Steffen Märcker

Computing Conditional Probabilities in Markovian Models Efficiently

The fundamentals of probabilistic model checking for Markovian models and temporal properties have been studied extensively in the past 20 years. Research on methods for computing conditional probabilities for temporal properties under temporal conditions is, however, comparably rare. For computing conditional probabilities or expected values under ω-regular conditions in Markov chains, we introduce a new transformation of Markov chains that incorporates the effect of the condition into the model. For Markov decision processes, we show that the task to compute maximal reachability probabilities under reachability conditions is solvable in polynomial time, while it was conjectured to be computationally hard. Using adaptions of known automata-based methods, our algorithm can be generalized for computing the maximal conditional probabilities for ω-regular events under ω-regular conditions. The feasibility of our algorithms is studied in two benchmark examples.

Advances in Symbolic Probabilistic Model Checking with PRISM

For modeling and reasoning about complex systems, symbolic methods provide a prominent way to tackle the state explosion problem. It is well known that for symbolic approaches based on binary decision diagrams BDD, the ordering of BDD variables plays a crucial role for compact representations and efficient computations. We have extended the popular probabilistic model checker PRISM with support for automatic variable reordering in its multi-terminal-BDD-based engines and report on benchmark results. Our extensions additionally allow the user to manually control the variable ordering at a finer-grained level. Furthermore, we present our implementation of the symbolic computation of quantiles and support for multi-reward-bounded properties, automata specifications and accepting end component computations for Streett conditions.

Locks: Picking key methods for a scalable quantitative analysis ✩

Abstract Functional correctness of low-level operating-system (OS) code is an indispensable requirement. However, many applications rely also on quantitative aspects such as speed, energy efficiency, resilience with regards to errors and other cost factors. We report on our experiences of applying probabilistic model-checking techniques for analysing the quantitative long-run behaviour of low-level OS-code. Our approach, illustrated in a case study analysing a simple test-and-test-and-set (TTS) spinlock protocol, combines measure-based simulation with probabilistic model-checking to obtain high-level models of the performance of realistic systems and to tune the models to predict future system behaviour. We report how we obtained a nearly perfect match of analytic results and measurements and how we tackled the state-explosion problem to obtain model-checking results for a large number of processes where measurements are no longer feasible. These results gave us valuable insights in the delicate interplay between lock load, average spinning times and other performance measures.

Waiting for Locks: How Long Does It Usually Take?

Reliability of low-level operating-system (OS) code is an indispensable requirement. This includes functional properties from the safety-liveness spectrum, but also quantitative properties stating, e.g., that the average waiting time on locks is sufficiently small or that the energy requirement of a certain system call is below a given threshold with a high probability. This paper reports on our experiences made in a running project where the goal is to apply probabilistic model checking techniques and to align the results of the model checker with measurements to predict quantitative properties of low-level OS code.

A Probabilistic Quantitative Analysis of Probabilistic-Write/Copy-Select

Probabilistic-Write/Copy-Select (PWCS) is a novel synchronization scheme suggested by Nicholas Mc Guire which avoids expensive atomic operations for synchronizing access to shared objects. Instead, PWCS makes inconsistencies detectable and recoverable. It builds on the assumption that, for typical workloads, the probability for data races is very small. Mc Guire describes PWCS for multiple readers but only one writer of a shared data structure. In this paper, we report on the formal analysis of the PWCS protocol using a continuous-time Markov chain model and probabilistic model checking techniques. Besides the original PWCS protocol, we also considered a variant with multiple writers. The results were obtained by the model checker PRISM and served to identify scenarios in which the use of the PWCS protocol is justified by guarantees on the probability of data races. Moreover, the analysis showed several other quantitative properties of the PWCS protocol.

Chiefly Symmetric: Results on the Scalability of Probabilistic Model Checking for Operating-System Code

Reliability in terms of functional properties from the safety-liveness spectrum is an indispensable requirement of low-level operating-system (OS) code. However, with evermore complex and thus less predictable hardware, quantitative and probabilistic guarantees become more and more important. Probabilistic model checking is one technique to automatically obtain these guarantees. First experiences with the automated quantitative analysis of low-level operating-system code confirm the expectation that the naive probabilistic model checking approach rapidly reaches its limits when increasing the numbers of processes. This paper reports on our work-in-progress to tackle the state explosion problem for low-level OS-code caused by the exponential blow-up of the model size when the number of processes grows. We studied the symmetry reduction approach and carried out our experiments with a simple test-and-test-and-set lock case study as a representative example for a wide range of protocols with natural inter-process dependencies and long-run properties. We quickly see a state-space explosion for scenarios where inter-process dependencies are insignificant. However, once inter-process dependencies dominate the picture models with hundred and more processes can be constructed and analysed.

Probabilistic Model Checking and Non-standard Multi-objective Reasoning

Probabilistic model checking is a well-established method for the automated quantitative system analysis. It has been used in various application areas such as coordination algorithms for distributed systems, communication and multimedia protocols, biological systems, resilient systems or security. In this paper, we report on the experiences we made in inter-disciplinary research projects where we contribute with formal methods for the analysis of hardware and software systems. Many performance measures that have been identified as highly relevant by the respective domain experts refer to multiple objectives and require a good balance between two or more cost or reward functions, such as energy and utility. The formalization of these performance measures requires several concepts like quantiles, conditional probabilities and expectations and ratios of cost or reward functions that are not supported by state-ofthe- art probabilistic model checkers. We report on our current work in this direction, including applications in the field of software product line verification.

Advances in probabilistic model checking with PRISM: variable reordering, quantiles and weak deterministic Büchi automata

The popular model checker PRISM has been successfully used for the modeling and analysis of complex probabilistic systems. As one way to tackle the challenging state explosion problem, PRISM supports symbolic storage and manipulation using multi-terminal binary decision diagrams for representing the models and in the computations. However, it lacks automated heuristics for variable reordering, even though it is well known that the order of BDD variables plays a crucial role for compact representations and efficient computations. In this article, we present a collection of extensions to PRISM. First, we provide support for automatic variable reordering within the symbolic engines of PRISM and allow users to manually control the variable ordering at a fine-grained level. Second, we provide extensions in the realm of reward-bounded properties, namely symbolic computations of quantiles in Markov decision processes and, for both the explicit and symbolic engines, the approximative computation of quantiles for continuous-time Markov chains as well as support for multi-reward-bounded properties. Finally, we provide an implementation for obtaining minimal weak deterministic Büchi automata for the obligation fragment of linear temporal logic (LTL), with applications for expected accumulated reward computations with a finite horizon given by a co-safe LTL formula.

A Hardware/Software Stack for Heterogeneous Systems

Plenty of novel emerging technologies are being proposed and evaluated today, mostly at the device and circuit levels. It is unclear what the impact of different new technologies at the system level will be. What is clear, however, is that new technologies will make their way into systems and will increase the already high complexity of heterogeneous parallel computing platforms, making it ever so difficult to program them. This paper discusses a programming stack for heterogeneous systems that combines and adapts well-understood principles from different areas, including capability-based operating systems, adaptive application runtimes, dataflow programming models, and model checking. We argue why we think that these principles built into the stack and the interfaces among the layers will also be applicable to future systems that integrate heterogeneous technologies. The programming stack is evaluated on a tiled heterogeneous multicore.

Decision making improves sperm chemotaxis in the presence of noise

To navigate their surroundings, cells rely on sensory input that is corrupted by noise. In cells performing chemotaxis, such noise arises from the stochastic binding of signalling molecules at low chemoattractant concentrations. We reveal a fundamental relationship between the speed of chemotactic steering and the strength of directional fluctuations that result from the amplification of noise in a chemical input signal. This relation implies a trade-off between steering that is slow and reliable, and steering that is fast but less reliable. We show that dynamic switching between these two modes of steering can substantially increase the probability to find a target, such as an egg to be found by sperm cells. This decision making confers no advantage in the absence of noise, but is beneficial when chemical signals are detectable, yet characterized by low signal-to-noise ratios. The latter applies at intermediate distances from a target, where signalling molecules are diluted, thus defining a ‘noise zone’ that cells have to cross. Our results explain decision making observed in recent experiments on sea urchin sperm chemotaxis. More generally, our theory demonstrates how decision making enables chemotactic agents to cope with high levels of noise in gradient sensing by dynamically adjusting the persistence length of a biased random walk.