Towards efficient analysis of Markov automata

One of the most expressive formalisms to model concurrent systems is Markov automata. They serve as a semantics for many higher-level formalisms, such as generalised stochastic Petri nets and dynamic fault trees. Two of the most challenging problems for Markov automata to date are (i) the optimal time-bounded reachability probability and (ii) the optimal long-run average rewards. In this thesis, we aim at designing efficient sound techniques to analyse them. We approach the problem of time-bounded reachability from two different angles. First, we study the properties of the optimal solution and exploit this knowledge to construct an efficient algorithm that approximates the optimal values up to a guaranteed error bound. This algorithm is exhaustive, i. e. it computes values for each state of the Markov automaton. This may be a limitation for very large or even infinite Markov automata. To address this issue we design a second algorithm that approximates the optimal solution by only working with part of the total state-space. For the problem of long-run average rewards there exists a polynomial algorithm based on linear programming. Instead of chasing a better theoretical complexity bound we search for a practical solution based on an iterative approach. We design a value iteration algorithm that in our empirical evaluation turns out to scale several orders of magnitude better than the linear programming based approach.Markov-Automaten bilden einen der ausdrucksstärksten Formalismen um Nebenläufige Systeme zu modellieren. Sie werden benutzt um die Semantik vieler höherer Formalismen wie stochastischer Petri-Netze [Mar95, EHZ10] und Dynamic Fault Trees [DBB90] zu beschreiben. Die zwei herausfordernder Probleme im Bereich der Analyse großer Markov- Automaten sind (i) die zeitbeschränkten Erreichbarkeitwahrscheinlichkeit und (ii) optimale langfristige durchschnittliche Rewards. Diese Arbeit zielt auf das Design effizienter und korrekter Techniken um sie zu untersuchen. Das Problem der zeitbeschränkten Erreichbarkeitswahrscheinlichkeit gehen wir aus zwei verschiedenen Richtungen an: Zum einen studieren wir die Eigenschaften optimaler Lösungen und nutzen dieses Wissen um einen effizienten Approximationsalgorithmus zu bilden, der optimale Werte bis auf eine garantierte Fehlertoleranz berechnet. Dieser Algorithmus basiert darauf, Werte für jeden Zustand des Markov-Automaten zu berechnen. Dies kann die Anwendbarkeit für große oder gar unendliche Automaten einschränken. Um diese Problem zu lösen präsentieren wir einen zweiten Algorithmus, der die optimale Lösung approximiert, und dabei ausschließlich einen Teil des Zustandsraumes betrachtet. Für das Problem der optimalen langfristigen durchschnittlichen Rewards gibt es einen polynomiellen Algorithmus auf Basis linearer Programmierung. Anstelle eine bessere theoretische Komplexität anzustreben, konzentrieren wir uns darauf, eine praktische Lösung auf Basis eines iterativen Ansatzes zu finden. Wie entwickeln einen Werte-iterierenden Algorithmus der in unserer empirischen Evaluation um mehrere Größenordnungen besser als der auf linearer Programmierung basierende Ansatz skaliert

A modest approach to Markov automata

A duplicate of https://zenodo.org/record/5758839. Reason: The submitter forgot to indicate the DOI before publishing, so it got another one assigned automatically, which is unchangeable

A Modest Approach to Modelling and Checking Markov Automata (Artifact)

Markov automata are a compositional modelling formalism with continuous stochastic time, discrete probabilities, and nondeterministic choices. In our QEST 2019 paper titled "A Modest Approach to Modelling and Checking Markov Automata", we present extensions to the Modest language and the 'mcsta' model checker of the Modest Toolset to describe and analyse Markov automata models. The verification of Markov automata models requires dedicated algorithms for time-bounded probabilistic reachability and long-run average rewards. In the paper, we describe several recently developed such algorithms as implemented in 'mcsta' and evaluate them on a comprehensive set of benchmarks. Our evaluation shows that 'mcsta' improves the performance and scalability of Markov automata model checking compared to earlier and alternative tools. This artifact contains (1) the version of 'mcsta' and (2) the model files used for our experiments, (3) the raw experimental results, and (4) Linux scripts to replicate the experiments

A Modest Approach to Modelling and Checking Markov Automata

Markov automata are a compositional modelling formalism with continuous stochastic time, discrete probabilities, and nondeterministic choices. In this paper, we present extensions to the Modest language and the mcsta model checker to describe and analyse Markov automata models. Modest is an expressive high-level language with roots in process algebra that allows large models to be specified in a succinct, modular way. We explain its use for Markov automata and illustrate the advantages over alternative languages. The verification of Markov automata models requires dedicated algorithms for time-bounded probabilistic reachability and long-run average rewards. We describe several recently developed such algorithms as implemented in mcsta and evaluate them on a comprehensive set of benchmarks. Our evaluation shows that mcsta improves the performance and scalability of Markov automata model checking compared to earlier and alternative tools

Effect of Radiation Therapy on Composition of Lymphocyte Populations in Patients with Primary Breast Cancer

Background: Radiation therapy (RT) is an important step in the treatment of primary breast cancer as it is one of the leading contributors to cancer incidence among women. Most patients with this disease acquire radiation-induced lymphopenia in the early post-radiation period; however, little is known about the effect of RT on the composition of lymphocyte populations in such patients. This study was aimed at investigating the effect of adjuvant remote RT—performed in the classical mode for patients with primary breast cancer—on the main components of cell-mediated immunity (major lymphocyte populations), including those in patients receiving chemotherapy. Methods: Between 2020 and 2022, 96 patients with stage I–III breast cancer were included in this study. All patients in the final stage of complex treatment received RT via a 3D conformal technique (3DCRT). The clinical target volume of this RT included the breast or chest wall and locoregional lymphatics. Flow cytometry was used to assess the levels and phenotypes of circulating lymphocytes before and after RT (no more than 7 days before and after RT). The evaluation of the impact of polychemotherapy (PCT) was conducted to determine whether it was a risk factor for the onset of radio-induced lymphopenia (RIL) in the context of RT. Results: When assessing the immune status in the general group of patients (n = 96), before the start of adjuvant external beam radiotherapy (EBRT), the average number of lymphocytes was 1.68 ± 0.064 × 109/L; after the course of adjuvant EBRT, it decreased to 1.01 ± 0.044 × 109/L (p t-test, p < 0.05). Conclusion: The adaptive immune system in breast cancer patients changed in the early post-radiation period. The absolute levels of B-, T- and natural killer cells significantly reduced after RT regardless of whether the patients previously underwent chemotherapy courses. RT for patients with primary breast cancer should be considered in clinical management because it significantly alters lymphocyte levels and should be considered when assessing antitumor immunity, as significant changes in T-cell immunity have been observed. In addition, the identified changes are critical if specific targeted therapy or immunotherapy is needed

Influence of Sports Training in Foothills on the Professional Athlete’s Immunity

Neuroplasticity and inflammation play important part in the body’s adaptive reactions in response to prolonged physical activity. These processes are associated with the cross-interaction of the nervous and immune systems, which is realized through the transmission of signals from neurotransmitters and cytokines. Using the methods of flow cytometry and advanced biochemical analysis of blood humoral parameters, we showed that intense and prolonged physical activity at the anaerobic threshold, without nutritional and metabolic support, contributes to the development of exercise-induced immunosuppression in sportsmen. These athletes illustrate the following signs of a decreased immune status: fewer absolute indicators of the content of leukocytes, lowered values in the immunoregulatory index (CD4+/CD8+), and diminished indicators of humoral immunity (immunoglobulins A, M, and G, and IFN-γ). These factors characterize the functional state of cellular and humoral immunity and their reduction affects the prenosological risk criteria, indicative of the athletes’ susceptibility to develop exercise-induced immunosuppression