8,569 research outputs found
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
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
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
On Formal Methods for Collective Adaptive System Engineering. {Scalable Approximated, Spatial} Analysis Techniques. Extended Abstract
In this extended abstract a view on the role of Formal Methods in System
Engineering is briefly presented. Then two examples of useful analysis
techniques based on solid mathematical theories are discussed as well as the
software tools which have been built for supporting such techniques. The first
technique is Scalable Approximated Population DTMC Model-checking. The second
one is Spatial Model-checking for Closure Spaces. Both techniques have been
developed in the context of the EU funded project QUANTICOL.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200
Technical Report: Distribution Temporal Logic: Combining Correctness with Quality of Estimation
We present a new temporal logic called Distribution Temporal Logic (DTL)
defined over predicates of belief states and hidden states of partially
observable systems. DTL can express properties involving uncertainty and
likelihood that cannot be described by existing logics. A co-safe formulation
of DTL is defined and algorithmic procedures are given for monitoring
executions of a partially observable Markov decision process with respect to
such formulae. A simulation case study of a rescue robotics application
outlines our approach.Comment: More expanded version of "Distribution Temporal Logic: Combining
Correctness with Quality of Estimation" to appear in IEEE CDC 201
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
Technical report: Distribution Temporal Logic: combining correctness with quality of estimation
We present a new temporal logic called Distribution Temporal Logic (DTL) defined over predicates of belief states and hidden states of partially observable systems. DTL can express properties involving uncertainty and likelihood that cannot be described by existing logics. A co-safe formulation of DTL is defined and algorithmic procedures are given for monitoring executions of a partially observable Markov decision process with respect to such formulae. A simulation case study of a rescue robotics application outlines our approach
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