18 research outputs found
Extending Markov Automata with State and Action Rewards
This presentation introduces the Markov Reward Automaton (MRA), an extension of the Markov automaton that allows the modelling of systems incorporating rewards in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Our models support both rewards that are acquired instantaneously when taking certain transitions (action rewards) and rewards that are based on the duration that certain conditions hold (state rewards). In addition to introducing the MRA model, we extend the process-algebraic language MAPA to easily specify MRAs. Also, we provide algorithms for computing the expected reward until reaching one of a certain set of goal states, as well as the long-run average reward. We extended the MAMA tool chain (consisting of the tools SCOOP and IMCA) to implement the reward extension of MAPA and these algorithms
MeGARA: Menu-based Game Abstraction and Abstraction Refinement of Markov Automata
Markov automata combine continuous time, probabilistic transitions, and
nondeterminism in a single model. They represent an important and powerful way
to model a wide range of complex real-life systems. However, such models tend
to be large and difficult to handle, making abstraction and abstraction
refinement necessary. In this paper we present an abstraction and abstraction
refinement technique for Markov automata, based on the game-based and
menu-based abstraction of probabilistic automata. First experiments show that a
significant reduction in size is possible using abstraction.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Static Analysis of Deterministic Negotiations
Negotiation diagrams are a model of concurrent computation akin to workflow
Petri nets. Deterministic negotiation diagrams, equivalent to the much studied
and used free-choice workflow Petri nets, are surprisingly amenable to
verification. Soundness (a property close to deadlock-freedom) can be decided
in PTIME. Further, other fundamental questions like computing summaries or the
expected cost, can also be solved in PTIME for sound deterministic negotiation
diagrams, while they are PSPACE-complete in the general case.
In this paper we generalize and explain these results. We extend the
classical "meet-over-all-paths" (MOP) formulation of static analysis problems
to our concurrent setting, and introduce Mazurkiewicz-invariant analysis
problems, which encompass the questions above and new ones. We show that any
Mazurkiewicz-invariant analysis problem can be solved in PTIME for sound
deterministic negotiations whenever it is in PTIME for sequential
flow-graphs---even though the flow-graph of a deterministic negotiation diagram
can be exponentially larger than the diagram itself. This gives a common
explanation to the low-complexity of all the analysis questions studied so far.
Finally, we show that classical gen/kill analyses are also an instance of our
framework, and obtain a PTIME algorithm for detecting anti-patterns in
free-choice workflow Petri nets.
Our result is based on a novel decomposition theorem, of independent
interest, showing that sound deterministic negotiation diagrams can be
hierarchically decomposed into (possibly overlapping) smaller sound diagrams.Comment: To appear in the Proceedings of LICS 2017, IEEE Computer Societ
Analysis of Timed and Long-Run Objectives for Markov Automata
Markov automata (MAs) extend labelled transition systems with random delays
and probabilistic branching. Action-labelled transitions are instantaneous and
yield a distribution over states, whereas timed transitions impose a random
delay governed by an exponential distribution. MAs are thus a nondeterministic
variation of continuous-time Markov chains. MAs are compositional and are used
to provide a semantics for engineering frameworks such as (dynamic) fault
trees, (generalised) stochastic Petri nets, and the Architecture Analysis &
Design Language (AADL). This paper considers the quantitative analysis of MAs.
We consider three objectives: expected time, long-run average, and timed
(interval) reachability. Expected time objectives focus on determining the
minimal (or maximal) expected time to reach a set of states. Long-run
objectives determine the fraction of time to be in a set of states when
considering an infinite time horizon. Timed reachability objectives are about
computing the probability to reach a set of states within a given time
interval. This paper presents the foundations and details of the algorithms and
their correctness proofs. We report on several case studies conducted using a
prototypical tool implementation of the algorithms, driven by the MAPA
modelling language for efficiently generating MAs.Comment: arXiv admin note: substantial text overlap with arXiv:1305.705
Modelling and analysis of Markov reward automata
Costs and rewards are important ingredients for many types of systems, modelling critical aspects like energy consumption, task completion, repair costs, and memory usage. This paper introduces Markov reward automata, an extension of Markov automata that allows the modelling of systems incorporating rewards (or costs) in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Rewards come in two flavours: action rewards, acquired instantaneously when taking a transition; and state rewards, acquired while residing in a state. We present algorithms to optimise three reward functions: the expected cumulative reward until a goal is reached, the expected cumulative reward until a certain time bound, and the long-run average reward. We have implemented these algorithms in the SCOOP/IMCA tool chain and show their feasibility via several case studies
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