Monitoring Temporal Properties Using Interval Analysis

Daisuke ISHII  Naoki YONEZAKI  Alexandre GOLDSZTEJN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.2   pp.442-453
Publication Date: 2016/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.442
Type of Manuscript: INVITED PAPER (Special Section on Mathematical Systems Science and its Applications)
continuous-time dynamical systems,  interval analysis,  linear temporal logic,  falsification method,  

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Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic. We relax the problem so that if the verification process cannot succeed at the prescribed precision, it outputs an inconclusive result. The problem is solved by an efficient and rigorous monitoring algorithm. This algorithm performs a forward simulation of a continuous-time dynamical system, detects a set of time intervals in which the atomic propositions hold, and validates the property by propagating the time intervals. In each step, the continuous state at a certain time is enclosed by an interval vector that is proven to contain a unique solution. We experimentally demonstrate the utility of the proposed method in formal analysis of nonlinear and complex continuous systems.