Incremental Control Synthesis in Probabilistic Environments with Temporal Logic Constraints

In this paper, we present a method for optimal control synthesis of a plant that interacts with a set of agents in a graph-like environment. The control specification is given as a temporal logic statement about some properties that hold at the vertices of the environment. The plant is assumed to be deterministic, while the agents are probabilistic Markov models. The goal is to control the plant such that the probability of satisfying a syntactically co-safe Linear Temporal Logic formula is maximized. We propose a computationally efficient incremental approach based on the fact that temporal logic verification is computationally cheaper than synthesis. We present a case-study where we compare our approach to the classical non-incremental approach in terms of computation time and memory usage.Comment: Extended version of the CDC 2012 pape

Modelling, reduction and analysis of Markov automata (extended version)

Markov automata (MA) constitute an expressive continuous-time compositional modelling formalism. They appear as semantic backbones for engineering frameworks including dynamic fault trees, Generalised Stochastic Petri Nets, and AADL. Their expressive power has thus far precluded them from effective analysis by probabilistic (and statistical) model checkers, stochastic game solvers, or analysis tools for Petri net-like formalisms. This paper presents the foundations and underlying algorithms for efficient MA modelling, reduction using static analysis, and most importantly, quantitative analysis. We also discuss implementation pragmatics of supporting tools and present several case studies demonstrating feasibility and usability of MA in practice

Analysis of Timed and Long-Run Objectives for Markov Automata

Markov automata (MAs) extend labelled transition systems with random delays and probabilistic branching. Action-labelled transitions are instantaneous and yield a distribution over states, whereas timed transitions impose a random delay governed by an exponential distribution. MAs are thus a nondeterministic variation of continuous-time Markov chains. MAs are compositional and are used to provide a semantics for engineering frameworks such as (dynamic) fault trees, (generalised) stochastic Petri nets, and the Architecture Analysis & Design Language (AADL). This paper considers the quantitative analysis of MAs. We consider three objectives: expected time, long-run average, and timed (interval) reachability. Expected time objectives focus on determining the minimal (or maximal) expected time to reach a set of states. Long-run objectives determine the fraction of time to be in a set of states when considering an infinite time horizon. Timed reachability objectives are about computing the probability to reach a set of states within a given time interval. This paper presents the foundations and details of the algorithms and their correctness proofs. We report on several case studies conducted using a prototypical tool implementation of the algorithms, driven by the MAPA modelling language for efficiently generating MAs.Comment: arXiv admin note: substantial text overlap with arXiv:1305.705

Synthesis of Data Word Transducers

In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata over infinite sequences of signals ($\omega$-words), while implementations are represented as transducers. In the classical setting, the set of signals is assumed to be finite. In this paper, we consider data $\omega$-words instead, i.e., words over an infinite alphabet. In this context, we study specifications and implementations respectively given as automata and transducers extended with a finite set of registers. We consider different instances, depending on whether the specification is nondeterministic, universal or deterministic, and depending on whether the number of registers of the implementation is given or not. In the unbounded setting, we show undecidability for both universal and nondeterministic specifications, while decidability is recovered in the deterministic case. In the bounded setting, undecidability still holds for nondeterministic specifications, but can be recovered by disallowing tests over input data. The generic technique we use to show the latter result allows us to reprove some known result, namely decidability of bounded synthesis for universal specifications

Efficient First-Order Temporal Logic for Infinite-State Systems

In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex properties such as liveness and fairness properties. These aspects appear difficult for many other approaches to infinite-state verification.Comment: 16 pages, 2 figure

Taming Uncertainty in the Assurance Process of Self-Adaptive Systems: a Goal-Oriented Approach

Goals are first-class entities in a self-adaptive system (SAS) as they guide the self-adaptation. A SAS often operates in dynamic and partially unknown environments, which cause uncertainty that the SAS has to address to achieve its goals. Moreover, besides the environment, other classes of uncertainty have been identified. However, these various classes and their sources are not systematically addressed by current approaches throughout the life cycle of the SAS. In general, uncertainty typically makes the assurance provision of SAS goals exclusively at design time not viable. This calls for an assurance process that spans the whole life cycle of the SAS. In this work, we propose a goal-oriented assurance process that supports taming different sources (within different classes) of uncertainty from defining the goals at design time to performing self-adaptation at runtime. Based on a goal model augmented with uncertainty annotations, we automatically generate parametric symbolic formulae with parameterized uncertainties at design time using symbolic model checking. These formulae and the goal model guide the synthesis of adaptation policies by engineers. At runtime, the generated formulae are evaluated to resolve the uncertainty and to steer the self-adaptation using the policies. In this paper, we focus on reliability and cost properties, for which we evaluate our approach on the Body Sensor Network (BSN) implemented in OpenDaVINCI. The results of the validation are promising and show that our approach is able to systematically tame multiple classes of uncertainty, and that it is effective and efficient in providing assurances for the goals of self-adaptive systems

Formal Executable Models for Automatic Detection of Timing Anomalies

A timing anomaly is a counterintuitive timing behavior in the sense that a local fast execution slows down an overall global execution. The presence of such behaviors is inconvenient for the WCET analysis which requires, via abstractions, a certain monotony property to compute safe bounds. In this paper we explore how to systematically execute a previously proposed formal definition of timing anomalies. We ground our work on formal designs of architecture models upon which we employ guided model checking techniques. Our goal is towards the automatic detection of timing anomalies in given computer architecture designs