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.
Many previous studies have applied interval methods to reachability analysis of hybrid systems @cite_5 @cite_13 @cite_2 @cite_25 @cite_22 @cite_26 @cite_9 . The outcome of these methods is an over-approximation of a set of reachable states with a set of boxes. In interval analysis, a computation often provides a proof of unique existence of a solution within a resulting interval. This technique also applies in interval-based reachability analysis @cite_25 @cite_15 , but it is not considered in most of the methods for hybrid systems. Our method enforces the use of the proof to verify more generic temporal properties.
@cite_26 @cite_22 @cite_9 @cite_2 @cite_5 @cite_15 @cite_13 @cite_25
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This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well. These algorithms are not subject to the wrapping effect and therefore our approximations are tight. We show that these approximations are useful in the context of hybrid systems verification and control synthesis. The performance of a prototype implementation of the algorithm confirms its qualities and gives hope for scaling up verification technology for continuous and hybrid systems. This paper presents a bounded model checking tool called @math for hybrid systems. It translates a reachability problem of a nonlinear hybrid system into a predicate logic formula involving arithmetic constraints and checks the satisfiability of the formula based on a satisfiability modulo theories method. We tightly integrate (i) an incremental SAT solver to enumerate the possible sets of constraints and (ii) an interval-based solver for hybrid constraint systems (HCSs) to solve the constraints described in the formulas. The HCS solver verifies the occurrence of a discrete change by using a set of boxes to enclose continuous states that may cause the discrete change. We utilize the existence property of a unique solution in the boxes computed by the HCS solver as (i) a proof of the reachability of a model and (ii) a guide in the over-approximation refinement procedure. Our @math implementation successfully handled several examples including those with nonlinear constraints. 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. We present a scalable reachability algorithm for hybrid systems with piecewise affine, non-deterministic dynamics. It combines polyhedra and support function representations of continuous sets to compute an over-approximation of the reachable states. The algorithm improves over previous work by using variable time steps to guarantee a given local error bound. In addition, we propose an improved approximation model, which drastically improves the accuracy of the algorithm. The algorithm is implemented as part of SpaceEx, a new verification platform for hybrid systems, available at spaceex.imag.fr. Experimental results of full fixed-point computations with hybrid systems with more than 100 variables illustrate the scalability of the approach.