200 research outputs found
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
Counterexample Generation for Infinite-State Chemical Reaction Networks
Counterexample generation is an indispensable part of model checking process.
In stochastic model checking, counterexample generation is a challenging
problem as it is not enough to find a single trace that violates the given
property. Instead, a potentially large set of traces with enough probability to
violate the property needs to be found. This paper considers counterexample
generation for chemical reaction network (CRN) models with potentially infinite
state space. A method based on bounded model checking using SMT solving is
developed for counterexample generation for CRNs. It intends to find a small
set of property violating paths of a given model such that they collectively
have a total probability that is above a given threshold. A unique challenge is
due to the highly connected state space of CRNs where a counterexample is only
a tiny subset of all property violating paths. To address such challenges, this
paper presents a number of optimizations including a divide-and-conquer
technique to scale up the counterexample generation method for large CRN
models. This paper reports results from experiments on a number of
infinite-state CRN models
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
Parameter Synthesis for Markov Models
Markov chain analysis is a key technique in reliability engineering. A
practical obstacle is that all probabilities in Markov models need to be known.
However, system quantities such as failure rates or packet loss ratios, etc.
are often not---or only partially---known. This motivates considering
parametric models with transitions labeled with functions over parameters.
Whereas traditional Markov chain analysis evaluates a reliability metric for a
single, fixed set of probabilities, analysing parametric Markov models focuses
on synthesising parameter values that establish a given reliability or
performance specification . Examples are: what component failure rates
ensure the probability of a system breakdown to be below 0.00000001?, or which
failure rates maximise reliability? This paper presents various analysis
algorithms for parametric Markov chains and Markov decision processes. We focus
on three problems: (a) do all parameter values within a given region satisfy
?, (b) which regions satisfy and which ones do not?, and (c)
an approximate version of (b) focusing on covering a large fraction of all
possible parameter values. We give a detailed account of the various
algorithms, present a software tool realising these techniques, and report on
an extensive experimental evaluation on benchmarks that span a wide range of
applications.Comment: 38 page
Shepherding Hordes of Markov Chains
This paper considers large families of Markov chains (MCs) that are defined
over a set of parameters with finite discrete domains. Such families occur in
software product lines, planning under partial observability, and sketching of
probabilistic programs. Simple questions, like `does at least one family member
satisfy a property?', are NP-hard. We tackle two problems: distinguish family
members that satisfy a given quantitative property from those that do not, and
determine a family member that satisfies the property optimally, i.e., with the
highest probability or reward. We show that combining two well-known
techniques, MDP model checking and abstraction refinement, mitigates the
computational complexity. Experiments on a broad set of benchmarks show that in
many situations, our approach is able to handle families of millions of MCs,
providing superior scalability compared to existing solutions.Comment: Full version of TACAS'19 submissio
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