155 research outputs found
Bounded Model Checking for Probabilistic Programs
In this paper we investigate the applicability of standard model checking
approaches to verifying properties in probabilistic programming. As the
operational model for a standard probabilistic program is a potentially
infinite parametric Markov decision process, no direct adaption of existing
techniques is possible. Therefore, we propose an on-the-fly approach where the
operational model is successively created and verified via a step-wise
execution of the program. This approach enables to take key features of many
probabilistic programs into account: nondeterminism and conditioning. We
discuss the restrictions and demonstrate the scalability on several benchmarks
Parameter-Independent Strategies for pMDPs via POMDPs
Markov Decision Processes (MDPs) are a popular class of models suitable for
solving control decision problems in probabilistic reactive systems. We
consider parametric MDPs (pMDPs) that include parameters in some of the
transition probabilities to account for stochastic uncertainties of the
environment such as noise or input disturbances.
We study pMDPs with reachability objectives where the parameter values are
unknown and impossible to measure directly during execution, but there is a
probability distribution known over the parameter values. We study for the
first time computing parameter-independent strategies that are expectation
optimal, i.e., optimize the expected reachability probability under the
probability distribution over the parameters. We present an encoding of our
problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem
to computing optimal strategies in POMDPs.
We evaluate our method experimentally on several benchmarks: a motivating
(repeated) learner model; a series of benchmarks of varying configurations of a
robot moving on a grid; and a consensus protocol.Comment: Extended version of a QEST 2018 pape
Reachability in Parametric Interval Markov Chains using Constraints
Parametric Interval Markov Chains (pIMCs) are a specification formalism that
extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into
account imprecision in the transition probability values: transitions in pIMCs
are labeled with parametric intervals of probabilities. In this work, we study
the difference between pIMCs and other Markov Chain abstractions models and
investigate the two usual semantics for IMCs: once-and-for-all and
at-every-step. In particular, we prove that both semantics agree on the
maximal/minimal reachability probabilities of a given IMC. We then investigate
solutions to several parameter synthesis problems in the context of pIMCs --
consistency, qualitative reachability and quantitative reachability -- that
rely on constraint encodings. Finally, we propose a prototype implementation of
our constraint encodings with promising results
Change Mining in Adaptive Process Management Systems
The wide-spread adoption of process-aware information systems has resulted in a bulk of computerized information about real-world processes. This data can be utilized for process performance analysis as well as for process improvement. In this context process mining offers promising perspectives. So far, existing mining techniques have been applied to operational processes, i.e., knowledge is extracted from execution logs (process discovery), or execution logs are compared with some a-priori process model (conformance checking). However, execution logs only constitute one kind of data gathered during process enactment. In particular, adaptive processes provide additional information about process changes (e.g., ad-hoc changes of single process instances) which can be used to enable organizational learning. In this paper we present an approach for mining change logs in adaptive process management systems. The change process discovered through process mining provides an aggregated overview of all changes that happened so far. This, in turn, can serve as basis for all kinds of process improvement actions, e.g., it may trigger process redesign or better control mechanisms
The Complexity of Graph-Based Reductions for Reachability in Markov Decision Processes
We study the never-worse relation (NWR) for Markov decision processes with an
infinite-horizon reachability objective. A state q is never worse than a state
p if the maximal probability of reaching the target set of states from p is at
most the same value from q, regard- less of the probabilities labelling the
transitions. Extremal-probability states, end components, and essential states
are all special cases of the equivalence relation induced by the NWR. Using the
NWR, states in the same equivalence class can be collapsed. Then, actions
leading to sub- optimal states can be removed. We show the natural decision
problem associated to computing the NWR is coNP-complete. Finally, we ex- tend
a previously known incomplete polynomial-time iterative algorithm to
under-approximate the NWR
PrIC3: Property Directed Reachability for MDPs
IC3 has been a leap forward in symbolic model checking. This paper proposes
PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic
model checking of MDPs. Our main focus is to develop the theory underlying
PrIC3. Alongside, we present a first implementation of PrIC3 including the key
ingredients from IC3 such as generalization, repushing, and propagation
Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games
Probabilistic model checking for stochastic games enables formal verification
of systems that comprise competing or collaborating entities operating in a
stochastic environment. Despite good progress in the area, existing approaches
focus on zero-sum goals and cannot reason about scenarios where entities are
endowed with different objectives. In this paper, we propose probabilistic
model checking techniques for concurrent stochastic games based on Nash
equilibria. We extend the temporal logic rPATL (probabilistic alternating-time
temporal logic with rewards) to allow reasoning about players with distinct
quantitative goals, which capture either the probability of an event occurring
or a reward measure. We present algorithms to synthesise strategies that are
subgame perfect social welfare optimal Nash equilibria, i.e., where there is no
incentive for any players to unilaterally change their strategy in any state of
the game, whilst the combined probabilities or rewards are maximised. We
implement our techniques in the PRISM-games tool and apply them to several case
studies, including network protocols and robot navigation, showing the benefits
compared to existing approaches
One Net Fits All: A unifying semantics of Dynamic Fault Trees using GSPNs
Dynamic Fault Trees (DFTs) are a prominent model in reliability engineering.
They are strictly more expressive than static fault trees, but this comes at a
price: their interpretation is non-trivial and leaves quite some freedom. This
paper presents a GSPN semantics for DFTs. This semantics is rather simple and
compositional. The key feature is that this GSPN semantics unifies all existing
DFT semantics from the literature. All semantic variants can be obtained by
choosing appropriate priorities and treatment of non-determinism.Comment: Accepted at Petri Nets 201
Value Iteration for Simple Stochastic Games: Stopping Criterion and Learning Algorithm
Simple stochastic games can be solved by value iteration (VI), which yields a
sequence of under-approximations of the value of the game. This sequence is
guaranteed to converge to the value only in the limit. Since no stopping
criterion is known, this technique does not provide any guarantees on its
results. We provide the first stopping criterion for VI on simple stochastic
games. It is achieved by additionally computing a convergent sequence of
over-approximations of the value, relying on an analysis of the game graph.
Consequently, VI becomes an anytime algorithm returning the approximation of
the value and the current error bound. As another consequence, we can provide a
simulation-based asynchronous VI algorithm, which yields the same guarantees,
but without necessarily exploring the whole game graph.Comment: CAV201
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