyzes specific structural properties of the Petri net (such as siphons, traps, and invariants) rather than computing the complete reachability graph. By taking out and analyzing these critical substructures, the method verifies system properties without enumerating all possible states, thus avoiding the state explosion problem and reducing computation time.
2Measurement precision
If the complete reachability graph is computed, then all reachable states are identified, but the memory and computational resources required become excessive for very large systems
Solution Approach 1:
The controlled part and free-choice part are segmented and analyzed separately. The controlled part's structure is exploited to determine reachability without computing the complete state space. This segmentation allows precise reachability information to be obtained while significantly reducing memory and computational resource requirements.
Solution Approach 2:
The patent extracts key structural features (siphons, traps, invariants) from the Petri net to characterize reachability properties. By analyzing these extracted features rather than the complete state space, the method maintains measurement precision for reachability information while reducing device complexity and resource requirements.
3Productivity
If mixed integer programming is applied for system control, then optimization can be achieved, but the NP-hard characteristic limits the size of real-time systems that can be modeled
Solution Approach 1:
The patent segments the Petri net into controlled and free-choice parts, allowing optimization to be performed on the controlled part using structural analysis rather than full MIP. This segmentation enables system optimization capability while improving scalability to larger systems by avoiding the NP-hard complexity of applying MIP to the entire system.
Solution Approach 2:
The patent extracts and analyzes specific structural properties (siphons, traps, invariants) to enable optimization without requiring full MIP formulation. By taking out and analyzing these critical substructures, the method achieves system optimization capability while improving adaptability and scalability to larger real-time systems.
Data Source
AI summary
A method for analyzing reachability of a Petri net and deriving the control-related state of the PN extended from the kth variant closed-form formula (CFF) system for numbers, comprising by proving that the first system Gen-Right(k, gen) and the second system Gen_Left(k, k−gen) are topological inverse networks of Gen-Left(k, gen), the first system and the second system An invertible one-to-one mapping between; wherein the first series Gen-Right(k, gen) and Gen-Left(k, k−gen) have the same closed-form formula, and by putting Gen-Left(k, gen) in the verified closed-form formula The parameter gen can be obtained by replacing it with k−gen, and its corresponding reachability state can be directly obtained through a reversible one-to-one mapping.