Monitoring Bounded LTL Properties Using Interval Analysis

Abstract

Verification of temporal logic properties plays a crucial role in proving the desired behaviors of hybrid systems. In this paper, we propose an interval method for verifying the properties described by a bounded linear temporal logic. We relax the problem to allow outputting an inconclusive result when verification process cannot succeed with a prescribed precision, and present an efficient and rigorous monitoring algorithm that demonstrates that the problem is decidable. This algorithm performs a forward simulation of a hybrid automaton, detects a set of time intervals in which the atomic propositions hold, and validates the property by propagating the time intervals. A continuous state at a certain time computed in each step is enclosed by an interval vector that is proven to contain a unique solution. In the experiments, we show that the proposed method provides a useful tool for formal analysis of nonlinear and complex hybrid systems.

Property-Directed Verified Monitoring of Signal Temporal Logic

“…The most closely related work is the verified STL monitoring algorithm of Ishii et al [25][26][27]. We build upon their approach of monitoring atomic propositions using interval root finding to derive verified signals; however, whilst their method treats the result of verified integration as a generic interval function, we work directly with the symbolic Taylor model flowpipes produced by Flow*.…”

“…Whilst this representation is extremely powerful, allowing Flow* to handle nonlinear systems with complex continuous dynamics, it can be expensive to work with the generated flowpipes: each pair of preconditioned Taylor models must be composed symbolically (and then be placed into Horner form [12,39]) in order to carry out accurate interval evaluation. This step is a prerequisite for applying most forms of analysis to the flowpipe including reach-avoidance checking, plotting [13], and the verified monitoring algorithm [26].…”

HySIA: Tool for Simulating and Monitoring Hybrid Automata Based on Interval Analysis

“…In contrast, HySIA regards a continuous and a discrete change as a composite function and evaluates it with a single overapproximation process. Comparison results between HySIA and Flow* or dReach are reported in [12] or [13], respectively. With sufficiently small uncertainties, HySIA outperforms other tools.…”

“…HySIA evaluates the property to valid or unsat only when the result is reliable. In the first experiment, the monitoring process successfully checks whether or not the property holds; we count the number of outputs valid and unsat in Table 2 (the result differs from that in [13] because the value of f is different and the verification process is slightly modified). When a monitoring run is badly conditioned, so that the verification process in the monitoring process fails, HySIA will output unknown (or terminate with an error information for some cases).…”