On the Robustness of Temporal Properties for Stochastic Models

• DOI: 10.4204/eptcs.125.1
• Publication Date: 2013-08-26T20:35:53Z
• Authors: Ezio Bartocci; Luca Bortolussi; Laura Nenzi; Guido Sanguinetti
• Keywords: FOS: Computer and information sciences; Computer Science - Logic in Computer Science; Computer Science - Machine Learning; System design; G.3 PROBABILITY AND STATISTICS; Computer Science - Artificial Intelligence; Systems and Control (eess.SY); 0102 computer and information sciences; Stochastic processe; SP2-Ideas; Electrical Engineering and Systems Science - Systems and Control; 01 natural sciences; 60Jxx Markov processes; Machine Learning (cs.LG); fet-fp7; Signal Temporal Logic; QA1-939; FOS: Electrical engineering, electronic engineering, information engineering; European Commission; FP7; EC; Robustness of temporal formulae; proactive; SP1-Cooperation; Signal Temporal Logic; Stochastic processes; Robustness of temporal formulae; System design; ERC; A Quantitative Approach to Management and Design of Collective and Adaptive Behaviours; QA75.5-76.95; Information and Communication Technologies; Robust System Design; FET FP7; Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI); Electronic computers. Computer science; I.6.4 Model Validation and Analysis; FET Proactive: Fundamentals of Collective Adaptive Systems (FOCAS); Mathematics; F.3.1 Specifying and Verifying and Reasoning about Programs

In Proceedings HSB 2013, arXiv:1308.5724<br/>Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling is the model checking problem. i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process. However, one may not only be interested in the notion of satisfiability, but also in the capacity of a system to mantain a particular emergent behaviour unaffected by the perturbations, caused e.g. from extrinsic noise, or by possible small changes in the model parameters. To address this issue, researchers from the verification community have recently proposed several notions of robustness for temporal logic providing suitable definitions of distance between a trajectory of a (deterministic) dynamical system and the boundaries of the set of trajectories satisfying the property of interest. The contributions of this paper are twofold. First, we extend the notion of robustness to stochastic systems, showing that this naturally leads to a distribution of robustness scores. By discussing two examples, we show how to approximate the distribution of the robustness score and its key indicators: the average robustness and the conditional average robustness. Secondly, we show how to combine these indicators with the satisfaction probability to address the system design problem, where the goal is to optimize some control parameters of a stochastic model in order to best maximize robustness of the desired specifications.<br/>