State Explosion Research Articles

Quantum Probabilistic Model Checking for Time-Bounded Properties

Probabilistic model checking (PMC) is a verification technique for analyzing the properties of probabilistic systems. However, existing techniques face challenges in verifying large systems with high accuracy. PMC struggles with state explosion, where the number of states grows exponentially with the size of the system, making large system verification infeasible. While statistical model checking (SMC) avoids PMC’s state explosion problem by using a simulation approach, it suffers from runtime explosion, requiring numerous samples for high accuracy. To address these limitations in verifying large systems with high accuracy, we present quantum probabilistic model checking (QPMC), the first method leveraging quantum computing for PMC with respect to time-bounded properties. QPMC addresses state explosion by encoding PMC problems into quantum circuits that superpose states within qubits. Additionally, QPMC resolves runtime explosion through Quantum Amplitude Estimation, efficiently estimating the probabilities of specified properties. We prove that QPMC correctly solves PMC problems and achieves a quadratic speedup in time complexity compared to SMC.

Program Dependence Net and on-demand slicing for property verification of concurrent system and software

When checking concurrent software using a finite-state model, we face a formidable state explosion problem. One solution to this problem is dependence-based program slicing, whose use can effectively reduce verification time. It is orthogonal to other model-checking reduction techniques. However, when slicing concurrent programs for model checking, there are conversions between multiple irreplaceable models, and dependencies need to be found for variables irrelevant to the verified property, which results in redundant computation. To resolve this issue, we propose a Program Dependence Net (PDNet) based on Petri net theory. It is a unified model that combines a control-flow structure with dependencies to avoid conversions. For reduction, we present a PDNet slicing method to capture the relevant variables’ dependencies when needed. PDNet and its on-demand slicing in verifying linear temporal logic are used to significantly reduce computation cost. We implement a model-checking tool based on PDNet and its on-demand slicing and validate the advantages of our proposed methods.

Applied static analysis and specialization of cross-core syscalls for multi-core AUTOSAR OS

The development of static real-time control systems often follows a closed-world assumption, allowing extensive RTOS-aware whole-program optimization. For single-core systems, previous work could show the high potential of control-flow-aware static system-call tailoring. However, due to an exponential state explosion in the analysis phase, it cannot simply be extended to a multi-core setting, since the core’s relative timing to each other is undetermined. In this work, we present MultiSSE, a multi-core capable and RTOS-aware static whole-system optimization. First, MultiSSE analyzes the system by determining the relative positions of multiple cores only when necessary. For that, it exploits structural control flow and optionally timing information to handle each core separately as much as possible. Based on the analysis result, a synthesis applies lock elision and system-call optimization to generate specialized multi-core real-time systems for AUTOSAR OS. To enable a static prediction of the run-time reduction, we additionally provide cost models for the optimized cross-core system calls and evaluate the approach with synthetic benchmarks and a real-world quadrotor application. MultiSSE was able to optimize or even completely elide costly cross-core system calls and system objects leading to a reduction of up to 14% of a task’s execution time. In this extended version of a conference publication (Entrup et al. 2023), we provide an advanced description, new cost models, and an end-to-end measurement by developing a synthesis complementing the analysis.

Detection of Cyber-Attacks in a Discrete Event System Based on Deep Learning

This paper addresses the problem of cyber-attack detection in a discrete event system by proposing a novel model. The model utilizes graph convolutional networks to extract spatial features from event sequences. Subsequently, it employs gated recurrent units to re-extract spatio-temporal features from these spatial features. The obtained spatio-temporal features are then fed into an attention model. This approach enables the model to learn the importance of different event sequences, ensuring that it is sufficiently general for identifying cyber-attacks, obviating the need to specify attack types. Compared with traditional methods that rely on synchronous product computations to synthesize diagnosers, our deep learning-based model circumvents state explosion problems. Our method facilitates real-time and efficient cyber-attack detection, eliminating the necessity to specifically identify system states or distinguish attack types, thereby significantly simplifying the diagnostic process. Additionally, we set an adjustable probability threshold to determine whether an event sequence has been compromised, allowing for customization to meet diverse requirements. Experimental results demonstrate that the proposed method performs well in cyber-attack detection, achieving over 99.9% accuracy at a 1% threshold and a weighted F1-score of 0.8126, validating its superior performance.

SPIN-Based Linear Temporal Logic Path Planning for Ground Vehicle Missions with Motion Constraints on Digital Elevation Models.

Linear temporal logic (LTL) formalism can ensure the correctness of mobile robot planning through concise, readable, and verifiable mission specifications. For uneven terrain, planning must consider motion constraints related to asymmetric slope traversability and maneuverability. However, even though model checker tools like the open-source Simple Promela Interpreter (SPIN) include search optimization techniques to address the state explosion problem, defining a global LTL property that encompasses both mission specifications and motion constraints on digital elevation models (DEMs) can lead to complex models and high computation times. In this article, we propose a system model that incorporates a set of uncrewed ground vehicle (UGV) motion constraints, allowing these constraints to be omitted from LTL model checking. This model is used in the LTL synthesizer for path planning, where an LTL property describes only the mission specification. Furthermore, we present a specific parameterization for path planning synthesis using a SPIN. We also offer two SPIN-efficient general LTL formulas for representative UGV missions to reach a DEM partition set, with a specified or unspecified order, respectively. Validation experiments performed on synthetic and real-world DEMs demonstrate the feasibility of the framework for complex mission specifications on DEMs, achieving a significant reduction in computation cost compared to a baseline approach that includes a global LTL property, even when applying appropriate search optimization techniques on both path planners.

Correctness Verification of Mutual Exclusion Algorithms by Model Checking

Mutual exclusion algorithms are at the heart of concurrent/parallel and distributed systems. It is well known that such algorithms are very difficult to analyze, and in the literature, different conjectures about starvation freedom and the number of by-passes (also called the overtaking factor) exist. The overtaking factor affects the (hopefully) bounded waiting time that a process competing for entering the critical section has to suffer before accessing the shared resource. This paper proposes a novel modeling approach based on Timed Automata and the Uppaal toolset, which proves effective for studying all the properties of a mutual exclusion algorithm for N≥2 processes, by exhaustive model checking. Although the approach, as already confirmed by similar experiments reported in the literature, is not scalable due to state explosion problems and can be practically applied until N≤5, it is of great value for revealing the true properties of analyzed algorithms. For dimensions N>5, the Statistical Model Checker of Uppaal can be used, which, although based on simulations, can confirm properties by estimations and probabilities. This paper describes the proposed modeling and verification method and applies it to several mutual exclusion algorithms, thus retrieving known properties but also showing new results about properties often studied by informal reasoning.

Multi-valued verification of commitment systems with uncertainty and inconsistency in multi-source data settings

In the dynamic landscape of Internet of Things (IoT) applications within multi-source data environments, ensuring the reliability and correctness of system communications has become a paramount concern. This is particularly evident in the presence of commitment protocols with inconsistency and uncertainty. This paper tackles these challenges by introducing a new logic, termed Six-Values Computation Tree Logic for Commitment (6V-CTLC), specifically crafted to adeptly model IoT systems with both inconsistency and uncertainty. Employing this logic, we devise an innovative reduction-based multi-valued model checking approach to verify the systems under scrutiny. Our method is implemented through a Java transformation tool we developed to translate the 6V-CTLC logic to the classical logic of commitment (CTLC) and seamlessly interfaces with the efficient model checker MCMAS+. Applying this approach, we verify an abstracted 6V-CTLC model featuring uncertainty and inconsistency, as well as the original model of our system before abstraction. Furthermore, we assess the scalability of our approach through ten experiments, comparing the results obtained from verifying the two models. The findings demonstrate the effectiveness of system abstraction in mitigating the state explosion problem, while the developed multi-valued model checking technique yields precise results.

Modeling and Analysis of Dekker-Based Mutual Exclusion Algorithms

Mutual exclusion is a fundamental problem in concurrent/parallel/distributed systems. The first pure-software solution to this problem for two processes, which is not based on hardware instructions like test-and-set, was proposed in 1965 by Th.J. Dekker and communicated by E.W. Dijkstra. The correctness of this algorithm has generally been studied under the strong memory model, where the read and write operations on a memory cell are atomic or indivisible. In recent years, some variants of the algorithm have been proposed to make it RW-safe when using the weak memory model, which makes it possible, e.g., for multiple read operations to occur simultaneously to a write operation on the same variable, with the read operations returning (flickering) a non-deterministic value. This paper proposes a novel approach to formal modeling and reasoning on a mutual exclusion algorithm using Timed Automata and the Uppaal tool, and it applies this approach through exhaustive model checking to conduct a thorough analysis of the Dekker’s algorithm and some of its variants proposed in the literature. This paper aims to demonstrate that model checking, although necessarily limited in the scalability of the number N of the processes due to the state explosions problem, is effective yet powerful for reasoning on concurrency and process action interleaving, and it can provide significant results about the correctness and robustness of the basic version and variants of the Dekker’s algorithm under both the strong and weak memory models. In addition, the properties of these algorithms are also carefully studied in the context of a tournament-based binary tree for N≥2 processes.

Switching, explosion, and chaos of multi-wavelength soliton states in ultrafast fiber lasers

Switching, explosion, and chaos of multi-wavelength soliton states in ultrafast fiber lasers

The Importance of Reaction Energy in Predicting Chemical Reaction Barriers with Machine Learning Models.

Improving our fundamental understanding of complex heterocatalytic processes increasingly relies on electronic structure simulations and microkinetic models based on calculated energy differences. In particular, calculation of activation barriers, usually achieved through compute-intensive saddle point search routines, remains a serious bottleneck in understanding trends in catalytic activity for highly branched reaction networks. Although the well-known Brønsted-Evans-Polyani (BEP) scaling - a one-feature linear regression model - has been widely applied in such microkinetic models, they still rely on calculated reaction energies and may not generalize beyond a single facet on a single class of materials, e. g., a terrace sites on transition metals. For highly branched and energetically shallow reaction networks, such as electrochemical CO2 reduction or wastewater remediation, calculating even reaction energies on many surfaces can become computationally intractable due to the combinatorial explosion of states that must be considered. Here, we investigate the feasibility of activation barrier prediction without knowledge of the reaction energy using linear and nonlinear machine learning (ML) models trained on a new database of over 500 dehydrogenation activation barriers. We also find that inclusion of the reaction energy significantly improves both classes of ML models, but complex nonlinear models can achieve performance similar to the simplest BEP scaling when predicting activation barriers on new systems. Additionally, inclusion of the reaction energy significantly improves generalizability to new systems beyond the training set. Our results suggest that the reaction energy is a critical feature to consider when building models to predict activation barriers, indicating that efforts to reliably predict reaction energies through, e. g., the Open Catalyst Project and others, will be an important route to effective model development for more complex systems.

Development of a method for fuzz testing of programs for file parsing using the PolyTracker tool

The article proposes a method of phasing-testing programs for parsing using the PolyTracker tool. During the research, types of parsers are considered and their disadvantages are revealed. The proposed method eliminates the identified drawbacks, increasing code coverage and leveling the problem of state explosion.

An Efficient Reduction of Timer Interrupts for Model Checking of Embedded Assembly Programs

In verifying programs for embedded systems, it is essential to reduce the verification time because state explosion may occur during model checking. One solution is to reduce the number of interrupt handler executions. In particular, when periodic interrupts such as timer interrupts are incorporated, it is necessary to know the physical time. In this paper, we define a control flow automaton (CFA) that can handle time and propose an algorithm based on interrupt handler execution reduction (IHER). The proposed method reduces the number of interrupt executions, including timer interrupts. A case study verified the effectiveness of this algorithm.

Non-interference assessment in colored net systems via integer linear programming

Event-related information leaks are a potential security hazard in information systems. Non-interference is a security property to describe event-related information security. Non-interference assessment is to detect whether a public observer can infer the occurrences of private events from the observation of public ones. To assess the non-interference of information systems, the utilization of formal modeling tools, especially Petri nets (PNs), is an effective way used in most previous works. However, for large-scale systems, non-interference assessment leads to the problem of state explosion in the context of basic net systems (NSs) defined by PNs. In this paper, considering the structural similarity of large-scale systems, colored PNs are used to model them more compactly and efficiently. We focus on the assessment of two typical non-interference properties, i.e., strong nondeterministic non-interference (SNNI) and bisimulation SNNI (BSNNI), in colored NSs (CNSs). Specifically, we propose a non-interference assessment method for bounded CNSs based on the definitions of SNNI and BSNNI in the context of CNSs. This method involves coarse and fine assessments. A coarse assessment is achieved via integer linear programming (ILP) by leveraging the structural similarity of systems. In contrast, the fine assessment can be fulfilled using ILP-based analysis or firing way analysis based on the results obtained by the coarse assessment, which is not essentially necessary. In particular, a fine assessment is necessary only if a coarse assessment is failed to obtain accurate assessment results. Finally, efficiency analysis reveals that our method reduces assessment redundancy and improves assessment efficiency.

Reliability and Performance Measurement of Safety-Critical Systems Based on Petri Nets: A Case Study of Nuclear Power Plant

Safety-critical systems (SCSs) mitigate the risk of catastrophic loss of assets and hence do have high dependability targets. Performance and reliability are the critical dependability attributes, particularly in control and safety systems, and hence essential to measure to ensure the dependability. Traditional methods either are not capable to capture the system dynamics or encounter state explosion problem. Also, the methods are not able to measure all critical performance attributes. This article proposes a novel approach to measure the performance and reliability of SCSs. Such systems contain multiple interconnecting processing nodes, the functional requirements of which are modeled using Petri net (PN). A set of ordinary differential equations (ODEs) is derived from the PN model that represents the state of the system. The ODE solution can be used to measure the critical performance attributes, such as latency time and throughput of the system. The proposed method can avoid the state explosion problem and also introduces new metrics of performance, along with their measurement: deadlock, liveness, stability, boundedness, and steady state. The proposed technique is applied to a case study of nuclear power plant. We obtained 99.887% and 99.939% accuracy of performance and reliability measurement, respectively, which proves the effectiveness of our approach.

Dynamic probabilistic risk assessment with K-shortest-paths planning for generating discrete dynamic event trees

Conventional risk assessment methods are often not well suited for fast-changing dynamic and complex systems since the results from the analysis may be averages or valid for a short time before the system’s state changes. A response to this problem is dynamic probabilistic risk assessment (DPRA), which considers the ever-changing nature of such systems and how their dynamic behavior affects the likelihood of future accident scenarios. Performing DPRA is difficult for complex systems — i.e., systems with many interconnected subsystems and components, for example, autonomous systems. There is a combinatorial “explosion” when considering how component failures affect one another and the overall system performance, known in the DPRA literature as the “state explosion problem”, causing DPRA methods to have poor computational performance for large-scale systems. Although solutions to state explosion alleviate the average-case performance, most DPRA methods remain computationally expensive, with exponential worst-case time complexities. In this paper, a method for solving DPRA problems with K-Shortest-Paths planning algorithms is proposed. The method, called KPRA, consists in framing a subset of DPRA problems as relaxed versions of the K-Shortest-Paths (KSP) planning problem, allowing these DPRA problems to be solved by a graph search algorithm called K*, which has a theoretical log-linear worst-case complexity. Therefore, in theory, KPRA with K* solves DPRA problems with computational performance better than exponential. KPRA was implemented and applied to a case study of DPRA for an autonomous ship for validation and comparison with conventional DPRA methods. The case study consists of two ships, one of them autonomous, in a crossing encounter with a possible collision risk. The task is to find the most critical situations for the autonomous ship, i.e., the scenarios where its collision risk is the highest. KPRA’s performance in solving the case study is compared with two conventional DPRA methods. The results show that the KPRA implementation in this work can solve the case study, i.e., produce an output equivalent to the other methods, with a polynomial worst-case computational complexity, i.e., more efficiently than the other methods with exponential complexities.

Predicting 3D RNA structure from the nucleotide sequence using Euclidean neural networks

Fast and accurate 3D RNA structure prediction remains a major challenge in structural biology, mostly due to the size and flexibility of RNA molecules, as well as the lack of diverse experimentally determined structures of RNA molecules. Unlike DNA structure, RNA structure is far less constrained by basepair hydrogen bonding, resulting in an explosion of potential stable states. Here, we propose a convolutional neural network that predicts all pairwise distances between residues in an RNA, using a recently described smooth parametrization of Euclidean distance matrices. We achieve high-accuracy predictions on RNAs up to 100 nt in length in fractions of a second, a factor of 107 faster than existing molecular dynamics-based methods. We also convert our coarse-grained machine learning output into an all-atom model using discrete molecular dynamics with constraints. Our proposed computational pipeline predicts all-atom RNA models solely from the nucleotide sequence. However, this method suffers from the same limitation as nucleic acid molecular dynamics: the scarcity of available RNA crystal structures for training.

Modeling and Verification of Uncertain Cyber-Physical System Based on Decision Processes

Currently, there is uncertainty in the modeling techniques of cyber-physical systems (CPS) when faced with the multiple possibilities and distributions of complex system behavior. This uncertainty leads to the system’s inability to handle uncertain data correctly, resulting in lower reliability of the system model. Additionally, existing technologies struggle to verify the activity and safety of CPS after modeling, lacking a dynamic verification and analysis approach for uncertain CPS properties.This paper introduces a generalized possibility decision process as a system model. Firstly, the syntax and semantics of generalized possibility temporal logic with decision processes are defined. Uncertain CPS is extended by modeling it based on time-based differential equations and uncertainty hybrid time automaton. After that, model checking is performed on the properties of activity and safety using fuzzy linear time properties. Finally, a cold–hot hybrid constant-temperature system model is used for simulation experiments. By combining theory and experiments, this paper provides a new approach to the verification of uncertain CPS, effectively addressing the state explosion problem. It plays a crucial role in the design of uncertain CPS and offers a key solution for model checking in the presence of uncertainty.

Mobility-aware multi-user service placement and resource allocation in edge computing

The rise of Mobile Edge Computing (MEC) has brought us its enormous potential and value in mobile service applications. By pushing computing and storage resources from the cloud to the network edge, it reduces transmission latency, and supports applications that require low latency, such as virtual reality and video analytics IoT services. However, many existing works only consider the problem of service placement in MEC, and the problem of computing resource allocation has received less attention. This paper focuses on the joint optimization of Service Placement and computational Resource Allocation (SPRA) in the MEC environment, with the goal of minimizing the total cost of service latency, communication latency, and service migration. For offline cases, we propose an optimal algorithm, D-SPA , based on dynamic programming and an improved algorithm, S-SPA, based on state sampling, which effectively alleviates the state explosion problem in D-SPA. In the online case, due to the unpredictability of future environmental information, we propose the online greedy algorithm OGA, and theoretically show the approximate ratio of OGA. Extensive experiments show that our algorithm is more efficient than other baseline algorithms, and it reduces the total cost by 28.6% on average.

Liveness enforcement for production systems modeled by time Petri nets

This research reports a liveness enforcement approach in time Petri nets with the control of time intervals of controllable transitions. According to the T-invariants of the timeless counterpart of a time Petri net, a necessary condition is established for the solvability of the liveness enforcement problem. Then, a critical state class graph is designed with the nodes containing critical constraints of the controllable transitions. The existing parametric models to enforce liveness of a time Petri net with controllable and uncontrollable transitions are in general subject to the state explosion issue. To mitigate this problem, we introduce the concept of the first weakly live nodes and transitional nodes to avoid the enumeration of all constraints on unnecessary weakly live nodes. We develop an algorithm to transform a non-live time Petri net into live by controlling the time intervals of controllable transitions. Two production examples are used to illustrate the approach. This approach is efficient since it avoids the extensive enumeration with regard to the constraints on each node in a critical state class graph.

A Survey on Formal Verification and Validation Techniques for Internet of Things

The Internet of Things (IoT) has brought about a new era of connected devices and systems, with applications ranging from healthcare to transportation. However, the reliability and security of these systems are critical concerns that must be addressed to ensure their safe and effective operation. This paper presents a survey of formal verification and validation (FV&V) techniques for IoT systems, with a focus on the challenges and open issues in this field. We provide an overview of formal methods and testing techniques for the IoT and discuss the state explosion problem and techniques to address it. We also examined the use of AI in software testing and describe examples of tools that use AI in this context. Finally, we discuss the challenges and open issues in FV&V for the IoT and present possible future directions for research. This survey paper aimed to provide a comprehensive understanding of the current state of FV&V techniques for IoT systems and to highlight areas for further research and development.