Thao Dang

SpaceEx: scalable verification of 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.

Hierarchical modeling and analysis of embedded systems

This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in the design of embedded control software using examples from automated highways concerning vehicle coordination.

Predicate abstraction for reachability analysis of hybrid systems

Embedded systems are increasingly finding their way into a growing range of physical devices. These embedded systems often consist of a collection of software threads interacting concurrently with each other and with a physical, continuous environment. While continuous dynamics have been well studied in control theory, and discrete and distributed systems have been investigated in computer science, the combination of the two complexities leads us to the recent research on hybrid systems. This paper addresses the formal analysis of such hybrid systems. Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state discrete programs. This paper presents algorithms and tools for reachability analysis of hybrid systems by combining the notion of predicate abstraction with recent techniques for approximating the set of reachable states of linear systems using polyhedra. Given a hybrid system and a set of predicates, we consider the finite discrete quotient whose states correspond to all possible truth assignments to the input predicates. The tool performs an on-the-fly exploration of the abstract system. We present the basic techniques for guided search in the abstract state-space, optimizations of these techniques, implementation of these in our verifier, and case studies demonstrating the promise of the approach. We also address the completeness of our abstraction-based verification strategy by showing that predicate abstraction of hybrid systems can be used to prove bounded safety.

Hierarchical Hybrid Modeling of Embedded Systems

This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy, and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools, and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in design of embedded control software using examples from automated highways concerning vehicle coordination.

Reachability Analysis of Hybrid Systems via Predicate Abstraction

Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state discrete programs. Th is paper presents algorithms and tools for reachability analysis of hybrid systems by combining the notion of predicate abstraction with recent techniques for approximating the set of reachable states of linear systems using polyhedra. Given a hybrid system and a set of user-defined boolean predicates, we consider the finite discrete quotient whose states correspond to all possible truth assignments to the input predicates. The tool performs an on-the-fly exploration of the abstract system. We demonstrate the feasibility of the proposed technique by analyzing a parametric timing-based mutual exclusion protocol and safety of a simple controller for vehicle coordination.

Counter-example guided predicate abstraction of hybrid systems

Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state systems, and has been recently shown to enhance the effectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set of linear predicates, the verifier performs an on-the-fly search of the finite discrete quotient whose states correspond to the truth assignments to the input predicates. The success of this approach depends on the choice of the predicates used for abstraction. In this paper, we focus on identifying these predicates automatically by analyzing spurious counter-examples generated by the search in the abstract state-space. We present the basic techniques for discovering new predicates that will rule out closely related spurious counter-examples, optimizations of these techniques, implementation of these in the verification tool, and case studies demonstrating the promise of the approach.

Progress on reachability analysis of hybrid systems using predicate abstraction

Predicate abstraction has emerged to be a powerful technique for extracting finite-state models from infinite-state systems, and has been recently shown to enhance the effectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set of linear predicates, the verifier performs an on-the-fly search of the finite discrete quotient whose states correspond to the truth assignments to the input predicates. To compute the transitions out of an abstract state, the tool needs to compute the set of discrete and continuous successors, and find out all the abstract states that this set intersects with. The complexity of this computation grows exponentially with the number of abstraction predicates. In this paper we present various optimizations that are aimed at speeding up the search in the abstract state-space, and demonstrate their benefits via case studies. We also discuss the completeness of the predicate abstraction technique for proving safety of hybrid systems.

Symbolic model checking of hybrid systems using template polyhedra

We propose techniques for the verification of hybrid systems using template polyhedra, i.e., polyhedra whose inequalities have fixed expressions but with varying constant terms. Given a hybrid system description and a set of template linear expressions as inputs, our technique constructs over-approximations of the reachable states using template polyhedra. Therefore, operations used in symbolic model checking such as intersection, union and post-condition across discrete transitions over template polyhedra can be computed efficiently using template polyhedra without requiring expensive vertex enumeration. Additionally, the verification of hybrid systems requires techniques to handle the continuous dynamics inside discrete modes. We propose a new flowpipe construction algorithm using template polyhedra. Our technique uses higher-order Taylor series expansion to approximate the time trajectories. The terms occurring in the Taylor series expansion are bounded using repeated optimization queries. The location invariant is used to enclose the remainder term of the Taylor series, and thus truncate the expansion. Finally, we have implemented our technique as a part of the tool TimePass for the analysis of affine hybrid automata.

Stability and reachability analysis of a hybrid model of luminescence in the marine bacterium Vibrio fischeri

Addresses the mathematical modeling and analysis of the quorum sensing system found in unicellular bacteria that exhibit bioluminescence. The luminescence is governed by the expression of genes in the cell, which in turn is controlled by the density of cells in a population. The paper illustrates the application of standard tools in control theory and some tools in hybrid systems to the quorum sensing system, and demonstrates that bioluminescence can be modeled and understood as the output of a switched dynamical system.

Computing Reachable States for Nonlinear Biological Models

In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We then develop a novel algorithm for computing reachable states for nonlinear systems and report experimental results obtained using a prototype implementation. We believe these results constitute a promising contribution to the analysis of complex models of biological systems.