67 research outputs found
Falsification of Cyber-Physical Systems with Robustness-Guided Black-Box Checking
For exhaustive formal verification, industrial-scale cyber-physical systems
(CPSs) are often too large and complex, and lightweight alternatives (e.g.,
monitoring and testing) have attracted the attention of both industrial
practitioners and academic researchers. Falsification is one popular testing
method of CPSs utilizing stochastic optimization. In state-of-the-art
falsification methods, the result of the previous falsification trials is
discarded, and we always try to falsify without any prior knowledge. To
concisely memorize such prior information on the CPS model and exploit it, we
employ Black-box checking (BBC), which is a combination of automata learning
and model checking. Moreover, we enhance BBC using the robust semantics of STL
formulas, which is the essential gadget in falsification. Our experiment
results suggest that our robustness-guided BBC outperforms a state-of-the-art
falsification tool.Comment: Accepted to HSCC 202
Reachability analysis of linear hybrid systems via block decomposition
Reachability analysis aims at identifying states reachable by a system within
a given time horizon. This task is known to be computationally expensive for
linear hybrid systems. Reachability analysis works by iteratively applying
continuous and discrete post operators to compute states reachable according to
continuous and discrete dynamics, respectively. In this paper, we enhance both
of these operators and make sure that most of the involved computations are
performed in low-dimensional state space. In particular, we improve the
continuous-post operator by performing computations in high-dimensional state
space only for time intervals relevant for the subsequent application of the
discrete-post operator. Furthermore, the new discrete-post operator performs
low-dimensional computations by leveraging the structure of the guard and
assignment of a considered transition. We illustrate the potential of our
approach on a number of challenging benchmarks.Comment: Accepted at EMSOFT 202
Data-driven Reachability using Christoffel Functions and Conformal Prediction
An important mathematical tool in the analysis of dynamical systems is the
approximation of the reach set, i.e., the set of states reachable after a given
time from a given initial state. This set is difficult to compute for complex
systems even if the system dynamics are known and given by a system of ordinary
differential equations with known coefficients. In practice, parameters are
often unknown and mathematical models difficult to obtain. Data-based
approaches are promised to avoid these difficulties by estimating the reach set
based on a sample of states. If a model is available, this training set can be
obtained through numerical simulation. In the absence of a model, real-life
observations can be used instead. A recently proposed approach for data-based
reach set approximation uses Christoffel functions to approximate the reach
set. Under certain assumptions, the approximation is guaranteed to converge to
the true solution. In this paper, we improve upon these results by notably
improving the sample efficiency and relaxing some of the assumptions by
exploiting statistical guarantees from conformal prediction with training and
calibration sets. In addition, we exploit an incremental way to compute the
Christoffel function to avoid the calibration set while maintaining the
statistical convergence guarantees. Furthermore, our approach is robust to
outliers in the training and calibration set
ΠΡΡΡΠ΅ΡΡΠ²Π»Π΅Π½ΠΈΠ΅ ΡΠ²ΡΠ·ΠΈ Π²ΡΠ·ΠΎΠ²ΡΠΊΠΎΠΉ Π½Π°ΡΠΊΠΈ Π‘ΠΈΠ±ΠΈΡΠΈ Ρ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²ΠΎΠΌ ΠΈ ΠΈΠ½Π½ΠΎΠ²Π°ΡΠΈΠΎΠ½Π½ΡΡ ΠΌΠ΅ΡΠΎΠΏΡΠΈΡΡΠΈΠΉ Π² 70-80-Π΅ Π³Π³. Π₯Π₯ Π².
ΠΡΡΠ°ΠΆΠ°ΡΡΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ, ΠΊΠ°ΡΠ°ΡΡΠΈΠ΅ΡΡ ΠΈΠ½ΡΠ΅Π³ΡΠ°ΡΠΈΠΈ Π²ΡΠ·ΠΎΠ²ΡΠΊΠΎΠΉ Π½Π°ΡΠΊΠΈ Π‘ΠΈΠ±ΠΈΡΠΈ Ρ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²ΠΎΠΌ Π² 70-80-Π΅ Π³Π³. Π₯Π₯ Π². ΠΠ½Π°Π»ΠΈΠ·ΠΈΡΡΠ΅ΡΡΡ Π΄Π΅ΡΡΠ΅Π»ΡΠ½ΠΎΡΡΡ ΠΈΠ½ΡΡΠΈΡΡΡΠΎΠ² ΠΈ ΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΠΎΠ² ΡΠ΅Π³ΠΈΠΎΠ½Π° ΠΏΠΎ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΠΈ ΡΠΊΡΠ΅ΠΏΠ»Π΅Π½ΠΈΡ ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΠΎΡΠΌ ΡΠΎΠ΄ΡΡΠΆΠ΅ΡΡΠ²Π° Π½Π°ΡΠΊΠΈ Ρ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²ΠΎΠΌ: Ρ
ΠΎΠ·ΡΠΉΡΡΠ²Π΅Π½Π½ΡΡ
Π΄ΠΎΠ³ΠΎΠ²ΠΎΡΠΎΠ², ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΡΡ
ΡΠ²ΠΎΡΡΠ΅ΡΠΊΠΈΡ
Π±ΡΠΈΠ³Π°Π΄, ΡΠ΅ΡΡΡΠ²Π° ΡΡΠ΅Π½ΡΡ
ΠΈ ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠΎΠ² Π½Π°Π΄ ΡΠ°Π±ΠΎΡΠΈΠΌΠΈ, ΡΡΠ°ΡΡΠΈΡ Π½Π°ΡΡΠ½ΠΎ-ΠΏΠ΅Π΄Π°Π³ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ°Π±ΠΎΡΠ½ΠΈΠΊΠΎΠ² Π² ΠΊΠΎΠ½ΡΡΠ»ΡΡΠ°ΡΠΈΡΡ
Π½Π° ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΡΡ
ΠΈ Π½Π°ΡΡΠ½ΠΎ-ΡΠ΅Ρ
Π½ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΡΠΎΠΏΠ°Π³Π°Π½Π΄Π΅
Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices
Approximating the set of reachable states of a dynamical system is an
algorithmic yet mathematically rigorous way to reason about its safety.
Although progress has been made in the development of efficient algorithms for
affine dynamical systems, available algorithms still lack scalability to ensure
their wide adoption in the industrial setting. While modern linear algebra
packages are efficient for matrices with tens of thousands of dimensions,
set-based image computations are limited to a few hundred. We propose to
decompose reach set computations such that set operations are performed in low
dimensions, while matrix operations like exponentiation are carried out in the
full dimension. Our method is applicable both in dense- and discrete-time
settings. For a set of standard benchmarks, it shows a speed-up of up to two
orders of magnitude compared to the respective state-of-the art tools, with
only modest losses in accuracy. For the dense-time case, we show an experiment
with more than 10.000 variables, roughly two orders of magnitude higher than
possible with previous approaches
LNCS
Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user or a heuristic, we present a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples. We show that for the class of convex hybrid automata, i.e., hybrid automata with (possibly nonlinear) convex constraints on derivatives, such directions always exist and can be found using convex optimization. We embed our method inside a CEGAR loop, thus enabling the time-unbounded reachability analysis of an important and richer class of hybrid automata than was previously possible. We evaluate our method on several benchmarks, demonstrating also its superior efficiency for the special case of linear hybrid automata
JuliaReach: a Toolbox for Set-Based Reachability
We present JuliaReach, a toolbox for set-based reachability analysis of
dynamical systems. JuliaReach consists of two main packages: Reachability,
containing implementations of reachability algorithms for continuous and hybrid
systems, and LazySets, a standalone library that implements state-of-the-art
algorithms for calculus with convex sets. The library offers both concrete and
lazy set representations, where the latter stands for the ability to delay set
computations until they are needed. The choice of the programming language
Julia and the accompanying documentation of our toolbox allow researchers to
easily translate set-based algorithms from mathematics to software in a
platform-independent way, while achieving runtime performance that is
comparable to statically compiled languages. Combining lazy operations in high
dimensions and explicit computations in low dimensions, JuliaReach can be
applied to solve complex, large-scale problems.Comment: Accepted in Proceedings of HSCC'19: 22nd ACM International Conference
on Hybrid Systems: Computation and Control (HSCC'19
Numerical Verification of Affine Systems with up to a Billion Dimensions
Affine systems reachability is the basis of many verification methods. With
further computation, methods exist to reason about richer models with inputs,
nonlinear differential equations, and hybrid dynamics. As such, the scalability
of affine systems verification is a prerequisite to scalable analysis for more
complex systems. In this paper, we improve the scalability of affine systems
verification, in terms of the number of dimensions (variables) in the system.
The reachable states of affine systems can be written in terms of the matrix
exponential, and safety checking can be performed at specific time steps with
linear programming. Unfortunately, for large systems with many state variables,
this direct approach requires an intractable amount of memory while using an
intractable amount of computation time. We overcome these challenges by
combining several methods that leverage common problem structure. Memory is
reduced by exploiting initial states that are not full-dimensional and safety
properties (outputs) over a few linear projections of the state variables.
Computation time is saved by using numerical simulations to compute only
projections of the matrix exponential relevant for the verification problem.
Since large systems often have sparse dynamics, we use Krylov-subspace
simulation approaches based on the Arnoldi or Lanczos iterations. Our method
produces accurate counter-examples when properties are violated and, in the
extreme case with sufficient problem structure, can analyze a system with one
billion real-valued state variables
Monitoring Dynamical Signals while Testing Timed Aspects of a System
Abstract. We propose to combine timed automata and linear hybrid automata model checkers for formal testing and monitoring of embedded systems with a hybrid behavior, i.e., where the correctness of the system depends on discrete as well as continuous dynamics. System level testing is considered, where requirements capture abstract behavior and often include non-determinism due to parallelism, internal counters and subtle state of physical materials. The goal is achieved by integrating the tools Uppaal [2] and PHAVe
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