Team collaboration-oriented multi-agent pathfinding and probabilistic verification

The model-checking approach was originally formulated for verifying qualitative properties of systems, for example safety and liveness (see Chap. 2), and subsequently extended to also handle quantitative features, such as real time (see Chap. 29), continuous flows (see Chap. 30), as well as stochastic phenomena, where system evolution is governed by a given probability distribution. Probabilistic model checking aims to establish the correctness of probabilistic system models against quantitative probabilistic specifications, such as those capable of expressing, for example, the probability of an unsafe event occurring, expected time to termination, or expected power consumption in the start-up phase. In this chapter, we present the foundations of probabilistic model checking, focusing on finite-state Markov decision processes as models and quantitative properties expressed in probabilistic temporal logic. Markov decision processes can be thought of as a probabilistic variant of labelled transition systems in the following sense: transitions are labelled with actions, which can be chosen nondeterministically, and successor states for the chosen action are specified by means of discrete probabilistic distributions, thus specifying the probability of transiting to each successor state. To reason about expectations, we additionally annotate Markov decision processes with quantitative costs, which are incurred upon taking the selected action from a given state. Quantitative properties are expressed as formulas of the probabilistic computation tree logic (PCTL) or using linear temporal logic (LTL). We summarise the main model-checking algorithms for both PCTL and LTL, and illustrate their working through examples. The chapter ends with a brief overview of extensions to more expressive models and temporal logics, existing probabilistic model-checking tool support, and main application domains.

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.

As an important kind of DNN (deep neural network), CNN (convolutional neural network) has made remarkable progress and been widely used in the vision and decision-making of autonomous robots. Nonetheless, in many scenarios, even a minor perturbation in input for CNNs may lead to serious errors, which means CNNs lack robustness. Formal verification is an effective method to guarantee the robustness of CNNs. Existing works predominantly concentrate on local robustness verification, which requires considerable time and space. Probabilistic robustness quantifies the robustness of CNNs, which is a practical mode of potential measurement. The state-of-the-art of probabilistic robustness verification is a test-driven approach, which is used to manually decide whether a DNN satisfies the probabilistic robustness and does not involve robustness repair. Robustness repair can improve the robustness of CNNs further. To address this issue, we propose a probabilistic model checking-driven robustness guarantee framework for CNNs, i.e., PRG4CNN. This is the first automated and complete framework for guaranteeing the probabilistic robustness of CNNs. It comprises four steps, as follows: (1) modeling a CNN as an MDP (Markov decision processes) by model learning, (2) specifying the probabilistic robustness of the CNN via the PCTL (Probabilistic Computational Tree Logic) formula, (3) verifying the probabilistic robustness with a probabilistic model checker, and (4) probabilistic robustness repair by counterexample-guided sensitivity analysis, if probabilistic robustness does not hold on the CNN. We here conduct experiments on various scales of CNNs trained on the handwriting dataset MNIST, and demonstrate the effectiveness of PRG4CNN.

Model-driven engineering refers to a range of approaches that uses models throughout systems and software development life cycle. Towards sustaining such a successful approach in practice, we present a model-based verification framework that supports the quantitative and qualitative analysis of SysML activity diagrams. To this end, we propose an algorithm that maps SysML activity diagrams into Markov decision processes expressed using the language of the probabilistic symbolic model checker PRISM. Furthermore, we elaborate on the correctness of our translation algorithm by proving its soundness with respect to a SysML activity diagrams operational semantics that we also present in this work. The generated models can be verified against a set of properties expressed in the probabilistic computation tree logic. To automate our approach, we developed a prototype tool that interfaces a modeling environment and the probabilistic model checker. We also show how to leverage adversary generation to provide the developer with a useful counterexample/witness as a feedback on the verified properties. Finally, the established theoretical foundations are complemented with an illustrative case study that demonstrates the usability and benefit of such a framework.

This study proposes a hierarchical probabilistic computation tree logic, HpCTL, which is an extension of the standard probabilistic computation tree logic pCTL, as a theoretical basis for hierarchical probabilistic CTL model checking. Hierarchical probabilistic model checking is a new paradigm that can appropriately verify hierarchical randomized (or stochastic) systems. Furthermore, a probability-measure-independent translation from HpCTL into pCTL is defined, and a theorem for embedding HpCTL into pCTL is proved using this translation. Finally, the relative decidability of HpCTL with respect to pCTL is proved using this embedding theorem. These embedding and relative decidability results allow us to reuse the standard pCTL-based probabilistic model checking algorithms to verify hierarchical randomized systems that can be described using HpCTL.

With the rapid development of IoT in recent years, Smart Home, one of the IoT application markets, has also been gaining popularity. The emergence of Smart Homes has brought convenience to people’s lives, especially for people who live alone with physical illness. Smart Home users normally have higher expectations for reliability and safety of sensor systems, particularly in light of how complicated and uncertain the living environment is. The present work attempts to propose a data-knowledge integrated solution to analyze, model and evaluate the reliability of sensor systems in a smart home by combining quantitative reliability analysis and probabilistic model checking. Probabilistic model checking techniques use logical reasoning to check quantitative properties (as system requirements) and provide mathematical guarantee for them. More specifically, Smart Home Sensor Systems (SHSS) is described as a Markov Chain, commonly used probabilistic model, which models the system behaviour (e.g., probabilistic choice of state transition), and SHSS reliability properties are defined by Probabilistic Computation Tree Logic (PCTL). These choices of model and specification formula allow us to use one of the most recently developed open source probabilistic model checkers, PRISM, to perform the model checking of reliability verification task in SHSS. A real world smart home dataset (Van Kasteren dataset) is employed along with PRISM to illustrate the modeling approach and demonstrate the feasibility and applicability of the proposed approach.

Solving Multi-Agent Path Finding (MAPF) instances optimally is NP-hard, and existing optimal and bounded suboptimal MAPF solvers thus usually do not scale to large MAPF instances. Greedy MAPF solvers scale to large MAPF instances, but their solution qualities are often bad. In this paper, we therefore propose a novel MAPF solver, Hierarchical Multi-Agent Path Planner (HMAPP), which creates a spatial hierarchy by partitioning the environment into multiple regions and decomposes a MAPF instance into smaller MAPF sub-instances for each region. For each sub-instance, it uses a bounded-suboptimal MAPF solver to solve it with good solution quality. Our experimental results show that HMAPP is able to solve as large MAPF instances as greedy MAPF solvers while achieving better solution qualities on various maps.

TCP (transportation control protocol) is widely used for supporting communications between robotic nodes with ROS (robotic operation system) for critical-task implementation. The probability of bit errors and lost packets is much higher for moving nodes under WLAN. So it is essential to analyze the performance and the reliability of the communication processes for nodes with ROS. It is built that the communication model of nodes for TCP in ROS by MDP(Markov Decision Process) and the reliability of that is analyzed in this paper. The Specifications of the TCP for nodes communication is formalized into the objective properties by PCTL(Probabilistic Computation Tree Logic), and the satisfiability of the properties is verified by the probabilistic model checker. The results can help the designers to make better strategies for the communication process over TCP in ROS of robotic nodes.

In this paper, a probabilistic model checking method for mobile robots path planning problem is proposed. Since surroundings always affect the behavior of mobile robots, four main environmental factors are analyzed as influencing parameters. With the map built by randomized sampling-based method, we model the uncertain motion behavior as a Markov Decision Process (MDP). Meanwhile, the properties are described in PCTL (Probabilistic Computation Tree Logic) which can be used to describe rich mission specifications. Then the path planning problem is mapped to the problem of generating an MDP control policy that maximizes the probability of accomplishing the mission objective satisfied a PCTL formula. We apply the PRISM platform to analyze model and verify properties. Our approach is demonstrated with illustrative case studies.

According to our survey about the express delivery from hundreds of campuses, we find that the location of commodity storage places impacts the delivery success rate and service quality. Thus, how to select the proper delivery location is vital to logistics enterprises, which contributes to improve the work efficiency and reduce delivery costs. In this paper, probabilistic model checking is used to verify the delivery fetch system, which evaluates the solution of location distributions in a quantitative way. First, it formalizes the fetch process of express delivery system between business and customer in the form of Discrete-Time Markov Chain (DTMC) when considering the stochastic behavior. Second, Probabilistic Computation Tree Logic (PCTL) is introduced as the verification property to the temporal behavior checking. Third, formal verifications are conducted by the supporting tool PRISM concerning on the transition probabilities computing. Furthermore, verification results are proven to follow the law of Bernouli Large Numbers, which aims to illustrate that the simulation result is close to the actual express delivery situation. Fourth, the express delivery location model is extended as new structure Co-DTMC in order to calculate time consumption and cost consumption, where the punishment factor is designed for the purpose of optimization. Finally, experiments are carried out to show that our approach can effectively select an optimal place for express delivery, which provides an alternative solution to integrate time and cost into the location selection.

In model checking, a counterexample is considered as a valuable tool for debugging. In Probabilistic Model Checking (PMC), counterexample generation has a quantitative aspect. The counterexample in PMC is a set of paths in which a path formula holds, and their accumulative probability mass violates the probability threshold. However, understanding the counterexample is not an easy task. In this paper we address the task of counterexample analysis for Markov Decision Processes (MDPs). We propose an aided-diagnostic method for probabilistic counterexamples based on the notions of causality, responsibility and blame. Given a counterexample for a Probabilistic CTL (PCTL) formula that does not hold over an MDP model, this method guides the user to the most relevant parts of the model that led to the violation.

Model checking can tell us whether a system is correct; probabilistic model checking can also tell us whether a system is timely and reliable. Moreover, probabilistic model checking allows one to verify properties that may not be true with probability one, but may still hold with an acceptable probability. The challenge in developing a probabilistic model checker able to handle realistic systems is the construction of the state space and the necessity to solve huge systems of linear equations. To address this problem, we have developed ProbVerus, a tool for the formal verification of probabilistic real-time systems. ProbVerus is an implementation of probabilistic computation tree logic (PCTL) model checking using symbolic techniques. We present ProbVerus, demonstrate its use with a simple manufacturing example, and report the current status of the tool. With ProbVerus, we have been able to analyze, within minutes, the safety logic of a railway interlocking controller with 1027 states.KeywordsModel CheckTransition Probability MatrixFormal VerificationAtomic PropositionBinary Decision DiagramThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The standard OMG/INCOSE SysML activity diagrams are behavioral models for specifying and analyzing probabilistic systems. In this paper, we present a formal verification framework for these diagrams that helps to mitigate the state-explosion problem in probabilistic model checking. To do so, we propose to reduce the size of SysML activity diagrams by eliminating and merging precise behaviors. The resulting model is checked using Probabilistic Computation Tree Logic (PCTL) properties. Moreover, we present a calculus for SysML activity diagrams (NuAC) that captures their underlying semantics. In addition, we prove the soundness of our approach by defining a probabilistic weak simulation relation between the semantics of the abstract and the concrete models. This relation is shown to preserve the satisfaction of the PCTL properties. Finally, we demonstrate the effectiveness of our approach on an online shopping system case study.

Recent works have made significant progress in multi-agent path finding (MAPF), with modern methods being able to scale to hundreds of agents, handle unexpected delays, work in groups, etc. The vast majority of these methods have focused on 2D "grid world" domains. However, modern warehouses often utilize multi-agent robotic systems that can move in 3D, enabling dense storage but resulting in a more complex multi-agent planning problem. Motivated by this, we introduce and experimentally analyze the application of MAPF to 3D warehouse management, and release the first (see http://mapf.info/index.php/Main/Benchmarks) open-source 3D MAPF dataset. We benchmark two state-of-the-art MAPF methods, EECBS and MAPF-LNS2, and show how different hyper-parameters affect these methods across various 3D MAPF problems. We also investigate how the warehouse structure itself affects MAPF performance. Based on our experimental analysis, we find that a fast low-level search is critical for 3D MAPF, EECBS's suboptimality significantly changes the effect of certain CBS techniques, and certain warehouse designs can noticeably influence MAPF scalability and speed. An additional important observation is that, overall, the tested 2D MAPF techniques scaled well to 3D warehouses and demonstrate how the MAPF community's progress in 2D can generalize to 3D warehouses.

In this study, an inconsistency-tolerant hierarchical probabilistic computation tree logic (IHpCTL) is developed to establish a new extended model-checking paradigm referred to as IHpCTL model checking, which is intended to verify randomized, open, large, and complex concurrent systems. The proposed IHpCTL is constructed based on several previously established extensions of the standard probabilistic temporal logic known as probabilistic computation tree logic (pCTL), which is widely used for probabilistic model checking. IHpCTL is shown to be embeddable into pCTL and is relatively decidable with respect to pCTL. This means that the decidability of pCTL with certain probability measures implies the decidability of IHpCTL. The results indicate that we can effectively reuse the previously proposed pCTL model-checking algorithms for IHpCTL model checking. Moreover, in this study, some new illustrative examples for clinical reasoning verification are addressed based on IHpCTL model checking.