1,234 research outputs found
Probabilistic Black-Box Checking via Active MDP Learning
We introduce a novel methodology for testing stochastic black-box systems,
frequently encountered in embedded systems. Our approach enhances the
established black-box checking (BBC) technique to address stochastic behavior.
Traditional BBC primarily involves iteratively identifying an input that
breaches the system's specifications by executing the following three phases:
the learning phase to construct an automaton approximating the black box's
behavior, the synthesis phase to identify a candidate counterexample from the
learned automaton, and the validation phase to validate the obtained candidate
counterexample and the learned automaton against the original black-box system.
Our method, ProbBBC, refines the conventional BBC approach by (1) employing an
active Markov Decision Process (MDP) learning method during the learning phase,
(2) incorporating probabilistic model checking in the synthesis phase, and (3)
applying statistical hypothesis testing in the validation phase. ProbBBC
uniquely integrates these techniques rather than merely substituting each
method in the traditional BBC; for instance, the statistical hypothesis testing
and the MDP learning procedure exchange information regarding the black-box
system's observation with one another. The experiment results suggest that
ProbBBC outperforms an existing method, especially for systems with limited
observation.Comment: Accepted to EMSOFT 202
Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata
We study the bisimilarity problem for probabilistic pushdown automata (pPDA)
and subclasses thereof. Our definition of pPDA allows both probabilistic and
non-deterministic branching, generalising the classical notion of pushdown
automata (without epsilon-transitions). We first show a general
characterization of probabilistic bisimilarity in terms of two-player games,
which naturally reduces checking bisimilarity of probabilistic labelled
transition systems to checking bisimilarity of standard (non-deterministic)
labelled transition systems. This reduction can be easily implemented in the
framework of pPDA, allowing to use known results for standard
(non-probabilistic) PDA and their subclasses. A direct use of the reduction
incurs an exponential increase of complexity, which does not matter in deriving
decidability of bisimilarity for pPDA due to the non-elementary complexity of
the problem. In the cases of probabilistic one-counter automata (pOCA), of
probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic
process algebras (i.e., single-state pPDA) we show that an implicit use of the
reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and
2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic
versions. The bisimilarity problems for OCA and vPDA are known to have matching
lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively);
we show that these lower bounds also hold for fully probabilistic versions that
do not use non-determinism
Statistical Model Checking : An Overview
Quantitative properties of stochastic systems are usually specified in logics
that allow one to compare the measure of executions satisfying certain temporal
properties with thresholds. The model checking problem for stochastic systems
with respect to such logics is typically solved by a numerical approach that
iteratively computes (or approximates) the exact measure of paths satisfying
relevant subformulas; the algorithms themselves depend on the class of systems
being analyzed as well as the logic used for specifying the properties. Another
approach to solve the model checking problem is to \emph{simulate} the system
for finitely many runs, and use \emph{hypothesis testing} to infer whether the
samples provide a \emph{statistical} evidence for the satisfaction or violation
of the specification. In this short paper, we survey the statistical approach,
and outline its main advantages in terms of efficiency, uniformity, and
simplicity.Comment: non
Multi-Objective Model Checking of Markov Decision Processes
We study and provide efficient algorithms for multi-objective model checking
problems for Markov Decision Processes (MDPs). Given an MDP, M, and given
multiple linear-time (\omega -regular or LTL) properties \varphi\_i, and
probabilities r\_i \epsilon [0,1], i=1,...,k, we ask whether there exists a
strategy \sigma for the controller such that, for all i, the probability that a
trajectory of M controlled by \sigma satisfies \varphi\_i is at least r\_i. We
provide an algorithm that decides whether there exists such a strategy and if
so produces it, and which runs in time polynomial in the size of the MDP. Such
a strategy may require the use of both randomization and memory. We also
consider more general multi-objective \omega -regular queries, which we
motivate with an application to assume-guarantee compositional reasoning for
probabilistic systems.
Note that there can be trade-offs between different properties: satisfying
property \varphi\_1 with high probability may necessitate satisfying \varphi\_2
with low probability. Viewing this as a multi-objective optimization problem,
we want information about the "trade-off curve" or Pareto curve for maximizing
the probabilities of different properties. We show that one can compute an
approximate Pareto curve with respect to a set of \omega -regular properties in
time polynomial in the size of the MDP.
Our quantitative upper bounds use LP methods. We also study qualitative
multi-objective model checking problems, and we show that these can be analysed
by purely graph-theoretic methods, even though the strategies may still require
both randomization and memory.Comment: 21 pages, 2 figure
Black-Box Testing Liveness Properties of Partially Observable Stochastic Systems
We study black-box testing for stochastic systems and arbitrary ?-regular specifications, explicitly including liveness properties. We are given a finite-state probabilistic system that we can only execute from the initial state. We have no information on the number of reachable states, or on the probabilities; further, we can only partially observe the states. The only action we can take is to restart the system. We design restart strategies guaranteeing that, if the specification is violated with non-zero probability, then w.p.1 the number of restarts is finite, and the infinite run executed after the last restart violates the specification. This improves on previous work that required full observability. We obtain asymptotically optimal upper bounds on the expected number of steps until the last restart. We conduct experiments on a number of benchmarks, and show that our strategies allow one to find violations in Markov chains much larger than the ones considered in previous work
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
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