Abstract
Micro-scale Cyber-Physical Systems (MCPSs) can be automatically and formally estimated by probabilistic model checking, on the level of system model MDPs (Markov Decision Processes) against desired requirements in PCTL (Probabilistic Computation Tree Logic). The counterexamples in probabilistic model checking are witnesses of requirements violation, which can provide the meaningful information for debugging, control, and synthesis of MCPSs. Solving the smallest counterexample for probabilistic model checking MDP has been proven to be an NPC (Non-deterministic Polynomial complete) problem. Although some heuristic methods are designed for this, it is usually difficult to fix the heuristic functions. In this paper, the Genetic algorithm optimized with heuristic, i.e., the heuristic Genetic algorithm, is firstly proposed to generate a counterexample for the probabilistic model checking MDP model of MCPSs. The diagnostic subgraph serves as a compact counterexample, and diagnostic paths of MDP constitute an AND/OR tree for constructing a diagnostic subgraph. Indirect path coding of the Genetic algorithm is used to extend the search range of the state space, and a heuristic crossover operator is used to generate more effective diagnostic paths. A prototype tool based on the probabilistic model checker PAT is developed, and some cases (dynamic power management and some communication protocols) are used to illustrate its feasibility and efficiency.
Highlights
Micro-scale Cyber-Physical Systems (MCPSs) are a special kind of CPS in micromachines, which are composed of micro/nanoscale components, and the integration of computation with physical processes in micro-/nano-assembly operations
We divide the existing works into two kinds of bound. It cannot be generated during the process of probabilistic model checking and methods for generating a counterexample in probabilistic model checking: the accurate needs the dedicated algorithm [17]
Compared with the existing works, we can see that HGA can generate a counterexample effectively for all 4 cases, even if the Eppstein algorithm, XUZ algorithm, and Genetic algorithm cannot get the counterexample for large state space of MCPSs, which are noted as “failed” in the corresponding tables
Summary
Micro-scale Cyber-Physical Systems (MCPSs) are a special kind of CPS in micromachines, which are composed of micro/nanoscale components, and the integration of computation with physical processes in micro-/nano-assembly operations. The achieved requirement properties, e.g., function, reliability, robust, etc., are specified by PCTL (Probabilistic Computation Tree Logic), LTL (Liner Temporal logic) with probability bounds, Micromachines 2021, 12, 1059. Etc., are specified by PCTL (Probabilistic Computation Tree Logic), LTL In this way, we canLogic) express logic) with probability bounds, PTCTL There are two dimensions adapt the probabilistic model extending system models, temporal logics, and corresponding algorithms to verify logics, more checking to estimate MCPSs: (1) horizontal, extending system models, temporal complex behaviors of MCPSs;. Better performance for verifying a certain part of MCPSs deeply This to the vertical dimension, whichwhich propose a counterexample generaThiswork workbelongs belongs to the vertical dimension, propose a counterexample tion method for probabilistic model checking. How confidentiality of systems can be broken, and the quality assurance of multi-agent systems [16]
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