Time-aware relational abstractions for hybrid systems

Self Cite

HybridSal is a tool for enabling verification of hybrid systems using infinite bounded model checking and k-induction. The core component of the tool is an abstraction engine that automatically creates a discrete, but infinite, state transition system abstraction of the continuous dynamics in the system. In this paper, we describe HybridSal's new capability to create time-aware relational abstractions, which gives users control over the precision of the abstraction. We also describe a novel approach for abstracting nonlinear expressions that allows us to create time-aware relational abstractions that are more precise than those described previously. We show that the new approach enables automatic verification of systems that could not be verified previously.

Section: Methodsmentioning

confidence: 99%

“…The first shortcoming of the time-oblivious abstraction computed by Hybrid-Sal was recently recognized and it resulted in the introduction of time-aware relational abstractions [10].…”

Section: Time-aware Relational Abstractionmentioning

confidence: 99%

Section: Time-aware Relational Abstractionmentioning

confidence: 99%

Section: Defective Matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Time-Aware Abstractions in HybridSal

Tiwari

2015

Self Cite

Implicit Semi-Algebraic Abstraction for Polynomial Dynamical Systems

Mover

Cimatti

Griggio

et al. 2021

Self Cite

Semi-algebraic abstraction is an approach to the safety verification problem for polynomial dynamical systems where the state space is partitioned according to the sign of a set of polynomials. Similarly to predicate abstraction for discrete systems, the number of abstract states is exponential in the number of polynomials. Hence, semi-algebraic abstraction is expensive to explicitly compute and then analyze (e.g., to prove a safety property or extract invariants).In this paper, we propose an implicit encoding of the semi-algebraic abstraction, which avoids the explicit enumeration of the abstract states: the safety verification problem for dynamical systems is reduced to a corresponding problem for infinite-state transition systems, allowing us to reuse existing model-checking tools based on Satisfiability Modulo Theory (SMT). The main challenge we solve is to express the semi-algebraic abstraction as a first-order logic formula that is linear in the number of predicates, instead of exponential, thus letting the model checker lazily explore the exponential number of abstract states with symbolic techniques. We implemented the approach and validated experimentally its potential to prove safety for polynomial dynamical systems.

Verifying LTL Properties of Hybrid Systems with K-Liveness

Cimatti

Griggio

Mover

et al. 2014

Self Cite

The verification of liveness properties is an important challenge in the design of real-time and hybrid systems. In contrast to the verification of safety properties, for which there are several solutions available, there are really few tools that support liveness properties such as general LTL formulas for hybrid systems, even in the case of timed automata. In the context of finite-state model checking, K-Liveness is a recently proposed algorithm that tackles the problem by proving that an accepting condition can be visited at most K times. K-Liveness has shown to be very efficient, thanks also to its tight integration with IC3, a very efficient technique for safety verification. Unfortunately, the approach is neither complete nor effective (even for simple properties) in the case of infinite-state systems with continuous time. In this paper, we extend K-Liveness to deal with LTL for hybrid systems. On the theoretical side, we show how to extend the reduction from LTL to the reachability of an accepting condition in order to make the algorithm work with continuous time. In particular, we prove that the new reduction is complete for a class of rectangular hybrid automata, in the sense that the LTL property holds if and only if there exists K such that the accepting condition is visited at most K times. On the practical side, we present an efficient integration of K-Liveness in an SMT-version of IC3, and demonstrate its effectiveness on several benchmarks. This work was carried out within the D-MILS project, which is partially funded under the European Commission's Seventh Framework Programme (FP7).