37,353 research outputs found
Probabilistic regular graphs
Deterministic graph grammars generate regular graphs, that form a structural
extension of configuration graphs of pushdown systems. In this paper, we study
a probabilistic extension of regular graphs obtained by labelling the terminal
arcs of the graph grammars by probabilities. Stochastic properties of these
graphs are expressed using PCTL, a probabilistic extension of computation tree
logic. We present here an algorithm to perform approximate verification of PCTL
formulae. Moreover, we prove that the exact model-checking problem for PCTL on
probabilistic regular graphs is undecidable, unless restricting to qualitative
properties. Our results generalise those of EKM06, on probabilistic pushdown
automata, using similar methods combined with graph grammars techniques.Comment: In Proceedings INFINITY 2010, arXiv:1010.611
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
Probabilistic modal {\mu}-calculus with independent product
The probabilistic modal {\mu}-calculus is a fixed-point logic designed for
expressing properties of probabilistic labeled transition systems (PLTS's). Two
equivalent semantics have been studied for this logic, both assigning to each
state a value in the interval [0,1] representing the probability that the
property expressed by the formula holds at the state. One semantics is
denotational and the other is a game semantics, specified in terms of
two-player stochastic parity games. A shortcoming of the probabilistic modal
{\mu}-calculus is the lack of expressiveness required to encode other important
temporal logics for PLTS's such as Probabilistic Computation Tree Logic (PCTL).
To address this limitation we extend the logic with a new pair of operators:
independent product and coproduct. The resulting logic, called probabilistic
modal {\mu}-calculus with independent product, can encode many properties of
interest and subsumes the qualitative fragment of PCTL. The main contribution
of this paper is the definition of an appropriate game semantics for this
extended probabilistic {\mu}-calculus. This relies on the definition of a new
class of games which generalize standard two-player stochastic (parity) games
by allowing a play to be split into concurrent subplays, each continuing their
evolution independently. Our main technical result is the equivalence of the
two semantics. The proof is carried out in ZFC set theory extended with
Martin's Axiom at an uncountable cardinal
A formal language towards the unification of model checking and performance evaluation
In computer science, model checking refers to a computation process that, given a formal structure, checks whether the structure satisfies a logic formula which encodes certain properties. If the structure is a discrete state system and the interested properties depend only on which states to be reached, not on the time or probability to reach them, traditional temporal logics such as linear temporal logic (LTL) and computation tree logic (CTL) are powerful mathematical formalisms that can express properties such as \u27\u27no collision shall occur in a traffic light control system\u27\u27, or \u27\u27eventually, a service is completed\u27\u27. To express performance-dependability related properties over discrete state stochastic systems, these logics have evolved into quantitative model checking logics such as probabilistic linear temporal logic (PLTL), probabilistic computation tree logic (PCTL), and computation tree stochastic logic (CSL), etc., and can express properties such as ``with probability at least 0.98, the system will not reach a deadlock state before time 100\u27\u27. While these logics and their model checking algorithms are powerful, they are inadequate in expressing complex performance measures, either because they are limited to producing only true/false responses (although in practice, a real valued response can sometimes be obtained for the outer-most path quantifier), or the computational complexity is too expensive to be practical.
To address these limitations, for this PhD work, we propose a novel mechanism with the following research aims: 1) Define general specification formalisms to express performance queries in real values while retaining the ability to express temporal properties. 2) Develop efficient mathematical algorithms for the proposed formalisms. 3)Implement the approach in tools and experiment on large-scaled Markov models for the analysis of example queries
Safety-Aware Apprenticeship Learning
Apprenticeship learning (AL) is a kind of Learning from Demonstration
techniques where the reward function of a Markov Decision Process (MDP) is
unknown to the learning agent and the agent has to derive a good policy by
observing an expert's demonstrations. In this paper, we study the problem of
how to make AL algorithms inherently safe while still meeting its learning
objective. We consider a setting where the unknown reward function is assumed
to be a linear combination of a set of state features, and the safety property
is specified in Probabilistic Computation Tree Logic (PCTL). By embedding
probabilistic model checking inside AL, we propose a novel
counterexample-guided approach that can ensure safety while retaining
performance of the learnt policy. We demonstrate the effectiveness of our
approach on several challenging AL scenarios where safety is essential.Comment: Accepted by International Conference on Computer Aided Verification
(CAV) 201
Reasoning about Cognitive Trust in Stochastic Multiagent Systems
We consider the setting of stochastic multiagent systems modelled as stochastic multiplayer games and formulate an automated verification framework for quantifying and reasoning about agents’ trust. To capture human trust, we work with a cognitive notion of trust defined as a subjective evaluation that agent A makes about agent B’s ability to complete a task, which in turn may lead to a decision by A to rely on B. We propose a probabilistic rational temporal logic PRTL*, which extends the probabilistic computation tree logic PCTL* with reasoning about mental attitudes (beliefs, goals, and intentions) and includes novel operators that can express concepts of social trust such as competence, disposition, and dependence. The logic can express, for example, that “agent A will eventually trust agent B with probability at least p that B will behave in a way that ensures the successful completion of a given task.” We study the complexity of the automated verification problem and, while the general problem is undecidable, we identify restrictions on the logic and the system that result in decidable, or even tractable, subproblems
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