2,064 research outputs found
On Frequency LTL in Probabilistic Systems
We study frequency linear-time temporal logic (fLTL) which extends the
linear-time temporal logic (LTL) with a path operator expressing that on
a path, certain formula holds with at least a given frequency p, thus relaxing
the semantics of the usual G operator of LTL. Such logic is particularly useful
in probabilistic systems, where some undesirable events such as random failures
may occur and are acceptable if they are rare enough.
Frequency-related extensions of LTL have been previously studied by several
authors, where mostly the logic is equipped with an extended "until" and
"globally" operator, leading to undecidability of most interesting problems.
For the variant we study, we are able to establish fundamental decidability
results. We show that for Markov chains, the problem of computing the
probability with which a given fLTL formula holds has the same complexity as
the analogous problem for LTL. We also show that for Markov decision processes
the problem becomes more delicate, but when restricting the frequency bound
to be 1 and negations not to be outside any operator, we can compute the
maximum probability of satisfying the fLTL formula. This can be again performed
with the same time complexity as for the ordinary LTL formulas.Comment: A paper presented at CONCUR 2015, with appendi
A Probabilistic Temporal Logic with Frequency Operators and Its Model Checking
Probabilistic Computation Tree Logic (PCTL) and Continuous Stochastic Logic
(CSL) are often used to describe specifications of probabilistic properties for
discrete time and continuous time, respectively. In PCTL and CSL, the
possibility of executions satisfying some temporal properties can be
quantitatively represented by the probabilistic extension of the path
quantifiers in their basic Computation Tree Logic (CTL), however, path formulae
of them are expressed via the same operators in CTL. For this reason, both of
them cannot represent formulae with quantitative temporal properties, such as
those of the form "some properties hold to more than 80% of time points (in a
certain bounded interval) on the path." In this paper, we introduce a new
temporal operator which expressed the notion of frequency of events, and define
probabilistic frequency temporal logic (PFTL) based on CTL\star. As a result,
we can easily represent the temporal properties of behavior in probabilistic
systems. However, it is difficult to develop a model checker for the full PFTL,
due to rich expressiveness. Accordingly, we develop a model-checking algorithm
for the CTL-like fragment of PFTL against finite-state Markov chains, and an
approximate model-checking algorithm for the bounded Linear Temporal Logic
(LTL) -like fragment of PFTL against countable-state Markov chains.Comment: In Proceedings INFINITY 2011, arXiv:1111.267
Efficient Parallel Statistical Model Checking of Biochemical Networks
We consider the problem of verifying stochastic models of biochemical
networks against behavioral properties expressed in temporal logic terms. Exact
probabilistic verification approaches such as, for example, CSL/PCTL model
checking, are undermined by a huge computational demand which rule them out for
most real case studies. Less demanding approaches, such as statistical model
checking, estimate the likelihood that a property is satisfied by sampling
executions out of the stochastic model. We propose a methodology for
efficiently estimating the likelihood that a LTL property P holds of a
stochastic model of a biochemical network. As with other statistical
verification techniques, the methodology we propose uses a stochastic
simulation algorithm for generating execution samples, however there are three
key aspects that improve the efficiency: first, the sample generation is driven
by on-the-fly verification of P which results in optimal overall simulation
time. Second, the confidence interval estimation for the probability of P to
hold is based on an efficient variant of the Wilson method which ensures a
faster convergence. Third, the whole methodology is designed according to a
parallel fashion and a prototype software tool has been implemented that
performs the sampling/verification process in parallel over an HPC
architecture
Learning Markov Decision Processes for Model Checking
Constructing an accurate system model for formal model verification can be
both resource demanding and time-consuming. To alleviate this shortcoming,
algorithms have been proposed for automatically learning system models based on
observed system behaviors. In this paper we extend the algorithm on learning
probabilistic automata to reactive systems, where the observed system behavior
is in the form of alternating sequences of inputs and outputs. We propose an
algorithm for automatically learning a deterministic labeled Markov decision
process model from the observed behavior of a reactive system. The proposed
learning algorithm is adapted from algorithms for learning deterministic
probabilistic finite automata, and extended to include both probabilistic and
nondeterministic transitions. The algorithm is empirically analyzed and
evaluated by learning system models of slot machines. The evaluation is
performed by analyzing the probabilistic linear temporal logic properties of
the system as well as by analyzing the schedulers, in particular the optimal
schedulers, induced by the learned models.Comment: In Proceedings QFM 2012, arXiv:1212.345
A Learning Based Approach to Control Synthesis of Markov Decision Processes for Linear Temporal Logic Specifications
We propose to synthesize a control policy for a Markov decision process (MDP)
such that the resulting traces of the MDP satisfy a linear temporal logic (LTL)
property. We construct a product MDP that incorporates a deterministic Rabin
automaton generated from the desired LTL property. The reward function of the
product MDP is defined from the acceptance condition of the Rabin automaton.
This construction allows us to apply techniques from learning theory to the
problem of synthesis for LTL specifications even when the transition
probabilities are not known a priori. We prove that our method is guaranteed to
find a controller that satisfies the LTL property with probability one if such
a policy exists, and we suggest empirically with a case study in traffic
control that our method produces reasonable control strategies even when the
LTL property cannot be satisfied with probability one
Should We Learn Probabilistic Models for Model Checking? A New Approach and An Empirical Study
Many automated system analysis techniques (e.g., model checking, model-based
testing) rely on first obtaining a model of the system under analysis. System
modeling is often done manually, which is often considered as a hindrance to
adopt model-based system analysis and development techniques. To overcome this
problem, researchers have proposed to automatically "learn" models based on
sample system executions and shown that the learned models can be useful
sometimes. There are however many questions to be answered. For instance, how
much shall we generalize from the observed samples and how fast would learning
converge? Or, would the analysis result based on the learned model be more
accurate than the estimation we could have obtained by sampling many system
executions within the same amount of time? In this work, we investigate
existing algorithms for learning probabilistic models for model checking,
propose an evolution-based approach for better controlling the degree of
generalization and conduct an empirical study in order to answer the questions.
One of our findings is that the effectiveness of learning may sometimes be
limited.Comment: 15 pages, plus 2 reference pages, accepted by FASE 2017 in ETAP
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