State Space Explosion Research Articles

Possibilistic Cost Computation Tree Logic and Related Equivalence, Abstraction Technique

Recently, probabilistic Kripke structures have been used to represent uncertain systems; nevertheless, important transition costs were ignored in earlier studies, making it impossible to model some uncertain systems with costs. To compensate for the major shortcoming, this research addresses the transition costs suggested in uncertain systems. First of all, we offer possibilistic Kripke cost structures and associated possibilistic costs such as cumulative cost and possibilistic expected cost. As the verification model, furthermore, we investigated the syntax and semantics of possibilistic cost computation tree logic and utilized them to develop verification characteristics of possibilistic Kripke cost structures. Finally, as solutions to the state space explosion problem of possibilistic cost computation tree logic model checking, abstraction and equivalence are presented as methods to reduce the state numbers and frameworks of possibilistic Kripke cost structures.

State Space Explosion Mitigation for Large-Scale Attack and Compliance Graphs Using Synchronous Exploit Firing

State Space Explosion Mitigation for Large-Scale Attack and Compliance Graphs Using Synchronous Exploit Firing

IoT Capabilities Composition and Decomposition: A Systematic Review

As billions of IoT devices join the Internet, researchers and innovators increasingly explore IoT capabilities achieved via service composition or reuse of existing capabilities via service decomposition. Many systematic literature reviews (SLRs) were produced on this subject; however, two issues remain to be addressed: i) a reference taxonomy of the different aspects of IoT capabilities composition and decomposition is needed, and ii) many formal questions (e.g., standards role, formal representations applications, state-space explosion countermeasures, etc.), technical questions (e.g., composition process types and automation levels synergies, service decomposition categories, the role of AI/ML, etc.), and QoS questions (e.g., privacy, interoperability, and scalability challenges and solutions, etc.) remain unanswered. We introduce this work by discussing notions of IoT capabilities composition and decomposition in a layered IoT architecture while highlighting the strengths and weaknesses of existing SLRs. We identify unanswered questions through gaps in related work and motivate these questions using the PICOC methodology. We explain the search methodology and organize the topic questions using the proposed reference taxonomy. The identified research questions are answered, and trends and gaps that need additional attention from the research community are highlighted. This effort benefits city planners and end-users of IoT systems as it contributes to a better understanding of the role of composition and decomposition of IoT capabilities in building value-added services or reusing existing ones for resource optimization. For researchers, this effort contributes a reference taxonomy for the topic and sheds light on important questions while highlighting corresponding trends and gaps requiring further attention.

Reduction of data-value-aware process models: A relevance-based approach

In many settings, verification of process models hinges on data values. A data value is a value in the domain of a data object, e.g., $1000 as the price of a product. Naive exploration of process models with data values, i.e., data-value-aware process models, tends to lead to state-space explosion. To tackle this problem, various reduction techniques have been proposed. These current techniques have a fundamental shortcoming: They do not take the modification of data values by process elements into consideration, in spite of its effects on execution behavior of processes. This may affect the verification result. In this paper, we propose a novel property-specific reduction technique to reduce data-value-aware process models supporting modification of data values. We detect the control-flow nodes and data elements that are necessary to verify a property in question, i.e., elements that are relevant for verification. Then we reduce the data-value-aware process model accordingly. We evaluate our approach by verifying a real-world application: the German 4G spectrum auction model.

Correctness-guaranteed strategy synthesis and compression for multi-agent autonomous systems

Planning is a critical function of multi-agent autonomous systems, which includes path finding and task scheduling. Exhaustive search-based methods such as model checking and algorithmic game theory can solve simple instances of multi-agent planning. However, these methods suffer from state-space explosion when the number of agents is large. Learning-based methods can alleviate this problem, but lack a guarantee of correctness of the results. In this paper, we introduce MoCReL, a new version of our previously proposed method that combines model checking with reinforcement learning in solving the planning problem. The approach takes advantage of reinforcement learning to synthesize path plans and task schedules for large numbers of autonomous agents, and of model checking to verify the correctness of the synthesized strategies. Further, MoCReL can compress large strategies into smaller ones that have down to 0.05% of the original sizes, while preserving their correctness, which we show in this paper. MoCReL is integrated into a new version of Uppaal Stratego that supports calling external libraries when running learning and verification of timed games models.

Performance measurement of safety-critical systems based on ordinary differential equations and Petri nets: A case study of nuclear power plant

This article proposes a novel approach to measure the performance of Safety-Critical Systems (SCS). Such systems contain multiple processing nodes that communicate with each other is modeled by a Petri nets (PN). The paper uses the PN for the performance evaluation of SCS. A set of ordinary differential equations (ODEs) is derived from the Petri net model that represent the state of the system, and the solutions can be used to measure the system's performance. The proposed method can avoid the state space 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 Shutdown System (SDS) of Nuclear Power Plant (NPP). We obtained 99.887% accuracy of performance measurement, which proves the effectiveness of our approach.

Temporary and permanent control of partially specified Boolean networks

Boolean networks (BNs) are a well-accepted modelling formalism in computational systems biology. Nevertheless, modellers often cannot identify only a single BN that matches the biological reality. The typical reasons for this is insufficient knowledge or a lack of experimental data. Formally, this uncertainty can be expressed using partially specified Boolean networks (PSBNs), which encode the wide range of network candidates into a single structure.In this paper, we target the control of PSBNs. The goal of BN control is to find perturbations which guarantee stabilisation of the system in the desired state. Specifically, we consider variable perturbations (gene knock-out and over-expression) with three types of application time-window: one-step, temporary, and permanent.While the control of fully specified BNs is a thoroughly explored topic, control of PSBNs introduces additional challenges that we address in this paper. In particular, the unspecified components of the model cause a significant amount of additional state space explosion. To address this issue, we propose a fully symbolic methodology that can represent the numerous system variants in a compact form.In fully specified models, the efficiency of a perturbation is characterised by the count of perturbed variables (the perturbation size). However, in the case of a PSBN, a perturbation might work only for a subset of concrete BN models. To that end, we introduce and quantify perturbation robustness. This metric characterises how efficient the given perturbation is with respect to the model uncertainty.Finally, we evaluate the novel control methods using non-trivial real-world PSBN models. We inspect the method’s scalability and efficiency with respect to the size of the state space and the number of unspecified components. We also compare the robustness metrics for all three perturbation types. Our experiments support the hypothesis that one-step perturbations are significantly less robust than temporary and permanent ones.

EtWExplorer: Multi-Priority Scheduling Path Exploration Technology Based on Abstract Syntax Tree Analysis

Symbolic execution is well known as a dynamic vulnerability discovery technique. Its greatest advantage is the capability to analyze the execution information of the program and to explore the path in the program deterministically. This is a more accurate way to determine if there are vulnerabilities in a program than randomized testing by fuzzing. In addition, symbolic execution does not suffer from the problem of decreasing the capability to discover new paths as more paths are discovered, similar to that caused by random-based fuzzing. However, the reason why symbolic execution is not widely used in vulnerability discovery is mainly due to the state space explosion in the program. The state space explosion severely affects the applicability of symbolic execution. To further improve the applicability of symbolic execution, this paper proposes a path exploration technology based on abstract syntax tree analysis. With the distance between the expression generated by the symbolic execution of the repeat location and the “unsatisfiable” condition of the “unsat” state, we can perform multi-priority scheduling for the repeat location state, thus mitigating the impact of the state space explosion on path exploration. We proposed and implemented EtWExplorer, a multi-priority scheduling technique based on abstract syntax tree analysis. With this technique, we can significantly improve the capability of symbolic execution to discover unknown paths even in state space exploration. Experiments show that EtWExplorer introduces a performance overhead of 72% in the worst case and can improve performance by 294% in the best case. EtWExplorer has a 95% improvement in state space explosion mitigation capability and a 199% to 983% improvement in the path exploration capability of block coverage and a 181% to 1047% improvement in the path exploration capability of edge coverage when facing programs that cause a state space explosion.

Deep Reinforcement Learning-Based Multichannel Access for Industrial Wireless Networks With Dynamic Multiuser Priority

In Industry 4.0, massive heterogeneous industrial devices generate a great deal of data with different quality of service requirements, and communicate via industrial wireless networks (IWNs). However, the limited time-frequency resources of IWNs cannot well support the high concurrent access of massive industrial devices with strict real-time and reliable communication requirements. To address this problem, a deep reinforcement learning-based dynamic priority multichannel access (DRL-DPMCA) algorithm is proposed in this article. Firstly, according to the time-sensitivity of industrial data, industrial devices are assigned with different priorities, based on which their channel access probabilities are dynamically adjusted. Then, the Markov decision process is utilized to model the dynamic priority multichannel access problem. To cope with the explosion of state space caused by the multichannel access of massive industrial devices with dynamic priorities, DRL is used to establish the mapping from states to actions. Next, the long-term cumulative reward is maximized to obtain an effective policy. Especially, with joint consideration of the access reward and priority reward, a compound reward for multichannel access and dynamic priority is designed. For breaking the time correlation of training data while accelerating the convergence of DRL-DPMCA, an experience replay with experience-weight is proposed to store and sample experiences categorically. Besides, the gated recurrent unit, dueling architecture and step-by-step <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -greedy method are employed to make states more comprehensive and reduce model oscillation. Extensive experiments show that, compared with slotted-Aloha and deep Q network algorithms, DRL-DPMCA converges quickly, and guarantees the highest channel access probability and the minimum queuing delay for high-priority industrial devices in the context of minimum access conflict and nearly 100% channel utilization.

Partial-order reduction for parity games and parameterised Boolean equation systems

In model checking, reduction techniques can be helpful tools to fight the state-space explosion problem. Partial-order reduction (POR) is a well-known example, and many POR variants have been developed over the years. However, none of these can be used in the context of model checking stutter-sensitive temporal properties. We propose POR techniques for parity games, a well-established formalism for solving a variety of decision problems, including model checking. As a result, we obtain the first POR method that is sound for the full modal upmu -calculus. We show how our technique can be applied to the fixed point logic called parameterised Boolean equation systems, which provides a high-level representation of parity games. Experiments with our implementation indicate that substantial reductions can be achieved.

Formal Analysis of the Security Protocol with Timestamp Using SPIN.

The verification of security protocols is an important basis for network security. Now, some security protocols add timestamps to messages to defend against replay attacks by network intruders. Therefore, verifying the security properties of protocols with timestamps is of great significance to ensure network security. However, previous formal analysis method of such protocols often extracted timestamps into random numbers in order to simplify the model before modeling and verification, which probably cause time-dependent security properties that are ignored. To solve this problem, a method for verifying security protocols with timestamps using model checking technique is proposed in this paper. To preserve the time-dependent properties of the protocol, Promela (process meta language) is utilized to define global clock representing the protocol system time, timer representing message transmission time, and the clock function representing the passage of time; in addition, a mechanism for checking timestamps in messages is built using Promela. To mitigate state space explosion in model checking, we propose a vulnerable channel priority method of using Promela to build intruder model. We take the famous WMF protocol as an example by modeling it with Promela and verifying it with model checker SPIN (Simple Promela Interpreter), and we have successfully found two attacks in the protocol. The results of our work can make some security schemes based on WMF protocol used in the Internet of things or other fields get security alerts. The results also show that our method is effective, and it can provide a direction for the analysis of other security protocols with timestamp in many fields.

Visual judgment approach of isomorphic GUI for automated mobile app testing

Currently, the rapid growth of mobile apps requires automated testing technology to ensure their quality. Automated testing of mobile apps is usually closely related to the recognition and judgment of their graphical user interface (GUI), but there usually are numerous isomorphic GUIs with different styles and contents, and similar structure and function in mobile apps. In automatic testing, isomorphic GUI is easy to cause the issue of state space explosion, which leads to low efficiency or failure of testing. In view of the limitations of traditional automatic recognition of isomorphic GUI, this paper presents a GUI similarity judgment approach based on visual feature information. Firstly, the GUI component elements are identified by object detection, and then the GUI skeleton is abstracted. Secondly, the visual features of the GUI skeleton are extracted by a convolutional autoencoder. Finally, the isomorphic GUI judgment is completed by comparing the similarity of GUI visual features. The experimental results show that the proposed approach can effectively shield the influence of GUI style and content, complete the isomorphic GUI recognition more accurately and optimize the efficiency of automated mobile app testing.

On Optimization of Automation Systems: Integrating Modular Learning and Optimization

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Compositional Optimization</i> (CompOpt) was recently proposed for optimization of discrete-event systems of systems. A modular optimization model allows CompOpt to divide the optimization into separate sub-problems, mitigating the state space explosion problem. This paper presents the Modular Optimization Learner (MOL), a method that interacts with a simulation of a system to automatically learn these modular optimization models. MOL uses a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">modular learning</i> that takes as input a hypothesis structure of the system and uses the provided structural information to split the acquired learning into a set of modules, and to prune parts of the search space. Experiments show that modular learning reduces the state space by many orders of magnitude compared to a monolithic learning, which enables learning of much larger systems. Furthermore, an integrated greedy search heuristic allows MOL to remove many sub-optimal paths in the individual modules, speeding up the subsequent optimization. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Automation systems are becoming increasingly large and complex and the automation of more and more advanced tasks often requires the coordination of multiple subsystems. Optimization can have a great impact on the efficiency of these systems in terms of cost and operation speed. Finding optimal solutions is, however, a difficult task. As the number of tasks and subsystems of the automation system increases, the search space of the optimization problems tends to grow exponentially. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Compositional Optimization</i> (CompOpt) is a method specifically designed for the optimization of large-scale automation systems. A challenge with the application of CompOpt is that it takes as input a specific type of optimization model that divides the system into subsystems; like machines, vehicles, etc. Formulating these models requires a high level of expertise and system knowledge. This paper addresses this challenge with an algorithm that learns these models from a simulation of the system. The simulation can be implemented in any software as long as a suitable interface exists or can be constructed. To divide the learning into subsystems, the algorithm uses an initial <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">plant structure hypothesis</i> (PSH). This can be viewed as a meta-model that includes known structural information, such as the number of subsystems and which actions that affect each subsystem. The more structural information that is added to PSH, the more efficient the learning and subsequent optimization will be. The purpose of this is to reduce the level of expertise and system knowledge needed in the application of optimization, to simplify the transition to Industry 4.0.

Automated Synthesis of Generalized Invariant Strategies via Counterexample-Guided Strategy Refinement

Strategy synthesis for multi-agent systems has proved to be a hard task, even when limited to two-player games with safety objectives. Generalized strategy synthesis, an extension of generalized planning which aims to produce a single solution for multiple (possibly infinitely many) planning instances, is a promising direction to deal with the state-space explosion problem. In this paper, we formalize the problem of generalized strategy synthesis in the situation calculus. The synthesis task involves second-order theorem proving generally. Thus we consider strategies aiming to maintain invariants; such strategies can be verified with first-order theorem proving. We propose a sound but incomplete approach to synthesize invariant strategies by adapting the framework of counterexample-guided refinement. The key idea for refinement is to generate a strategy using a model checker for a game constructed from the counterexample, and use it to refine the candidate general strategy. We implemented our method and did experiments with a number of game problems. Our system can successfully synthesize solutions for most of the domains within a reasonable amount of time.

Neural Network Action Policy Verification via Predicate Abstraction

Neural networks (NN) are an increasingly important representation of action policies. Verifying that such policies are safe is potentially very hard as it compounds the state space explosion with the difficulty of analyzing even single NN decision episodes. Here we address that challenge through abstract reachability analysis. We show how to compute predicate abstractions of the policy state space subgraph induced by fixing an NN action policy. A key sub-problem here is the computation of abstract state transitions that may be taken by the policy, which as we show can be tackled by connecting to off-the-shelf SMT solvers. We devise a range of algorithmic enhancements, leveraging relaxed tests to avoid costly calls to SMT. We empirically evaluate the resulting machinery on a collection of benchmarks. The results show that our enhancements are required for practicality, and that our approach can outperform two competing approaches based on explicit enumeration and bounded-length verification.

Specification and Verification of Timing Properties in Interoperable Medical Systems

To support the dynamic composition of various devices/apps into a medical system at point-of-care, a set of communication patterns to describe the communication needs of devices has been proposed. To address timing requirements, each pattern breaks common timing properties into finer ones that can be enforced locally by the components. Common timing requirements for the underlying communication substrate are derived from these local properties. The local properties of devices are assured by the vendors at the development time. Although organizations procure devices that are compatible in terms of their local properties and middleware, they may not operate as desired. The latency of the organization network interacts with the local properties of devices. To validate the interaction among the timing properties of components and the network, we formally specify such systems in Timed Rebeca. We use model checking to verify the derived timing requirements of the communication substrate in terms of the network and device models. We provide a set of templates as a guideline to specify medical systems in terms of the formal model of patterns. A composite medical system using several devices is subject to state-space explosion. We extend the reduction technique of Timed Rebeca based on the static properties of patterns. We prove that our reduction is sound and show the applicability of our approach in reducing the state space by modeling two clinical scenarios made of several instances of patterns.

Data-Driven Application-Oriented Reliability Model of a High-Performance Computing System

Reliability analysis and performance evaluation are complementary methods to quantify nonfunctional aspects of a system. However, a range of factors such as concurrency and heterogeneity quickly exacerbate the state-space explosion problem when attempting detailed system-level modeling and simulation of high-performance computing (HPC) systems. To overcome these impediments to modeling and analysis, this article develops a hierarchical model of an application that implements checkpointing running in an HPC environment subject to application, network, and system-wide outages. The modeling approach ensures that the number of states is linear in the number of checkpoints and possesses a low constant factor for the number of recovery states most relevant to the external influences contributing to degraded application performance. We illustrate the types of analysis enabled by the model through a series of examples with parameters determined empirically from data logs of the Blue Waters supercomputer located at the University of Illinois at Urbana–Champaign. A comprehensive comparative analysis of the model parameters indicates that lowering the failure rate of network nodes would most significantly reduce application downtime. We also discuss how the modeling approach can be used to objectively assess both current and hypothetical future systems to identify competitive designs and enhancements.

A Formal Verification Method for the SOPC Software

System on programmable chip (SOPC) is a kind of system on a programmable chip. The system architecture is superior to the traditional design pattern. The system has an <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> -chip bus between the processor and the programmable logic, which forms a high bandwidth, low latency, connection, and has rich flexible customization of IP. It also has advantages of low power consumption and high performance. The application in the field of high reliable proportion rising year by year. However, the change of system architecture and the expansion of software scale have brought great impact on the simulation test method and the physical test method. The existing dynamic testing methods are based on limited testing scenarios to investigate the system. It is difficult to find hidden errors in the design of complex connection segments, such as the errors in the <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> -chip bus transmission, the errors in the hardware and software coupling, and so on. Due to system scale of the state-space explosion problem and various forms IP, SOPC cannot apply formal verification techniques. In this article, we propose a SOPC formalized validation framework. It is based on polymorphous IP abstraction modeling, common formal properties analysis, and modeling methods in system architecture and other high-risk areas. The experimental results show that the proposed algorithm and the established SOPC formal verification framework can introduce the formal verification technique to SOPC high-risk area verification, and it can be used as the guidance of SOPC formal verification.

Predicting reliability of software in industrial systems using a Petri net based approach: A case study on a safety system used in nuclear power plant

Software reliability prediction in the early stages of development can be propitious in many ways. The combinatorial models used to predict reliability using architectures such as fault trees, binary decision diagrams, etc. have limitations in modeling complex system behavior. On the other hand, state-based models such as Markov chains suffer from the state-space explosion problem, and they need transition probability among different system states to measure reliability. These probabilities are usually assumed or are obtained from the operational profile for which the system should be used in the field.

The Refinement of Petri Net with Inhibitor Arcs Based Representation for Embedded Systems

Embedded systems are widely used in various devices. PRES+ (Petri net- based Representation for Embedded Systems) has been used to model and analyze embedded systems. However, it cannot characterize the priority of events, and cannot fully express the complex data flow and control flow. To solve this problem, inhibitor arcs are added to PRES+ and PIRES+ (PRES+ with Inhibitor arcs) is obtained. However, PIRES+’s state space explosion problem is a handicap when modeling, verifying, and controlling complex, large embedded systems. To mitigate the state space explosion problem of PIRES+ and analyze complex embedded systems, we propose the place refinement approach and the place set refinement approach for PIRES+. Under specific conditions, several important properties of PIRES+, such as timing, functionality, reachability, liveness, and boundedness, are preserved by using these refinement approaches. In order to illustrate the effectiveness of these refinement methods, as an example, the modeling and analysis of a network communication system is proposed. The refinement methods proposed have certain feasibility and practicability and provide a more practical theoretical basis for the modeling of some embedded systems.