10,392 research outputs found
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
Introducing probabilistic celular automata. A versatile extension of Game of Live
The "Game of life" model was created in 1970 by the mathematician Jonh Horton Conway
using cellular automata. Since then, di erent extensions of these cellular automata have been
used in many applications, such as car traffic control or baggage traffic in an airport.
These extensions introduce ideas not only from cellular automata models but also from neural
networks theory.
In this work, we introduce probabilistic cellular automata which include non-deterministic
rules for transitions between successive generations of the automaton together with probabilistic
decisions about life and death of the cells in next generation of the automaton. This way,
more realistic situations can be modeled and the obtained results are also non-deterministic.
As an example of use, an implementation of this probabilistic cellular automaton has been
developed using it for simulating tissues evolution. The authors are specially interested in
simulations of cancerous tissues.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
Parrondo games as lattice gas automata
Parrondo games are coin flipping games with the surprising property that
alternating plays of two losing games can produce a winning game. We show that
this phenomenon can be modelled by probabilistic lattice gas automata.
Furthermore, motivated by the recent introduction of quantum coin flipping
games, we show that quantum lattice gas automata provide an interesting
definition for quantum Parrondo games.Comment: 12 pages, plain TeX, 10 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages); for related work see
http://math.ucsd.edu/~dmeyer/research.htm
Tree games with regular objectives
We study tree games developed recently by Matteo Mio as a game interpretation
of the probabilistic -calculus. With expressive power comes complexity.
Mio showed that tree games are able to encode Blackwell games and,
consequently, are not determined under deterministic strategies.
We show that non-stochastic tree games with objectives recognisable by
so-called game automata are determined under deterministic, finite memory
strategies. Moreover, we give an elementary algorithmic procedure which, for an
arbitrary regular language L and a finite non-stochastic tree game with a
winning objective L decides if the game is determined under deterministic
strategies.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Game Characterization of Probabilistic Bisimilarity, and Applications to Pushdown Automata
We study the bisimilarity problem for probabilistic pushdown automata (pPDA)
and subclasses thereof. Our definition of pPDA allows both probabilistic and
non-deterministic branching, generalising the classical notion of pushdown
automata (without epsilon-transitions). We first show a general
characterization of probabilistic bisimilarity in terms of two-player games,
which naturally reduces checking bisimilarity of probabilistic labelled
transition systems to checking bisimilarity of standard (non-deterministic)
labelled transition systems. This reduction can be easily implemented in the
framework of pPDA, allowing to use known results for standard
(non-probabilistic) PDA and their subclasses. A direct use of the reduction
incurs an exponential increase of complexity, which does not matter in deriving
decidability of bisimilarity for pPDA due to the non-elementary complexity of
the problem. In the cases of probabilistic one-counter automata (pOCA), of
probabilistic visibly pushdown automata (pvPDA), and of probabilistic basic
process algebras (i.e., single-state pPDA) we show that an implicit use of the
reduction can avoid the complexity increase; we thus get PSPACE, EXPTIME, and
2-EXPTIME upper bounds, respectively, like for the respective non-probabilistic
versions. The bisimilarity problems for OCA and vPDA are known to have matching
lower bounds (thus being PSPACE-complete and EXPTIME-complete, respectively);
we show that these lower bounds also hold for fully probabilistic versions that
do not use non-determinism
Computing Probabilistic Bisimilarity Distances for Probabilistic Automata
The probabilistic bisimilarity distance of Deng et al. has been proposed as a
robust quantitative generalization of Segala and Lynch's probabilistic
bisimilarity for probabilistic automata. In this paper, we present a
characterization of the bisimilarity distance as the solution of a simple
stochastic game. The characterization gives us an algorithm to compute the
distances by applying Condon's simple policy iteration on these games. The
correctness of Condon's approach, however, relies on the assumption that the
games are stopping. Our games may be non-stopping in general, yet we are able
to prove termination for this extended class of games. Already other algorithms
have been proposed in the literature to compute these distances, with
complexity in and \textbf{PPAD}. Despite the
theoretical relevance, these algorithms are inefficient in practice. To the
best of our knowledge, our algorithm is the first practical solution.
The characterization of the probabilistic bisimilarity distance mentioned
above crucially uses a dual presentation of the Hausdorff distance due to
M\'emoli. As an additional contribution, in this paper we show that M\'emoli's
result can be used also to prove that the bisimilarity distance bounds the
difference in the maximal (or minimal) probability of two states to satisfying
arbitrary -regular properties, expressed, eg., as LTL formulas
On the Problem of Computing the Probability of Regular Sets of Trees
We consider the problem of computing the probability of regular languages of
infinite trees with respect to the natural coin-flipping measure. We propose an
algorithm which computes the probability of languages recognizable by
\emph{game automata}. In particular this algorithm is applicable to all
deterministic automata. We then use the algorithm to prove through examples
three properties of measure: (1) there exist regular sets having irrational
probability, (2) there exist comeager regular sets having probability and
(3) the probability of \emph{game languages} , from automata theory,
is if is odd and is otherwise
Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)
We consider the problem of verifying liveness for systems with a finite, but
unbounded, number of processes, commonly known as parameterised systems.
Typical examples of such systems include distributed protocols (e.g. for the
dining philosopher problem). Unlike the case of verifying safety, proving
liveness is still considered extremely challenging, especially in the presence
of randomness in the system. In this paper we consider liveness under arbitrary
(including unfair) schedulers, which is often considered a desirable property
in the literature of self-stabilising systems. We introduce an automatic method
of proving liveness for randomised parameterised systems under arbitrary
schedulers. Viewing liveness as a two-player reachability game (between
Scheduler and Process), our method is a CEGAR approach that synthesises a
progress relation for Process that can be symbolically represented as a
finite-state automaton. The method is incremental and exploits both
Angluin-style L*-learning and SAT-solvers. Our experiments show that our
algorithm is able to prove liveness automatically for well-known randomised
distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher
Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon
Protocol). To the best of our knowledge, this is the first fully-automatic
method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape
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