PRISM: Probabilistic Symbolic Model Checker

This paper extends the graphical and formal language of UML-B to provide the ability to model probabilities. Discrete probabilities, interval probabilities, and stochastic delays are added to the UML-B's state-machine syntax, and their corresponding semantics are defined in Event-B. In addition, as a secondary contribution, UML-B (probabilistic) state-machine models are defined as MDP (Markov Decision Process) models in order to provide a means of quantitative verification in PRISM (Probabilistic Symbolic Model Checker). As an important feature of the proposed method, it does not change the Event-B syntax or semantics. To evaluate this work, as a case study, the Zeroconf protocol will be modeled in the extended UML-B using the Rodin tool, and its Event-B counterpart is converted to a PRISM model. The results of evaluations indicate that this study's additions provide the capability of modeling and verification of probabilistic and stochastic systems.

Recently, probabilistic systems have been widely used. People have drawn attention to counterexample generation for probabilistic system model checking. Current works are mainly focusing on the counterexample generation for Markov chains. Probabilistic timed automata (PTA) is the extension of Markov chain with non-determinism and system clocks. This paper focuses on counterexample representation while model checking PTA. Firstly, the semantic of PTA can be regarded as Markov decision process (MDP); secondly, we use adversary to convert MDP into discrete-time Markov chains (DTMCs); thirdly, we convert DTMCs into weighted graph. So, counterexample generation for PTA can be converted into shortest path problem for weighted digraph. Finally, we use regular expressions to represent the counterexample.

We describe the dual-processor parallelisation of a symbolic (BDD-based) implementation of probabilistic model checking. We use multi-terminal BDDs (binary decision diagrams), which allow a compact representation of large, structured Markov chains. We show that they also provide a convenient block decomposition of the Markov chain which we use to implement a parallelised version of the Gauss-Seidel iterative method. We provide experimental results on a range of case studies to illustrate the effectiveness of the technique, observing an average speed-up of 1.8 with two processors. Furthermore, we present an optimisation for our method based on preconditioning.

We study a quantum entanglement switch that serves $k$ users in a star topology. We model variants of the system using Markov chains and standard queueing theory and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. While it is more accurate to use a discrete-time Markov chain (DTMC) to model such systems, we quickly encounter practical constraints of using this technique and switch to using continuous-time Markov chains (CTMCs). Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can model the effects of decoherence of quantum states fairly easily using CTMCs. We also compare the results we obtain from the DTMC against the CTMC in the case of homogeneous links and infinite buffer, and learn that the CTMC is a reasonable approximation of the DTMC. From numerical observations, we discover that decoherence has little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating close to stability constraints, buffer size and decoherence can have significant effects on performance metrics. We also learn that in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, while increasing the buffer size further yields diminishing returns.

Effective and automated verification techniques able to provide assurances of performance and scalability are highly demanded in the context of microservices systems. In this paper, we introduce a methodology that applies specification-driven load testing to learn the behavior of the target microservices system under multiple deployment configurations. Testing is driven by realistic workload conditions sampled in production. The sampling produces a formal description of the users’ behavior through a Discrete Time Markov Chain. This model drives multiple load testing sessions that query the system under test and feed a Bayesian inference process which incrementally refines the initial model to obtain a complete specification from run-time evidence as a Continuous Time Markov Chain. The complete specification is then used to conduct automated verification by using probabilistic model checking and to compute a configuration score that evaluates alternative deployment options. This paper introduces the methodology, its theoretical foundation, and the toolchain we developed to automate it. Our empirical evaluation shows its applicability, benefits, and costs on a representative microservices system benchmark. We show that the methodology detects performance issues, traces them back to system-level requirements, and, thanks to the configuration score, provides engineers with insights on deployment options. The comparison between our approach and a selected state-of-the-art baseline shows that we are able to reduce the cost up to 73% in terms of number of tests. The verification stage requires negligible execution time and memory consumption. We observed that the verification of 360 system-level requirements took ∼1 minute by consuming at most 34 KB. The computation of the score involved the verification of ∼7k (automatically generated) properties verified in ∼72 seconds using at most ∼50 KB.

With the rapid development of IoT in recent years, Smart Home, one of the IoT application markets, has also been gaining popularity. The emergence of Smart Homes has brought convenience to people’s lives, especially for people who live alone with physical illness. Smart Home users normally have higher expectations for reliability and safety of sensor systems, particularly in light of how complicated and uncertain the living environment is. The present work attempts to propose a data-knowledge integrated solution to analyze, model and evaluate the reliability of sensor systems in a smart home by combining quantitative reliability analysis and probabilistic model checking. Probabilistic model checking techniques use logical reasoning to check quantitative properties (as system requirements) and provide mathematical guarantee for them. More specifically, Smart Home Sensor Systems (SHSS) is described as a Markov Chain, commonly used probabilistic model, which models the system behaviour (e.g., probabilistic choice of state transition), and SHSS reliability properties are defined by Probabilistic Computation Tree Logic (PCTL). These choices of model and specification formula allow us to use one of the most recently developed open source probabilistic model checkers, PRISM, to perform the model checking of reliability verification task in SHSS. A real world smart home dataset (Van Kasteren dataset) is employed along with PRISM to illustrate the modeling approach and demonstrate the feasibility and applicability of the proposed approach.

Towards enhanced threat modelling and analysis using a Markov Decision Process

Background and purpose Recent methodological reviews of evaluations of behaviour change interventions in public health have highlighted that the decay in effectiveness over time has been mostly overlooked, potentially leading to suboptimal decision-making. While, in principle, discrete-time Markov chains—the most commonly used modelling approach—can be adapted to account for decay in effectiveness, this framework inherently lends itself to strong model simplifications. The application of formal and more appropriate modelling approaches has been supported, but limited progress has been made to date. The purpose of this paper is to encourage this shift by offering a practical guide on how to model decay in effectiveness using a continuous-time Markov chain (CTMC)-based approach.MethodsA CTMC approach is demonstrated, with a contextualized tutorial being presented to facilitate learning and uptake. A worked example based on the stylized case study in physical activity promotion is illustrated with accompanying R code.DiscussionThe proposed framework presents a relatively small incremental change from the current modelling practice. CTMC represents a technical solution which, in absence of relevant data, allows for formally testing the sensitivity of results to assumptions regarding the long-term sustainability of intervention effects and improving model transparency.Conclusions The use of CTMC should be considered in evaluations where decay in effectiveness is likely to be a key factor to consider. This would enable more robust model-based evaluations of population-level programmes to promote behaviour change and reduce the uncertainty surrounding the decision to invest in these public health interventions.

ABSTRACTIn epidemic modelling, the emergence of a disease is characterized by the low numbers of infectious individuals. Environmental randomness impacts outcomes such as the outbreak or extinction of the disease in this case. This randomness can be accounted for by modelling the system as a continuous time Markov chain, . The probability of extinction given some initial state is the probability of hitting a subset of the state space associated with extinction for the initial state. This hitting probability can be studied by passing to the discrete time Markov chain (DTMC), . An approach is presented to approximate a DTMC on a countably infinite state space by a DTMC on a finite state space for the purpose of solving general hitting problems. This approach is applied to approximate the probability of disease extinction in an epidemic model. It is also applied to evaluate a heterogeneous disease control strategy in a metapopulation.

Problem statement: Membrane computing formalism has provided better modeling capabilities for biological systems in comparison to conventional mathematical models. Model checking could be used to reason about the biological system in detail and with precision by verifying formally whether membrane computing model meets the properties of the system. Approach: This study was carried to investigate the preservation of properties of two biological systems that had been modeled and simulated in membrane computing by a method of model checking using PRISM. The two biological systems were prey-predator population and signal processing in the legend-receptor networks of protein TGF-β. Results: The model checking of membrane computing model of the biological systems with five different properties showed that the properties of the biological systems could be preserved in the membrane computing model. Conclusion: Membrane computing model not only provides a better approach in representing and simulating a biological system but also able to sustain the basic properties of the system.

<b>Problem statement:</b> Most of the biological systems have been hierarchical in structure with processes interacting between different compartments. Membrane computing formalism has provided modeling capabilities in representing the structure of biological systems. <b>Approach:</b> This study was carried to investigate the modeling of a multi-compartment biological system by using membrane computing formalism. The hormone-induced calcium oscillations in liver cells which was modeled with ordinary differential equation was used as a case study. The membrane computing model of this case study was verified and validated by using simulation strategy of Gillespie algorithm and the method of model checking using probabilistic symbolic model checker. The results of membrane computing model were compared to the ordinary differential equation model. <b>Results:</b> The simulation and model checking of membrane computing model of the biological case study showed that the properties of the multi-compartments biological system could be preserved with the membrane computing model. Membrane computing model could also accommodate the structure and processes of the multi-compartments biological system which were absent in the ordinary differential equation model. <b>Conclusion:</b> Membrane computing model provides a better approach in representing a multi-compartment system and able to sustain the basic properties of the system. However appropriate value of parameters to represent the rules of the processes of the membrane computing model to manage the stochastic behavior should be formulated to meet the performance of the biological system.

Variations in timing can occur due to multiple sources on a chip. Many circuit level statistical techniques are used to analyze timing in the presence of these sources of variation. It is desirable to have “variation awareness” at the Register Transfer Level (RTL), and estimate block level delay distributions early in the design cycle, to evaluate design choices quickly and minimize post-synthesis simulation costs. We introduce SHARPE, a rigorous, systematic methodology to verify design correctness in RTL in the presence of variations. In this paper, we describe SHARPE in the context of computing statistical delay invariants in the presence of input variations. We treat the RTL source code as a program and use static program analysis techniques to compute probabilities. We model the probabilistic RTL modules as Discrete Time Markov Chains (DTMCs) that are then checked formally for probabilistic invariants using PRISM, a probabilistic model checker. Our technique is illustrated on the RTL description of the data path of OR1200, an open source embedded processor. We demonstrate the enhanced scalability of SHARPE by applying compositional reasoning for probabilistic model checking.

The contribution first describes the implementation of Continuous-Time Markov Chains (CTMC) in the language Modelica; this enables the simulation by powerful solvers making typical Functional Safety applications numerically more efficient and reliable than with classically used Discrete-Time Markov Chains (DTMC). Secondly, the CTMC are extended to Multi-Phase Markov Chains (CTMC MP ) enabling the inclusion of maintenance (restoration) actions as well as online diagnostics, which is finally elaborated to the online prediction of an individual system's safety quantities.

This study proposes a hierarchical probabilistic computation tree logic, HpCTL, which is an extension of the standard probabilistic computation tree logic pCTL, as a theoretical basis for hierarchical probabilistic CTL model checking. Hierarchical probabilistic model checking is a new paradigm that can appropriately verify hierarchical randomized (or stochastic) systems. Furthermore, a probability-measure-independent translation from HpCTL into pCTL is defined, and a theorem for embedding HpCTL into pCTL is proved using this translation. Finally, the relative decidability of HpCTL with respect to pCTL is proved using this embedding theorem. These embedding and relative decidability results allow us to reuse the standard pCTL-based probabilistic model checking algorithms to verify hierarchical randomized systems that can be described using HpCTL.

On the Complexity and Optimization of Branching Programs for Decision Diagram Machines