Computing Quantiles in Markov Reward Models

Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, namely quantiles. A typical quantile query takes as input a lower probability bound p and a reachability property. The task is then to compute the minimal reward bound r such that with probability at least p the target set will be reached before the accumulated reward exceeds r. Quantiles are well-known from mathematical statistics, but to the best of our knowledge they have not been addressed by the model checking community so far. In this paper, we study the complexity of quantile queries for until properties in discrete-time finite-state Markov decision processes with non-negative rewards on states. We show that qualitative quantile queries can be evaluated in polynomial time and present an exponential algorithm for the evaluation of quantitative quantile queries. For the special case of Markov chains, we show that quantitative quantile queries can be evaluated in time polynomial in the size of the chain and the maximum reward.Comment: 17 pages, 1 figure; typo in example correcte

Contextualized Programs for Ontology-Mediated Probabilistic System Analysis

Modeling context-dependent systems for their analysis is challenging as verification tools usually rely on an input language close to imperative programming languages which need not support description of contexts well. We introduce the concept of contextualized programs where operational behaviors and context knowledge are modeled separately using domain-specific formalisms. For behaviors specified in stochastic guarded-command language and contextual knowledge given by OWL description logic ontologies, we develop a technique to efficiently incorporate contextual information into behavioral descriptions by reasoning about the ontology. We show how our presented concepts support and facilitate the quantitative analysis of context-dependent systems using probabilistic model checking. For this, we evaluate our implementation on a case study issuing a multi-server system

Ontology-Mediated Probabilistic Model Checking: Extended Version

Probabilistic model checking (PMC) is a well-established method for the quantitative analysis of dynamic systems. On the other hand, description logics (DLs) provide a well-suited formalism to describe and reason about static knowledge, used in many areas to specify domain knowledge in an ontology. We investigate how such knowledge can be integrated into the PMC process, introducing ontology-mediated PMC. Specifically, we propose a formalism that links ontologies to dynamic behaviors specified by guarded commands, the de-facto standard input formalism for PMC tools such as Prism. Further, we present and implement a technique for their analysis relying on existing DL-reasoning and PMC tools. This way, we enable the application of standard PMC techniques to analyze knowledge-intensive systems. Our approach is implemented and evaluated on a multi-server system case study, where different DL-ontologies are used to provide specifications of different server platforms and situations the system is executed in

Quantitative Verification: Formal Guarantees for Timeliness, Reliability and Performance

Computerised systems appear in almost all aspects of our daily lives, often in safety-critical scenarios such as embedded control systems in cars and aircraft or medical devices such as pacemakers and sensors. We are thus increasingly reliant on these systems working correctly, despite often operating in unpredictable or unreliable environments. Designers of such devices need ways to guarantee that they will operate in a reliable and efficient manner. Quantitative verification is a technique for analysing quantitative aspects of a system's design, such as timeliness, reliability or performance. It applies formal methods, based on a rigorous analysis of a mathematical model of the system, to automatically prove certain precisely specified properties, e.g. ``the airbag will always deploy within 20 milliseconds after a crash'' or ``the probability of both sensors failing simultaneously is less than 0.001''. The ability to formally guarantee quantitative properties of this kind is beneficial across a wide range of application domains. For example, in safety-critical systems, it may be essential to establish credible bounds on the probability with which certain failures or combinations of failures can occur. In embedded control systems, it is often important to comply with strict constraints on timing or resources. More generally, being able to derive guarantees on precisely specified levels of performance or efficiency is a valuable tool in the design of, for example, wireless networking protocols, robotic systems or power management algorithms, to name but a few. This report gives a short introduction to quantitative verification, focusing in particular on a widely used technique called model checking, and its generalisation to the analysis of quantitative aspects of a system such as timing, probabilistic behaviour or resource usage. The intended audience is industrial designers and developers of systems such as those highlighted above who could benefit from the application of quantitative verification,but lack expertise in formal verification or modelling

A Temporal Logic for Hyperproperties

Hyperproperties, as introduced by Clarkson and Schneider, characterize the correctness of a computer program as a condition on its set of computation paths. Standard temporal logics can only refer to a single path at a time, and therefore cannot express many hyperproperties of interest, including noninterference and other important properties in security and coding theory. In this paper, we investigate an extension of temporal logic with explicit path variables. We show that the quantification over paths naturally subsumes other extensions of temporal logic with operators for information flow and knowledge. The model checking problem for temporal logic with path quantification is decidable. For alternation depth 1, the complexity is PSPACE in the length of the formula and NLOGSPACE in the size of the system, as for linear-time temporal logic

Modelling and analyzing adaptive self-assembling strategies with Maude

Building adaptive systems with predictable emergent behavior is a challenging task and it is becoming a critical need. The research community has accepted the challenge by introducing approaches of various nature: from software architectures, to programming paradigms, to analysis techniques. We recently proposed a conceptual framework for adaptation centered around the role of control data. In this paper we show that it can be naturally realized in a reflective logical language like Maude by using the Reflective Russian Dolls model. Moreover, we exploit this model to specify, validate and analyse a prominent example of adaptive system: robot swarms equipped with self-assembly strategies. The analysis exploits the statistical model checker PVeStA

Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

Enhancing the Main Characteristics of Active Methodologies: A Case with Micro Flip Teaching and Teamwork

All active methodologies have common objectives and processes. Their mission is to ensure that students participate actively in the learning process, cooperating with other students, reflecting, making decisions and creating knowledge. For this purpose, groups that work in a timely manner to carry out an activity or in a more stable way through work teams are usually formed. In both cases, active learning takes place within the groups. This work proposes fostering an active inter-team learning; that is, forming a meta-team where active learning takes place. The aim is checking if students who follow an active methodology, have the active habit; that is, if the work teams share knowledge among themselves and use it to improve their own knowledge. The proposed model contains a virtual layer that all teams can access, making possible the cooperation, the creation of new knowledge, reflection and decision making. This model is applicable to any active methodology and the proposed model has been applied to the Micro Flip Teaching methodology. This quasi experimental research methodology, based on quantitative and qualitative assessment, shows how the work teams, in an Engineering context, in this case, use this virtual layer and how that use impacts the academic performance of their members. Another conclusion of this work is that feedback must be included in active methodologies

QML-Morven : A Novel Framework for Learning Qualitative Models

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