19,701 research outputs found
Obligation Blackwell Games and p-Automata
We recently introduced p-automata, automata that read discrete-time Markov
chains. We used turn-based stochastic parity games to define acceptance of
Markov chains by a subclass of p-automata. Definition of acceptance required a
cumbersome and complicated reduction to a series of turn-based stochastic
parity games. The reduction could not support acceptance by general p-automata,
which was left undefined as there was no notion of games that supported it.
Here we generalize two-player games by adding a structural acceptance
condition called obligations. Obligations are orthogonal to the linear winning
conditions that define winning. Obligations are a declaration that player 0 can
achieve a certain value from a configuration. If the obligation is met, the
value of that configuration for player 0 is 1.
One cannot define value in obligation games by the standard mechanism of
considering the measure of winning paths on a Markov chain and taking the
supremum of the infimum of all strategies. Mainly because obligations need
definition even for Markov chains and the nature of obligations has the flavor
of an infinite nesting of supremum and infimum operators. We define value via a
reduction to turn-based games similar to Martin's proof of determinacy of
Blackwell games with Borel objectives. Based on this definition, we show that
games are determined. We show that for Markov chains with Borel objectives and
obligations, and finite turn-based stochastic parity games with obligations
there exists an alternative and simpler characterization of the value function.
Based on this simpler definition we give an exponential time algorithm to
analyze finite turn-based stochastic parity games with obligations. Finally, we
show that obligation games provide the necessary framework for reasoning about
p-automata and that they generalize the previous definition
Computation in Finitary Stochastic and Quantum Processes
We introduce stochastic and quantum finite-state transducers as
computation-theoretic models of classical stochastic and quantum finitary
processes. Formal process languages, representing the distribution over a
process's behaviors, are recognized and generated by suitable specializations.
We characterize and compare deterministic and nondeterministic versions,
summarizing their relative computational power in a hierarchy of finitary
process languages. Quantum finite-state transducers and generators are a first
step toward a computation-theoretic analysis of individual, repeatedly measured
quantum dynamical systems. They are explored via several physical systems,
including an iterated beam splitter, an atom in a magnetic field, and atoms in
an ion trap--a special case of which implements the Deutsch quantum algorithm.
We show that these systems' behaviors, and so their information processing
capacity, depends sensitively on the measurement protocol.Comment: 25 pages, 16 figures, 1 table; http://cse.ucdavis.edu/~cmg; numerous
corrections and update
Intrinsic Simulations between Stochastic Cellular Automata
The paper proposes a simple formalism for dealing with deterministic,
non-deterministic and stochastic cellular automata in a unifying and composable
manner. Armed with this formalism, we extend the notion of intrinsic simulation
between deterministic cellular automata, to the non-deterministic and
stochastic settings. We then provide explicit tools to prove or disprove the
existence of such a simulation between two stochastic cellular automata, even
though the intrinsic simulation relation is shown to be undecidable in
dimension two and higher. The key result behind this is the caracterization of
equality of stochastic global maps by the existence of a coupling between the
random sources. We then prove that there is a universal non-deterministic
cellular automaton, but no universal stochastic cellular automaton. Yet we
provide stochastic cellular automata achieving optimal partial universality.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
A Compositional Semantics for Stochastic Reo Connectors
In this paper we present a compositional semantics for the channel-based
coordination language Reo which enables the analysis of quality of service
(QoS) properties of service compositions. For this purpose, we annotate Reo
channels with stochastic delay rates and explicitly model data-arrival rates at
the boundary of a connector, to capture its interaction with the services that
comprise its environment. We propose Stochastic Reo automata as an extension of
Reo automata, in order to compositionally derive a QoS-aware semantics for Reo.
We further present a translation of Stochastic Reo automata to Continuous-Time
Markov Chains (CTMCs). This translation enables us to use third-party CTMC
verification tools to do an end-to-end performance analysis of service
compositions.Comment: In Proceedings FOCLASA 2010, arXiv:1007.499
On the decomposition of stochastic cellular automata
In this paper we present two interesting properties of stochastic cellular
automata that can be helpful in analyzing the dynamical behavior of such
automata. The first property allows for calculating cell-wise probability
distributions over the state set of a stochastic cellular automaton, i.e.
images that show the average state of each cell during the evolution of the
stochastic cellular automaton. The second property shows that stochastic
cellular automata are equivalent to so-called stochastic mixtures of
deterministic cellular automata. Based on this property, any stochastic
cellular automaton can be decomposed into a set of deterministic cellular
automata, each of which contributes to the behavior of the stochastic cellular
automaton.Comment: Submitted to Journal of Computation Science, Special Issue on
Cellular Automata Application
Probabilistic Bisimulation: Naturally on Distributions
In contrast to the usual understanding of probabilistic systems as stochastic
processes, recently these systems have also been regarded as transformers of
probabilities. In this paper, we give a natural definition of strong
bisimulation for probabilistic systems corresponding to this view that treats
probability distributions as first-class citizens. Our definition applies in
the same way to discrete systems as well as to systems with uncountable state
and action spaces. Several examples demonstrate that our definition refines the
understanding of behavioural equivalences of probabilistic systems. In
particular, it solves a long-standing open problem concerning the
representation of memoryless continuous time by memory-full continuous time.
Finally, we give algorithms for computing this bisimulation not only for finite
but also for classes of uncountably infinite systems
Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically
Labeled state-to-function transition systems, FuTS for short, are
characterized by transitions which relate states to functions of states over
general semirings, equipped with a rich set of higher-order operators. As such,
FuTS constitute a convenient modeling instrument to deal with process languages
and their quantitative extensions in particular. In this paper, the notion of
bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A
correspondence result is established stating that FuTS-bisimilarity coincides
with behavioural equivalence of the associated functor. As generic examples,
the equivalences underlying substantial fragments of major examples of
quantitative process algebras are related to the bisimilarity of specific FuTS.
The examples range from a stochastic process language, PEPA, to a language for
Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a
language for Markov Automata, MAL. The equivalences underlying these languages
are related to the bisimilarity of their specific FuTS. By the correspondence
result coalgebraic justification of the equivalences of these calculi is
obtained. The specific selection of languages, besides covering a large variety
of process interaction models and modelling choices involving quantities,
allows us to show different classes of FuTS, namely so-called simple FuTS,
combined FuTS, nested FuTS, and general FuTS
A Hierarchy of Scheduler Classes for Stochastic Automata
Stochastic automata are a formal compositional model for concurrent
stochastic timed systems, with general distributions and non-deterministic
choices. Measures of interest are defined over schedulers that resolve the
nondeterminism. In this paper we investigate the power of various theoretically
and practically motivated classes of schedulers, considering the classic
complete-information view and a restriction to non-prophetic schedulers. We
prove a hierarchy of scheduler classes w.r.t. unbounded probabilistic
reachability. We find that, unlike Markovian formalisms, stochastic automata
distinguish most classes even in this basic setting. Verification and strategy
synthesis methods thus face a tradeoff between powerful and efficient classes.
Using lightweight scheduler sampling, we explore this tradeoff and demonstrate
the concept of a useful approximative verification technique for stochastic
automata
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