Transient Reward Approximation for Continuous-Time Markov Chains

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit

Partially-shared zero-suppressed multi-terminal BDDs: concept, algorithms and applications

Multi-Terminal Binary Decision Diagrams (MTBDDs) are a well accepted technique for the state graph (SG) based quantitative analysis of large and complex systems specified by means of high-level model description techniques. However, this type of Decision Diagram (DD) is not always the best choice, since finite functions with small satisfaction sets, and where the fulfilling assignments possess many 0-assigned positions, may yield relatively large MTBDD based representations. Therefore, this article introduces zero-suppressed MTBDDs and proves that they are canonical representations of multi-valued functions on finite input sets. For manipulating DDs of this new type, possibly defined over different sets of function variables, the concept of partially-shared zero-suppressed MTBDDs and respective algorithms are developed. The efficiency of this new approach is demonstrated by comparing it to the well-known standard type of MTBDDs, where both types of DDs have been implemented by us within the C++-based DD-package JINC. The benchmarking takes place in the context of Markovian analysis and probabilistic model checking of systems. In total, the presented work extends existing approaches, since it not only allows one to directly employ (multi-terminal) zero-suppressed DDs in the field of quantitative verification, but also clearly demonstrates their efficienc

A New Algorithm for Partitioned Symbolic Reachability Analysis

AbstractBinary Decision Diagrams (BDDs) and their multi-terminal extensions have shown to be very helpful for the quantitative verification of systems. Many different approaches have been proposed for deriving symbolic state graph (SG) representations from high-level model descriptions, where compositionality has shown to be crucial for the efficiency of the schemes. Since the symbolic composition schemes deliver the potential SG of a high-level model, one must execute a reachability analysis on the level of the symbolic structures. This step is the main resource of CPU-time and peak memory consumption when it comes to symbolic SG generation. In this work a new operator for zero-suppressed BDDs and their multi-terminal extensions for carrying out (partitioned) symbolic reachability analysis is presented. This algorithm not only replaces standard BDD-based schemes, it even makes symbolic composition as found in contemporary symbolic model checkers such as Prism and Caspa obsolete

Transient Reward Approximation for Continuous-Time Markov Chains

Abstract We are interested in the analysis of very large continuoustime Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e. g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies

Tools and Algorithms for the Construction and Analysis of Systems

This book is Open Access under a CC BY licence. The LNCS 11427 and 11428 proceedings set constitutes the proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019. The total of 42 full and 8 short tool demo papers presented in these volumes was carefully reviewed and selected from 164 submissions. The papers are organized in topical sections as follows: Part I: SAT and SMT, SAT solving and theorem proving; verification and analysis; model checking; tool demo; and machine learning. Part II: concurrent and distributed systems; monitoring and runtime verification; hybrid and stochastic systems; synthesis; symbolic verification; and safety and fault-tolerant systems

Decision diagrams: Extensions and applications to reachability analysis

Symbolic data structures and algorithms are increasingly popular tools for the analysis of complex systems. Given a high-level model of a system, such as a Petri Net, we can automatically verify certain properties about it. In this thesis, we develop data structures and techniques that can be used to improve such analyses. First, we show how decision diagrams can be used efficiently in traditional explicit generation algorithms. Next, we show how symbolic reachability analysis can be used to detect deadlocks in Petri Nets. We also present a symbolic approach that can detect deadlocks in unbounded Petri Nets. Finally, we introduce a new type of decision diagram, ESRBDD, that combines multiple reduction rules, is canonical, and produces a more compact representation than previous efforts. We show that operations on ESRBDDs are at least as efficient as those on the underlying decision diagrams and introduce extensions to ESRBDDs that improve on their compactness and operational efficiency

JINC - A Multi-Threaded Library for Higher-Order Weighted Decision Diagram Manipulation

Ordered Binary Decision Diagrams (OBDDs) have been proven to be an efficient data structure for symbolic algorithms. The efficiency of the symbolic methods de- pends on the underlying OBDD library. Available OBDD libraries are based on the standard concepts and so far only differ in implementation details. This thesis introduces new techniques to increase run-time and space-efficiency of an OBDD library. This thesis introduces the framework of Higher-Order Weighted Decision Diagrams (HOWDDs) to combine the similarities of different OBDD variants. This frame- work pioneers the basis for the new variant Toggling Algebraic Decision Diagrams (TADDs) which has been shown to be a space-efficient HOWDD variant for sym- bolic matrix representation. The concept of HOWDDs has been use to implement the OBDD library JINC. This thesis also analyzes the usage of multi-threading techniques to speed-up OBDD manipulations. A new reordering framework ap- plies the advantages of multi-threading techniques to reordering algorithms. This approach uses an abstraction layer so that the original reordering algorithms are not touched. The challenge that arise from a straight forward algorithm is that the computed-tables and the garbage collection are not as efficient as in a single- threaded environment. We resolve this problem by developing a new multi-operand APPLY algorithm that eliminates the creation of temporary nodes which could occur during computation and thus reduces the need for caching or garbage collection. The HOWDD framework leads to an efficient library design which has been shown to be more efficient than the established OBDD library CUDD. The HOWDD instance TADD reduces the needed number of nodes by factor two compared to ordinary ADDs. The new multi-threading approaches are more efficient than single-threading approaches by several factors. In the case of the new reordering framework the speed- up almost equals the theoretical optimal speed-up. The novel multi-operand APPLY algorithm reduces the memory usage for the n-queens problem by factor 50 which enables the calculation of bigger problem instances compared to the traditional APPLY approach. The new approaches improve the performance and reduce the memory footprint. This leads to the conclusion that applications should be reviewed whether they could benefit from the new multi-threading multi-operand approaches introduced and discussed in this thesis

High-Level Analysis of the Impact of Soft-Faults in Cyberphysical Systems

As digital systems grow in complexity and are used in a broader variety of safety-critical applications, there is an ever-increasing demand for assessing the dependability and safety of such systems, especially when subjected to hazardous environments. As a result, it is important to identify and correct any functional abnormalities and component faults as early as possible in order to minimize performance degradation and to avoid potential perilous situations. Existing techniques often lack the capacity to perform a comprehensive and exhaustive analysis on complex redundant architectures, leading to less than optimal risk evaluation. Hence, an early analysis of dependability of such safety-critical applications enables designers to develop systems that meets high dependability requirements. Existing techniques in the field often lack the capacity to perform full system analyses due to state-explosion limitations (such as transistor and gate-level analyses), or due to the time and monetary costs attached to them (such as simulation, emulation, and physical testing). In this work we develop a system-level methodology to model and analyze the effects of Single Event Upsets (SEUs) in cyberphysical system designs. The proposed methodology investigates the impacts of SEUs in the entire system model (fault tree level), including SEU propagation paths, logical masking of errors, vulnerability to specific events, and critical nodes. The methodology also provides insights on a system's weaknesses, such as the impact of each component to the system's vulnerability, as well as hidden sources of failure, such as latent faults. Moreover, the proposed methodology is able to identify and categorize the system's components in order of criticality, and to evaluate different approaches to the mitigation of such criticality (in the form of different configurations of TMR) in order to obtain the most efficient mitigation solution available. The proposed methodology is also able to model and analyze system components individually (system component level), in order to more accurately estimate the component's vulnerability to SEUs. In this case, a more refined analysis of the component is conducted, which enables us to identify the source of the component's criticality. Thereafter, a second mitigation mechanic (internal to the component) takes place, in order to evaluate the gains and costs of applying different configurations of TMR to the component internally. Finally, our approach will draw a comparison between the results obtained at both levels of analysis in order to evaluate the most efficient way of improving the targeted system design

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems