State Space Explosion Research Articles

Accelerating worst case execution time analysis of timed automata models with cyclic behaviour

Abstract The paper presents a new efficient algorithm for computing worst case execution time (WCET) of systems modelled as timed automata (TA). The algorithm uses a set of abstraction techniques that improve significantly the efficiency of WCET analysis of TA models with cyclic behaviour. We show that the proposed abstractions are exact with respect to the WCET problem in the sense that the WCET computed in the abstract model is equal to the one computed in the concrete model. We also compare our algorithm with the one implemented in the model checker UPPAAL which shows that when infinite cycles exist (i.e. cycles that can be run infinitely often), UPPAAL’s algorithm may not terminate, and when largely repetitive finite cycles exist (i.e. cycles that can be run a large number of times but finite), UPPAAL’s algorithm suffers from the state space explosion, thus leading to a low efficiency or resource exhaustion.

A Novel Fault Diagnosis Framework Based on Reliability Analysis and Arithmetic Circuit

To meet the real-time diagnosis requirements of complex systems, this paper presents a novel fault diagnosis framework based on dynamic fault tree and arithmetic circuit. It pays attention to meeting two challenges: model development and real-time reasoning. Specifically, we use a dynamic fault tree to model dynamic fault modes and calculate some quantitative parameters using algebraic technique and Bayesian network (BN) in order to avoid the state space explosion problem. Furthermore, we compile a BN into an arithmetic circuit to obtain answers to probabilistic queries by evaluating and differentiating the arithmetic circuit. In addition, we incorporate sensors information into diagnosis process and propose the schemes on how to update the diagnostic importance factor and the minimal cut sequences. Finally, the example of a train-ground communication system is used to demonstrate the proposed method.

Reliability analysis of complex dynamic fault trees based on an adapted K.D. Heidtmann algorithm

Dynamic fault tree as a powerful analyzing tool is used to model systems having sequence- and function-dependent failure behaviors. The problem is how to quantify a complex dynamic fault tree where different dynamic gates coexist and are highly coupled. Existing analytical methods for analyzing dynamic fault trees are mainly Markov-based, inclusion–exclusion-based and sequential binary decision diagram–based approaches. Unfortunately, all these methods have their own shortcomings. As to the Markov-based method, it is frequently subjected to the problem of state-space explosion and only applicable for systems having components with exponential time-to-failure distributions. For the inclusion–exclusion-based method, it is often vulnerable to the problem of combinatorial explosion. As to the sequential binary decision diagram method, it cannot be directly applied to a complex dynamic fault tree where dynamic gates are highly coupled together, and its computational efficiency greatly depends on the chosen variable index. In this article, we put forward using an adapted K.D. Heidtmann algorithm to analyze the reliability of a complex dynamic fault tree. To improve the computational efficiency of our proposed method, products are ordered according to their lengths and compositions. To illustrate the applicability and advantages of the proposed method, a case study is analyzed. The results show the proposed method is reasonable and efficient.

Model Checking Distributed Mandatory Access Control Policies

This work examines the use of model checking techniques to verify system-level security properties of a collection of interacting virtual machines. Specifically, we examine how local access control policies implemented in individual virtual machines and a hypervisor can be shown to satisfy global access control constraints. The SAL model checker is used to model and verify a collection of stateful domains with protected resources and local MAC policies attempting to access needed resources from other domains. The model is described along with verification conditions. The need to control state-space explosion is motivated and techniques for writing theorems and limiting domains explored. Finally, analysis results are examined along with analysis complexity.

Testing real-time systems from compositional symbolic specifications

Symbolic models for testing real-time systems that abstract both data and time have been investigated. The goal is to address the state space explosion problem that may occur during test case generation. In this context, testing is often investigated by abstracting the structure of the system under test and by observing traces of expected outputs. However, since real-time systems are usually composed of a number of communicating subsystems, the next challenge is to take into account how the composition of subsystems is specified, developed and possibly tested separately or as a whole system. This paper addresses this challenge by providing a sequential and a parallel operator for composing symbolic models of real-time systems and an integration testing strategy that makes use of them. Also, we present a case study from the avionics domain and discuss barriers regarding the considered conformance relation.

Analyzing the service availability of mobile cloud computing systems by fluid-flow approximation

Mobile cloud computing (MCC) has become a promising technique to deal with computation- or data-intensive tasks. It overcomes the limited processing power, poor storage capacity, and short battery life of mobile devices. Providing continuous and on-demand services, MCC argues that the service must be available for users at anytime and anywhere. However, at present, the service availability of MCC is usually measured by some certain metrics of a real-world system, and the results do not have broad representation since different systems have different load levels, different deployments, and many other random factors. Meanwhile, for large-scale and complex types of services in MCC systems, simulation-based methods (such as Monte-Carlo simulation) may be costly and the traditional state-based methods always suffer from the problem of state-space explosion. In this paper, to overcome these shortcomings, fluid-flow approximation, a breakthrough to avoid state-space explosion, is adopted to analyze the service availability of MCC. Four critical metrics, including response time of service, minimum sensing time of devices, minimum number of nodes chosen, and action throughput, are defined to estimate the availability by solving a group of ordinary differential equations even before the MCC system is fully deployed. Experimental results show that our method costs less time in analyzing the service availability of MCC than the Markov- or simulation-based methods.

A Hierarchical Multilayer Service Composition Model for Global Virtual Organizations

A major benefit of service composition is the ability to support agile global collaborative virtual organizations. However, being global in nature, collaborative virtual organizations can have several virtual industry clusters (VIC), where each VIC has hundreds to thousands of virtual enterprises that provide functionally similar services exposed as web services. These web services can be differentiated on a high dimensionality of quality of service attributes. The dilemma the virtual enterprise broker is faced with is how to dynamically select the best combination of component services to fulfill a complex consumer need within the shortest time possible. This composite service selection problem remains a Multi-Criteria Decision Making (MCDM) NP hard problem. Although existing MCDM methods based on local planning are linearly scalable for large problems, they lack capabilities to express critical intertask constraints that are practically relevant to service consumers. MCDM global planning methods on the other hand suffer exponential state space explosion making them severely limited for large problems of industrial relevance. This paper proposes HMSCM: Hierarchical Multi-Layer Service Composition Model. HMSCM is based on the theory of Layering as Optimization Decomposition (28-31). We view the service selection process as a layer network where each layer is a subproblem to be solved. The objective of one of the layers is to maximize a local utility function over a subset of web service QoS attributes from a service consumer perspective. The objective of the other layer is to maximize a local utility function over another subset of web service QoS attributes from the perspective of the Virtual enterprise broker. We develop the algorithm: Service Layered Utility Maximization (SLUM) that extends the Mixed Integer programming model in (9). We then formulate the problem at each layer in form of SLUM. Together, the two layers attempt to achieve the global optimization objective of the network. We show analytically how HMSCM overcomes the shortcomings of existing local planning and global planning service selection methods while retaining the strengths from each. i.e HMSCM is able to scale linearly with increasing number of QoS variables and number of web services while being able to enforce global intertask constraints.

Dynamic admission control for two customer classes with stochastic demands and strict due dates

We study a dynamic capacity allocation problem with admission control decisions of a company that caters for two demand classes with random arrivals, capacity requirements and strict due dates. We formulate the problem as a Markov decision process (MDP) in order to find the optimal admission control policy that maximises the expected profit of the company. Such a formulation suffers a state-space explosion. Moreover, it involves an additional dimension arising from the multiple possible order sizes that customers can request which further increases the complexity of the problem. To reduce the cardinality of possible policies, and, thus, the computational requirements, we propose a threshold-based policy. We formulate an MDP to generate such a policy. To deal with the curse of dimensionality, we develop threshold-based approximate algorithms based on the state-reduction heuristics with aggregation proposed previously. Our results reveal that for the majority of instances considered the optimal policy has a threshold structure. We then demonstrate the superiority of the proposed threshold-based approximate algorithms over two benchmark policies in terms of the generated profits and the robustness of the solutions to changes in operational conditions. Finally, we show that our proposed policies are also robust to changes in actual demand from its estimation.

Performance measurement of models specified through component-based software architectural styles

Designing scalable and executable architectural models has a particular importance in software system development, because it allows evaluating different functional and non-functional properties of a designed system at a high level of abstraction. Measuring the performance related properties at the architectural level and before implementation, is very important while designing complex software systems. In this paper, using component-based software architectural styles specified through graph transformation systems, we propose an approach to performance measurement and analysis of software architectural models. To do so, we enrich the style with performance and timing information. Then, we propose the necessary algorithms for transforming architectural models into PEPA (Performance Evaluation Process Algebra). PEPA provides the measurement of performance metrics such as utilization of different software components and throughput. This paper proposes an efficient algorithm for model transformation. The proposed approach solves the state space explosion problem which was occurred in our previous work by generating PEPA models from the host graph instead of state space. The accuracy of this approach and other concepts are illustrated through ‘e-map router’ case study.

A performance analytical model of automated material handling system for semiconductor wafer fabrication system

To effectively analyse and evaluate the performances of closed-loop automated material handling system (AMHS) with shortcut and blocking in semiconductor wafer fabrication system, a modified Markov chain model (MMCM) has been proposed. The system characteristics, such as vehicle blockage and system’s shortcut configuration, are well considered in the MMCM. The state space explosion problem and computational challenge due to the increase of AMHS scale can be effectively eliminated. With production data from Interbay material handling system of a 300-mm semiconductor wafer fabrication line, the proposed MMCM is compared with simulation analysis model. The results demonstrate that the proposed MMCM is an effective modelling methodology for AMHS’s performance analysis at system design stage.

Statistical model checking: challenges and perspectives

Statistical model checking (SMC) is a powerful and widely used approach that consists in estimating the probability for a system to satisfy a temporal property. This is done by monitoring a finite number of executions of the system, and then extrapolating the result using statistics. The answer is correct up to some confidence that can be parameterized by the user. It is known that SMC mitigates the state-space explosion problem and allows us to handle requirements that cannot be expressed in classical temporal logics. The approach has been implemented in several toolsets, and successfully applied in a wide range of diverse areas such as systems biology, robotic, or automotive. The objectives of this special issue are (1) to survey existing results on SMC, (2) to propose SMC algorithms for a larger class of systems, and (3) to show the applicability of SMC to new emerging applications.

Special issue on “Combining Compositionality and Concurrency”: part 2

This is the second part of the special issuemotivated by theworkshop “25Years of Combining Compositionality and Concurrency” that we organised in August 2013 in Konigswinter near Bonn, Germany. The first part was published in Acta Informatica (2015) 52(1):3–106. For an introduction to the topic see our editorial there. This second part comprises four papers. The paper Richer Interface Automata with Optimistic and Pessimistic Compatibility by Gerald Luttgen, Walter Vogler, and Sascha Fendrich addresses component-based reasoning for concurrent systems via modal interface automata (MIA). The authors study optimistic and pessimistic MIA variants with internal must-transitions. They define conjunction and disjunction on interfaces as well as mechanisms for extending alphabets. The paper Compositional Verification of Asynchronous Concurrent Systems using CADP by Hubert Garavel, Frederic Lang, and Radu Mateescu investigates how various compositional techniques help to fight the state-space explosion in the verification of asynchronous message-passing systems. The techniques are implemented in the toolbox CADP (Construction and Analysis of Distributed Processes). The authors compare the different approaches using a common case study. The paper Denotational Fixed-Point Semantics for Constructive Scheduling of Synchronous Concurrency by Joaquin Aguado, Michael Mendler, Reinhard von Hanxleden, and Insa Fuhrmann defines an abstract semantic domain and an associated denotational semantics for synchronous programs. The semantics induces three notions of constructiveness, among

An I/O Efficient Model Checking Algorithm for Large-Scale Systems

Model checking is a powerful approach for the formal verification of hardware and software systems. However, this approach suffers from the state space explosion problem, which limits its application to large-scale systems due to space shortage. To overcome this drawback, one of the most effective solutions is to use external memory algorithms. In this paper, we propose an I/O efficient model checking algorithm for large-scale systems. To lower I/O complexity and improve time efficiency, we combine three new techniques: 1) a linear hash-sorting technique; 2) a cached duplicate detection technique; and 3) a dynamic path management technique. We show that the new algorithm has a lower I/O complexity than state-of-the-art I/O efficient model checking algorithms, including detect accepting cycle, maximal accepting predecessors, and iterative-deepening depth-first search. In addition, the experiments show that our algorithm obviously outperforms these three algorithms on the selected representative benchmarks in terms of performance.

A meta-heuristic solution for automated refutation of complex software systems specified through graph transformations

One of the best approaches for verifying software systems (especially safety critical systems) is the model checking in which all reachable states are generated from an initial state. All of these states are searched for errors or desirable patterns. However, the drawback for many real and complex systems is the state space explosion in which model checking cannot generate all the possible states. In this situation, designers can use refutation to check refusing a property rather than proving it. In refutation, it is very important to handle the state space for finding errors efficiently. In this paper, we propose an efficient solution to implement refutation in complex systems modeled by graph transformation. Since meta-heuristic algorithms are efficient solutions for searching in the problems with very large state spaces, we use them to find errors (e.g., deadlocks) in systems which cannot be verified through existing model checking approaches due to the state space explosion. To do so, we employ a Particle Swarm Optimization (PSO) algorithm to consider only a subset of states (called population) in each step of the algorithm. To increase the accuracy, we propose a hybrid algorithm using PSO and Gravitational Search Algorithm (GSA). The proposed approach is implemented in GROOVE, a toolset for designing and model checking graph transformation systems. The experiments show improved results in terms of accuracy, speed and memory usage in comparison with other existing approaches.

Equivalence class verification of the contract net protocol-extension

The contract net protocol is a task allocation protocol that facilitates negotiation between bidders and an auctioneer in a multi-agent system to form a contract. The contract net protocol-extension (CNP-ext) allows the bidders to interact with more than one auctioneer concurrently, and to update their bids until a bid is granted. This introduces flexibility and ensures better selection of a bid. In earlier work, we modelled the CNP-ext with coloured petri nets and showed that it terminates correctly. We also analysed the terminal states and proved that the agents have consistent beliefs at the end of negotiations. Lastly, we showed how the number of terminal states and channel bounds are related to the number of bidders. However, due to state space explosion, our results were restricted to five bidders. As all bidders are considered identical, symmetries exist in the state space. Hence, we decided to tackle this problem using equivalence classes. In this paper, after first presenting an introduction to the CNP-ext, we present a substantial revision to our CNP-ext model and an intentionally didactic description of its operation. Then, we use equivalence classes to analyse the protocol and, importantly, present a proof that our equivalence specification is consistent. Using this technique, we are able to extend the verification results to twenty-four bidders.

Deadlock-Free Scheduling of Automated Manufacturing Systems Using Petri Nets and Hybrid Heuristic Search

This paper focuses on the deadlock-free scheduling problem of automated manufacturing systems with shared resources and route flexibility, and develops novel scheduling methods by combining deadlock control policies and hybrid heuristic search. Place-timed Petri nets are used to model the systems and find a feasible sequence of firing transitions in the built model such that the firing time of its last transition is as small as possible. Based on the reachability graph of the net and a minimum processing time matrix, new heuristic and selection functions are designed to guide search processes. The proposed hybrid heuristic search is based on state space exploration and hence suffers from the state space explosion problem. In order to reduce the explored space, the search is restrained within a limited local search window. By embedding the deadlock-avoidance policies into the search processes, a novel deadlock-free hybrid heuristic search algorithm is developed. Experimental results indicate the effectiveness and superiority of the proposed algorithm over the state-of-the-art method.

Marking Estimation of P-Time Petri Nets With Unobservable Transitions

This paper focuses on the problem of estimating the marking of an unlabeled P-time Petri net with partial information modeled by unobservable transitions. The proposed approach is based on a novel state observer synthesis method under partial observation. A procedure that, given a sequence of observable transitions with their firing time instants, allows to determine the set of markings consistent with the considered observation is given. The method relies on the feasibility in time (called schedulability) of particular firing sequences, namely the candidates firing sequences. Moreover, although time is taken into consideration, the proposed technique is not hampered by the state space explosion problem as it relies on the underlying untimed structure of the P-time model considered-the building of the state class graph is not necessary.

Reliability analysis of non‐repairable systems modeled by dynamic fault trees with priority AND gates

Many real‐life systems are typically involved in sequence‐dependent failure behaviors. Such systems can be modeled by dynamic fault trees (DFTs) with priority AND gates, in which the occurrence of the top events depends on not only combinations of basic events but also their failure sequences. To the author's knowledge, the existing methods for reliability assessment of DFTs with priority AND gates are mainly Markov‐state‐space‐based, inclusion–exclusion‐based, Monte Carlo simulation‐based, or sequential binary decision diagram‐based approaches. Unfortunately, all these methods have their shortcomings. They either suffer the problem of state space explosion or are restricted to exponential components time‐to‐failure distributions or need a long computation time to obtain a solution with a high accuracy. In this article, a novel method based on dynamic binary decision tree (DBDT) is first proposed. To build the DBDT model of a given DFT, we present an adapted format of the traditional Shannon's decomposition theorem. Considering that the chosen variable index has a great effect on the final scale of disjoint calculable cut sequences generated from a built DBDT, which to some extent determines the computational efficiency of the proposed method, some heuristic branching rules are presented. To validate our proposed method, a case study is analyzed. The results indicate that the proposed method is reasonable and efficient. Copyright © 2015 John Wiley & Sons, Ltd.

Untanglings: a novel approach to analyzing concurrent systems

Abstract Substantial research efforts have been expended to deal with the complexity of concurrent systems that is inherent to their analysis, e.g., works that tackle the well-known state space explosion problem. Approaches differ in the classes of properties that they are able to suitably check and this is largely a result of the way they balance the trade-off between analysis time and space employed to describe a concurrent system. One interesting class of properties is concerned with behavioral characteristics. These properties are conveniently expressed in terms of computations, or runs , in concurrent systems. This article introduces the theory of untanglings that exploits a particular representation of a collection of runs in a concurrent system. It is shown that a representative untangling of a bounded concurrent system can be constructed that captures all and only the behavior of the system. Representative untanglings strike a unique balance between time and space, yet provide a single model for the convenient extraction of various behavioral properties. Performance measurements in terms of construction time and size of representative untanglings with respect to the original specifications of concurrent systems, conducted on a collection of models from practice, confirm the scalability of the approach. Finally, this article demonstrates practical benefits of using representative untanglings when checking various behavioral properties of concurrent systems.

A decomposition algorithm of fuzzy Petri net using an index function and incidence matrix

As with Petri nets (PNs), the state space explosion has limited further studies of fuzzy Petri net (FPN), and with the rising scale of FPN, the algorithm complexity for related applications using FPN has also rapidly increased. To overcome this challenge, we propose a decomposition algorithm that includes a backwards search stage and forward strategy for further decomposition, one that divides a large-scale FPN model into a set of sub-FPN models using both a presented index function and incidence matrix. In the backward phase, according to different output places, various completed inference paths are recognized automatically. An additional decomposition operation is then executed if the “OR” rule exists for each inference path. After analysing the proposed algorithm to confirm its rigor, a proven theorem is presented that calculates the number of inference paths in any given FPN model. A case study is used to illustrate the feasibility and robust advantages of the proposed decomposition algorithm.