State Space Explosion Research Articles

A formal approach for the analysis of BPMN collaboration models

BPMN collaboration models have acquired increasing relevance in software development since they shorten the communication gap between domain experts and IT specialists and permit clarifying the characteristics of software systems needed to provide automatic support for the activities of complex organizations. Nonetheless, the lack of effective formal verification capabilities can hinder the full adoption of the BPMN standard by IT specialists, as it prevents precisely check the satisfaction of behavioral properties, with negative impacts on the quality of the software. To address these issues, this paper proposes BProVe, a novel verification approach for BPMN collaborations. This combines both standard model checking techniques, through the MAUDE’s LTL model checker, and statistical model checking techniques, through the statistical analyzer MultiVeStA. The latter makes BProVe effective also on those scenarios suffering from the state–space explosion problem, made even more acute by the presence of asynchronous message exchanges. To support the adoption of the BProVe approach, we propose a complete web-based tool-chain that allows for BPMN modeling, verification, and result exploration. The feasibility of BProVe has been validated both on synthetically-generated models and on models retrieved from two public repositories. The performed validation highlighted the importance and complementarity of the two supported verification strategies.

Proportional lumpability and proportional bisimilarity

In this paper, we deal with the lumpability approach to cope with the state space explosion problem inherent to the computation of the stationary performance indices of large stochastic models. The lumpability method is based on a state aggregation technique and applies to Markov chains exhibiting some structural regularity. Moreover, it allows one to efficiently compute the exact values of the stationary performance indices when the model is actually lumpable. The notion of quasi-lumpability is based on the idea that a Markov chain can be altered by relatively small perturbations of the transition rates in such a way that the new resulting Markov chain is lumpable. In this case, only upper and lower bounds on the performance indices can be derived. Here, we introduce a novel notion of quasi-lumpability, named proportional lumpability, which extends the original definition of lumpability but, differently from the general definition of quasi-lumpability, it allows one to derive exact stationary performance indices for the original process. We then introduce the notion of proportional bisimilarity for the terms of the performance process algebra PEPA. Proportional bisimilarity induces a proportional lumpability on the underlying continuous-time Markov chains. Finally, we prove some compositionality results and show the applicability of our theory through examples.

ForASec: Formal Analysis of Hardware Trojan-Based Security Vulnerabilities in Sequential Circuits

In this article, we propose a novel model checking-based methodology that analyzes the hardware trojan (HT)-based security vulnerabilities in sequential circuits with 100% coverage while addressing the state-space explosion issue and completeness issue. In this work, the state-space explosion issue is addressed by efficiently partitioning the larger state space into corresponding smaller state spaces to enable the distributed HT-based security analysis of complex sequential circuits. We analyze multiple ISCAS89 and trust-hub benchmarks for different ASIC technologies, i.e., 65, 45, and 22 nm, to demonstrate the efficacy of our framework in identifying HT-based security vulnerabilities. The experimental results show that ForASec successfully performs the complete analysis of the given complex and large sequential circuits, and provides approximately <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6\times $ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10\times $ </tex-math></inline-formula> speedup in analysis time compared to the state-of-the-art model checking-based techniques.

Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization

Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces with combinatorial optimization is the state-space explosion problem: the number of possibilities grows exponentially with the problem size, which makes solving intractable for large problems. In the last years, deep reinforcement learning (DRL) has shown its promise for designing good heuristics dedicated to solve NP-hard combinatorial optimization problems. However, current approaches have an important shortcoming: they only provide an approximate solution with no systematic ways to improve it or to prove optimality. In another context, constraint programming (CP) is a generic tool to solve combinatorial optimization problems. Based on a complete search procedure, it will always find the optimal solution if we allow an execution time large enough. A critical design choice, that makes CP non-trivial to use in practice, is the branching decision, directing how the search space is explored. In this work, we propose a general and hybrid approach, based on DRL and CP, for solving combinatorial optimization problems. The core of our approach is based on a dynamic programming formulation, that acts as a bridge between both techniques. We experimentally show that our solver is efficient to solve three challenging problems: the traveling salesman problem with time windows, the 4-moments portfolio optimization problem, and the 0-1 knapsack problem. Results obtained show that the framework introduced outperforms the stand-alone RL and CP solutions, while being competitive with industrial solvers.

A Fuzzy Q-Learning Algorithm for Storage Optimization in Islanding Microgrid

In islanding microgrids, energy storage plays a key role in obtaining flexible power control and operation. The energy storage solves the effects of randomness, intermittency and uncertainty of renewable energy through its peak regulation and frequency modulation. In order to better to improve the economics of the microgrid, this paper proposes a Q-learning algorithm based on fuzzy control. It is a model-free algorithm, without complicated modelling, the new algorithm can handle the state space explosion problem of the Q learning algorithm. This method improves the system's renewable resource utilization rate by controlling the energy flow of the energy storage and adjusting the system's energy scheduling. The results show that compared with the Q-learning, the fuzzy Q-learning algorithm reduced the use of fossil fuels by 33.7%, increases the utilization rate of renewable resources from 85.7 to 93.5%.

Correlation Dimension Based Stability Analysis for Cyber-Physical Systems

Cyber-physical systems (CPSs) realize the automatic control of entities through computing systems and networks. Stability is an important factor in CPS for system upgrading and troubleshooting. Traditional analysis methods focus on simulation and formal analysis, which have two major limitations: first, the current state information of CPS is difficult to obtain; second, most CPS face the state space explosion problem. These problems can be avoided and a good analysis can be provided based on empirical data. The main work of this article is summarized as follows: first, a phase space reconstruction method is designed to divide the dataset into several subsequences with the same shape; second, we propose a stability analysis method based on correlation dimensions. Results indicate that the proposed approach can obtain a stable correlation dimension. CPS perform better if the correlation dimension is maintained within a certain range; otherwise, a destabilizing factor exists. The proposed stability analysis has less complexity and running time.

DICER 2.0: A New Model Checker for Data-Flow Errors of Concurrent Software Systems

Petri nets are widely used to model concurrent software systems. Currently, there are many different kinds of Petri net tools that can analyze system properties such as deadlocks, reachability and liveness. However, most tools are not suitable to analyze data-flow errors of concurrent systems because they do not formalize data information and lack efficient computing methods for analyzing data-flows. Especially when a concurrent system has so many concurrent data operations, these Petri net tools easily suffer from the state–space explosion problem and pseudo-states. To alleviate these problems, we develop a new model checker DICER 2.0. By using this tool, we can model the control-flows and data-flows of concurrent software systems. Moreover, the errors of data inconsistency can be detected based on the unfolding techniques, and some model-checking can be done via the guard-driven reachability graph (GRG). Furthermore, some case studies and experiments are done to show the effectiveness and advantage of our tool.

Reliability Analysis of Dynamic Fault Tree Based on Binary Decision Diagrams for Explosive Vehicle

Dynamic fault tree is often used to analyze system reliability. The Markov model is a commonly used method, which can accurately reflect the relationship between the state transition process and the dynamic logic gate transfer in the dynamic fault tree. When the complexity or scale of system is increasing, the Markov model encountered a problem of state space explosion leading to increase troubles. To solve the above problems, a modular approach is needed. Based on the modular approach, a hybrid fault module was researched in this paper. Firstly, the stackable fault subtree containing complex static/dynamic logic gate is transformed into four common combinational logic gates through preprocessing of the dynamic gate in the module. Then, the complexity of the model was reduced by incorporating four common combinational logic gates and using the binary decision graph to solve variable ordering in the calculation of failure probability of static subtree. Moreover, the calculating process of complex mixed logic gate fault tree can be simplified. An example of the ammonium nitrate/fuel explosive production system for BCZH-15 explosive vehicle was used to verify the feasibility of the presented method.

An Incremental and Backward-Conflict Guided Method for Unfolding Petri Nets

The unfolding technique of Petri net can characterize the real concurrency and alleviate the state space explosion problem. Thus, it is greatly suitable to analyze/check some potential errors in concurrent systems. During the unfolding process of a Petri net, the calculations of configurations, cuts, and cut-off events are the key factors for the unfolding efficiency. However, most of the unfolding methods do not specify a highly efficient calculations on them. In this paper, we reveal some recursive relations and structural properties of these factors. Subsequently, we propose an improved method for computing configurations and cuts. Meanwhile, backward conflicts are used to guide the calculations of cut-off events. Moreover, a case study and a series of experiments are done to illustrate the effectiveness and application scenarios of our methods.

Reductions and abstractions for formal verification of distributed round-based algorithms

Model checking has advanced over the last decades to become an effective formal technique for verifying distributed and concurrent systems. As computers grew in memory and processing capacity, it became possible to exhaustively verify systems with billions of states, making it practical to model and verify real-world protocols and algorithms. However, writing a model is a manual task that potentially introduces defects which the model checker tool finds to fulfill the formal specification (e.g., an incorrect model that fulfills an incomplete specification). Furthermore, this kind of formal verification technique is limited by the well-known state-space explosion problem. This paper aims to provide a set of generic template models, appropriate for distributed round-based algorithms, to be used to focus modeling effort on algorithm-specific details. To mitigate state-space explosion, the paper proposes two reduction techniques, named partition symmetry reduction and message order reduction, that exploit symmetries in the state space to avoid expanding equivalent states. The reusable framework for verifying round-based algorithms and the two proposed reduction techniques provide the means for reducing by orders of magnitude the number of states required to analyze common distributed algorithms.

Using knowledge discovery to propose a two-phase model checking for safety analysis of graph transformations

Safety is one of the most important features of modern software systems, especially safety-critical systems such as nuclear power plants, which can be checked exactly by model checking. Model checking is a formal verification technique that analyzes system properties through exploring all reachable states (state space) of a model of a system. The problem of the technique is that it confronts the state space explosion in large and complex systems due to exponential memory usage. Recent researches show that a partial and intelligent exploration of the state space can be a suitable solution to overcome this problem. In this paper, we propose a two-phase model checking for safety analysis of systems specified formally through graph transformations. In the first phase, the beam-search algorithm explores the state space to a specific number of states. In case of failure of the phase, the second phase starts: in systems specified through graph transformations, the rule applied on the previous state can determine the rule that can perform on the next state. In other words, the rule on current state depends on only the rule applied to previous state, not the one on earlier states. Hence, a Markov chain (MC) is estimated to capture dependencies between the sequence of applied rules in the state space explored by the beam-search algorithm. The MC is then employed to explore the remainder of the state space intelligently. To evaluate the effectiveness of the two-phase model checking, we implement it in GROOVE, an open source toolset for designing and model checking graph transformation systems. Experimental results show that the two-phase model checking has the high speed and accuracy in comparison with the existing meta-heuristic and evolutionary techniques.

3D Analytical Modeling and Iterative Solution for High Performance Computing Clusters

Mobile Cloud Computing enables the migration of services to the edge of Internet. Therefore, high performance computing clusters are widely deployed to improve computational capabilities of such environments. However, they are prone to failures and need analytical models to predict their behavior in order to deliver desired quality-of-service and quality-of-experience to mobile users. This article proposes a 3D analytical model and a problem-solving approach for sustainability evaluation of high-performance computing clusters. The proposed solution uses an iterative approach to obtain performance measurements to overcome the state space explosion problem. The availability modeling and evaluation of master and computing nodes are performed using a multi-repairman approach. The optimum number of repairmen is also obtained to get realistic results and reduce the overall cost. The proposed model is validated using discrete event simulation. The analytical approach is much faster and in good agreement with the simulations. The analysis focuses on mean queue length, throughput and mean response time outputs. The maximum differences between analytical and simulation results in the considered scenarios of up to a billion states are less than 1.149, 3.82, and 3.76 percent, respectively. These differences are well within the 5 percent of confidence interval of the simulation and the proposed model.

Directed Test Generation for Activation of Security Assertions in RTL Models

Assertions are widely used for functional validation as well as coverage analysis for both software and hardware designs. Assertions enable runtime error detection as well as faster localization of errors. While there is a vast literature on both software and hardware assertions for monitoring functional scenarios, there is limited effort in utilizing assertions to monitor System-on-Chip (SoC) security vulnerabilities. We have identified common SoC security vulnerabilities and defined several classes of assertions to enable runtime checking of security vulnerabilities. A major challenge in assertion-based validation is how to activate the security assertions to ensure that they are valid. While existing test generation using model checking is promising, it cannot generate directed tests for large designs due to state space explosion. We propose an automated and scalable mechanism to generate directed tests using a combination of symbolic execution and concrete simulation of RTL models. Experimental results on diverse benchmarks demonstrate that the directed tests are able to activate security assertions non-vacuously.

Performance Analysis Methods for List-Based Caches With Non-Uniform Access

List-based caches can offer lower miss rates than single-list caches, but their analysis is challenging due to state space explosion. In this setting, we propose novel methods to analyze performance for a general class of list-based caches with tree structure, non-uniform access to items and lists, and random or first-in first-out replacement policies. Even though the underlying Markov process is shown to admit a product-form solution, this is difficult to exploit for large caches. Thus, we develop novel approximations for cache performance metrics, in particular by means of a singular perturbation method and a refined mean field approximation. We compare the accuracy of these approaches to simulations, finding that our new methods rapidly converge to the equilibrium distribution as the number of items and the cache capacity grow in a fixed ratio. We find that they are much more accurate than fixed point methods similar to prior work, with mean average errors typically below 1.5% even for very small caches. Our models are also generalized to account for synchronous requests, fetch latency, and item sizes, extending the applicability of approximations for list-based caches.

Compositional coordinator synthesis of extended finite automata

To avoid the state-space explosion problem, a set of supervisors may be synthesized using divide and conquer strategies, like modular or multilevel synthesis. Unfortunately, these supervisors may be conflicting, meaning that even though they are individually non-blocking, they are together blocking. Abstraction-based compositional nonblocking verification of extended finite automata provides means to verify whether a set of models is nonblocking. In case of a blocking system, a coordinator can be synthesized to resolve the blocking. This paper presents a framework for compositional coordinator synthesis for discrete-event systems modeled as extended finite automata. The framework allows for synthesis of a coordinator on the abstracted system in case compositional verification identifies the system to be blocking. As the abstracted system may use notions not present in the original model, like renamed events, the synthesized coordinator is refined such that it will be nonblocking, controllable, and maximally permissive for the original system. For each abstraction, it is shown how this refinement can be performed. It turns out that for the presented set of abstractions the coordinator refinement is straightforward.

Accelerating hardware security verification and vulnerability detection through state space reduction

Model checking is an effective technique for formal verification of hardware security properties in order to detect security vulnerabilities. However, a major challenge lies in state space explosion. In this work, we propose methods to accelerate hardware security verification and vulnerability detection through state space reduction. Specifically, we reduce state space of formal model by performing value reduction and transition relation reduction. The control flow and data dependent graphs control the process of value reduction and transition relation reduction. In addition, we provide an approach that allows the automated mining of security properties from register-transfer-level hardware designs. Experimental results using Trust-HUB benchmarks have demonstrated that our proposed methods can significantly reduce the complexity of the formal model and thus the formal security verification time for hardware Trojan detection.

Taming the State-space Explosion in the Makespan Optimization of Flexible Manufacturing Systems

This article presents a modular automaton-based framework to specify flexible manufacturing systems and to optimize the makespan of product batches. The Batch Makespan Optimization (BMO) problem is NP-Hard and optimization can therefore take prohibitively long, depending on the size of the state-space induced by the specification. To tame the state-space explosion problem, we develop an algebra based on automata equivalence and inclusion relations that consider both behavior and structure. The algebra allows us to systematically relate the languages induced by the automata, their state-space sizes, and their solutions to the BMO problem. Further, we introduce a novel constraint-based approach to systematically prune the state-space based on the the notions of nonpermutation-repulsiveness and permutation-attractiveness. We prove that constraining a nonpermutation-repulsing automaton with a permutation-attracting constraint always reduces the state-space. This approach allows us to (i) compute optimal solutions of the BMO problem when the (additional) constraints are taken into account and (ii) compute bounds for the (original) BMO problem (without using the constraints). We demonstrate the effectiveness of our approach by optimizing an industrial wafer handling controller.

A numerical simulation method for a repairable dynamic fault tree

Dynamic fault trees are important tools for modeling systems with sequence failure behaviors. The Markov chain state space method is the only analytical approach for a repairable dynamic fault tree (DFT). However, this method suffers from state space explosion, and is not suitable for analyzing a large scale repairable DFT. Furthermore, the Markov chain state space method requires the components’ time-to-failure to follow exponential distributions, which limits its application. In this study, motivated to efficiently analyze a repairable DFT, a Monte Carlo simulation method based on the coupling of minimal cut sequence set (MCSS) and its sequential failure region (SFR) is proposed. To validate the proposed method, a numerical case was studied. The results demonstrated that our proposed approach was more efficient than other methods and applicable for repairable DFTs with arbitrary time-to-failure distributed components. In contrast to the Markov chain state space method, the proposed method is straightforward, simple and efficient.

Handling State Space Explosion in Component-Based Software Verification: A Review

Component-based software development (CBSD) is an alternative approach to constructing software systems that offers numerous benefits, particularly in decreasing the complexity of system design. However, deploying components into a system is a challenging and error-prone task. Model-checking is one of the reliable methods to systematically analyze the correctness of a system. It is a bruce-force checking of the system's state space that assists to significantly expand the level of confidence in the system. Nevertheless, model-checking is limited by a critical problem called state-space explosion (SSE). To benefit from model-checking, an appropriate method is required to reduce SSE. In the past two decades, a great number of SSE reduction methods have been proposed containing many similarities, dissimilarities, and unclear concepts in some cases. This research, firstly, plans to present a review of SSE handling methods and classify them based on their similarities, principle, and characteristics. Second, it investigates the methods for handling the SSE problem in the verification process of CBSD and provides insight into the potential limitations, underlining the key challenges for future research efforts.

A performance model of automated material handling systems with double closed-loops and shortcuts in 300 mm semiconductor wafer fabrication systems

Automated material handling systems (AMHSs) with double closed-loops and shortcuts have been widely adopted by general 300mm semiconductor fabrication enterprises due to their higher transportation efficiency, more flexible vehicle routing, and lower vehicle congestion compared with those traditional ones with single-loop. An accurate and efficient performance analysis model is crucial to quickly and effectively evaluate the schemes in the early stage of AMHS design. This paper proposes an extended Markov chain model (EMCM) to rapidly and effectively analyze performances of the AMHS with double closed-loops and shortcuts. In the modeling process, the inner closed-loop and shortcuts are abstracted as virtual stations to discretely express the running process of overhead hoist transporters (OHTs) on them. OHT’s running process in AMHS is discretized and equivalent to the state change of Markov chain and a triple-structure model is presented to describe the Markov states, so that the system characteristics, including OHT blockage, system’s double closed-loops, and shortcuts configuration, can be fully considered. The complex Markov process with multiple OHTs is transformed into the process with multiple independent OHTs so as to effectively eliminate the model’s state space explosion. System state probabilities models and blocking probability models are built to effectively represent its state and blocking properties. The stability state equations of EMCM are built so that its steady-state visit ratio can be identified. With production data from a semiconductor fabrication enterprise, the proposed performance analysis model is compared with a simulation model. The result shows that two models have a small relative error in the aspect of empty OHT’s mean arrival time interval, interbay throughput capacity, and OHT’s mean utilization ratio. However, the computing efficiency of the EMCM is significantly higher than that of the simulation model. It demonstrates that the proposed EMCM is effective and efficient for performance analysis in the early stage of AMHS design.