69 research outputs found
HySIA: Tool for Simulating and Monitoring Hybrid Automata Based on Interval Analysis
We present HySIA: a reliable runtime verification tool for nonlinear hybrid
automata (HA) and signal temporal logic (STL) properties. HySIA simulates an HA
with interval analysis techniques so that a trajectory is enclosed sharply
within a set of intervals. Then, HySIA computes whether the simulated
trajectory satisfies a given STL property; the computation is performed again
with interval analysis to achieve reliability. Simulation and verification
using HySIA are demonstrated through several example HA and STL formulas.Comment: Appeared in RV'17; the final publication is available at Springe
Delta-Complete Decision Procedures for Satisfiability over the Reals
We introduce the notion of "\delta-complete decision procedures" for solving
SMT problems over the real numbers, with the aim of handling a wide range of
nonlinear functions including transcendental functions and solutions of
Lipschitz-continuous ODEs. Given an SMT problem \varphi and a positive rational
number \delta, a \delta-complete decision procedure determines either that
\varphi is unsatisfiable, or that the "\delta-weakening" of \varphi is
satisfiable. Here, the \delta-weakening of \varphi is a variant of \varphi that
allows \delta-bounded numerical perturbations on \varphi. We prove the
existence of \delta-complete decision procedures for bounded SMT over reals
with functions mentioned above. For functions in Type 2 complexity class C,
under mild assumptions, the bounded \delta-SMT problem is in NP^C.
\delta-Complete decision procedures can exploit scalable numerical methods for
handling nonlinearity, and we propose to use this notion as an ideal
requirement for numerically-driven decision procedures. As a concrete example,
we formally analyze the DPLL framework, which integrates Interval
Constraint Propagation (ICP) in DPLL(T), and establish necessary and sufficient
conditions for its \delta-completeness. We discuss practical applications of
\delta-complete decision procedures for correctness-critical applications
including formal verification and theorem proving.Comment: A shorter version appears in IJCAR 201
Abstraction of Elementary Hybrid Systems by Variable Transformation
Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing
elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in
practice, especially in safety-critical domains. Due to the non-polynomial
expressions which lead to undecidable arithmetic, verification of EHSs is very
hard. Existing approaches based on partition of state space or
over-approximation of reachable sets suffer from state explosion or inflation
of numerical errors. In this paper, we propose a symbolic abstraction approach
that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all
non-polynomial terms with newly introduced variables. Thus the verification of
EHSs is reduced to the one of PHSs, enabling us to apply all the
well-established verification techniques and tools for PHSs to EHSs. In this
way, it is possible to avoid the limitations of many existing methods. We
illustrate the abstraction approach and its application in safety verification
of EHSs by several real world examples
Probabilistic bounded reachability for stochastic hybrid systems
PhD ThesisStochastic parametric hybrid systems provide a means of formalising automata
with continuous nonlinear dynamics, discrete interruptions, and
parametric uncertainty (e.g. randomness and/or nondeterminism). They
can be used for modelling a vast class of cyber-physical systems â machines
comprising physical components orchestrated by a digital control (e.g. medical
devices, self-driving cars, and aircraft autopilots). Assuring correct and
safe behaviour of such systems is crucial as human lives are often involved.
One of the main problems in system verification is reachability analysis.
It amounts to determining whether the studied model reaches an unsafe
state during its evolution. Introduction of parametric randomness allows
the formulation of a quantitative version of the problem â computing the
probability of reaching the undesired state.
Reachability analysis is a highly challenging problem due to its general undecidability
for hybrid systems and undecidability of nonlinear arithmetic
(e.g. involving trigonometric functions) over the real numbers. A common
approach in this case is to solve a simpler, yet useful, problem. In particular,
there are techniques for solving reachability rigorously up to a given
numerical precision.
The central problem of this research is probabilistic reachability analysis of
hybrid systems with random and nondeterministic parameters. In this thesis
I have developed two new distinct techniques: a formal approach, based
on formal reasoning which provides absolute numerical guarantees; and a
statistical one, utilising Monte Carlo sampling that gives statistical guarantees.
Namely, the former computes an interval which is guaranteed to
contain the exact reachability probability value, while the latter returns an
interval containing the probability value with some statistical confidence.
By providing weaker guarantees, the statistical approach is capable of handling
difficult cases more efficiently than the formal one, which in turn, can
be used for parameter set synthesis in the absence of random uncertainty.
The latter is one of the key problems in system modelling: identifying sets
of parameter values for which a given model satisfies the desired behaviour.
I have implemented the described techniques in the publicly available tool
ProbReach, which I have then applied to several realistic case studies such
as the synthesis of safe and robust controllers for artificial pancreas and the
design of UVB treatment for psoriasis.award N00014-13-1-0090 of the US
Office of Naval Research
Input Synthesis for Sampled Data Systems by Program Logic
Inspired by a concrete industry problem we consider the input synthesis
problem for hybrid systems: given a hybrid system that is subject to input from
outside (also called disturbance or noise), find an input sequence that steers
the system to the desired postcondition. In this paper we focus on sampled data
systems--systems in which a digital controller interrupts a physical plant in a
periodic manner, a class commonly known in control theory--and furthermore
assume that a controller is given in the form of an imperative program. We
develop a structural approach to input synthesis that features forward and
backward reasoning in program logic for the purpose of reducing a search space.
Although the examples we cover are limited both in size and in structure,
experiments with a prototype implementation suggest potential of our program
logic based approach.Comment: In Proceedings HAS 2014, arXiv:1501.0540
Symbolic Methods for Chemical Reaction Networks (Dagstuhl Seminar 12462)
During 11-16 November 2012, the Dagstuhl Seminar 12462 "Symbolic Methods for Chemical Reaction Networks" was held in Schloss Dagstuhl - Leibneiz Center for Informatics. The seminar brought together researchers in symbolic computation, chemical engineering, and systems biology. During the seminar, participants presented ïŹve-minute talks introducing their research interests, ïŹve participants gave longer talks, and all participants had the opportunity to take part in various discussion groups. Abstracts of presentations and summaries of the discussion groups are compiled in this report
Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point
Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution
An evaluation of approximate probabilistic reachability techniques for stochastic parametric hybrid systems
Ph. D. ThesisStochastic parametric hybrid systems allow formalising automata with
discrete interruptions, continuous nonlinear dynamics and parametric
uncertainty (e.g. randomness and/or nondeterminism), and are a useful
framework for cyber-physical systems modelling. The problem of
designing safe cyber-physical systems is very timely, given that such
systems are ubiquitous in modern society, often in safety-critical contexts
(e.g., aircraft and cars) with possibly some level of decisional
autonomy. Therefore, the verification of cyber-physical systems (and
consequently of hybrid systems) is a problem urgently demanding innovative
solutions. Unfortunately, this problem is also extremely challenging.
Reachability checking is a crucial element of designing safe systems.
Given a system model, we specify a set of "goal" states (indicating
(un)wanted behaviour) and ask whether the system evolution can
reach these states or not. Probabilistic reachability is the corresponding
problem for stochastic systems, and it amounts to computing the
probability that the system reaches a goal state.
The main problem researched in this thesis is probabilistic reachability
analysis of hybrid systems with random and/or nondeterministic
parameters. For nondeterministic systems, this problem amounts to
computing a range of reachability probabilities depending on how nondeterminism
is resolved.
In this thesis I have investigated and developed three distinct techniques:
Statistical methods, involving Monte Carlo, Quasi-Monte Carlo
and Randomised Quasi-Monte Carlo sampling with interval estimation
techniques which give statistical guarantees;
An analytical approximation method, utilising Gaussian Processes
that offer a statistical approximation for an (unknown)
smooth function over its entire domain;
A promising combination of a formal approach, based on formal
reasoning which provides absolute numerical guarantees, and the
Gaussian Regression method.
This research offers contributions on two different levels to the verification
of stochastic parametric hybrid systems. From a theoretical
point of view, it offers a proof that the reachability probability function
is a smooth function of the uncertain parameters of the model,
and hence Gaussian Processes techniques can be used to obtain an
efficient analytical approximation of the function. From a practical
point of view, I have implemented all the above described statistical
and approximation techniques as part of the publicly available ProbReach
tool, including a Gaussian Process Expectation Propagation
algorithm that performs Gaussian Process classification and regression
for uni-variate and multiple class labels. My empirical evaluation of
the presented techniques to a number of case studies has shown a
great Gaussian Process approach advantage with respect to standard
statistical model checking techniques.SAgE Doctoral Training Scholarships
of Newcastle Universit
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