1,601 research outputs found
Distributed Synthesis in Continuous Time
We introduce a formalism modelling communication of distributed agents
strictly in continuous-time. Within this framework, we study the problem of
synthesising local strategies for individual agents such that a specified set
of goal states is reached, or reached with at least a given probability. The
flow of time is modelled explicitly based on continuous-time randomness, with
two natural implications: First, the non-determinism stemming from interleaving
disappears. Second, when we restrict to a subclass of non-urgent models, the
quantitative value problem for two players can be solved in EXPTIME. Indeed,
the explicit continuous time enables players to communicate their states by
delaying synchronisation (which is unrestricted for non-urgent models). In
general, the problems are undecidable already for two players in the
quantitative case and three players in the qualitative case. The qualitative
undecidability is shown by a reduction to decentralized POMDPs for which we
provide the strongest (and rather surprising) undecidability result so far
Verifying nondeterministic probabilistic channel systems against -regular linear-time properties
Lossy channel systems (LCSs) are systems of finite state automata that
communicate via unreliable unbounded fifo channels. In order to circumvent the
undecidability of model checking for nondeterministic
LCSs, probabilistic models have been introduced, where it can be decided
whether a linear-time property holds almost surely. However, such fully
probabilistic systems are not a faithful model of nondeterministic protocols.
We study a hybrid model for LCSs where losses of messages are seen as faults
occurring with some given probability, and where the internal behavior of the
system remains nondeterministic. Thus the semantics is in terms of
infinite-state Markov decision processes. The purpose of this article is to
discuss the decidability of linear-time properties formalized by formulas of
linear temporal logic (LTL). Our focus is on the qualitative setting where one
asks, e.g., whether a LTL-formula holds almost surely or with zero probability
(in case the formula describes the bad behaviors). Surprisingly, it turns out
that -- in contrast to finite-state Markov decision processes -- the
satisfaction relation for LTL formulas depends on the chosen type of schedulers
that resolve the nondeterminism. While all variants of the qualitative LTL
model checking problem for the full class of history-dependent schedulers are
undecidable, the same questions for finite-memory scheduler can be solved
algorithmically. However, the restriction to reachability properties and
special kinds of recurrent reachability properties yields decidable
verification problems for the full class of schedulers, which -- for this
restricted class of properties -- are as powerful as finite-memory schedulers,
or even a subclass of them.Comment: 39 page
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Containment and equivalence of weighted automata: Probabilistic and max-plus cases
This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain
Undecidability of model-checking branching-time properties of stateless probabilistic pushdown process
In this paper, we settle a problem in probabilistic verification of
infinite--state process (specifically, {\it probabilistic pushdown process}).
We show that model checking {\it stateless probabilistic pushdown process}
(pBPA) against {\it probabilistic computational tree logic} (PCTL) is
undecidable.Comment: Author's comments on referee's report added, Interestin
When is Containment Decidable for Probabilistic Automata?
The containment problem for quantitative automata is the natural quantitative generalisation of the classical language inclusion problem for Boolean automata. We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity. There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous. Furthermore, we show that this is close to the most general decidable fragment of this problem by proving that it is already undecidable if one of the automata is allowed to be linearly ambiguous
Probabilistic cellular automata, invariant measures, and perfect sampling
A probabilistic cellular automaton (PCA) can be viewed as a Markov chain. The
cells are updated synchronously and independently, according to a distribution
depending on a finite neighborhood. We investigate the ergodicity of this
Markov chain. A classical cellular automaton is a particular case of PCA. For a
1-dimensional cellular automaton, we prove that ergodicity is equivalent to
nilpotency, and is therefore undecidable. We then propose an efficient perfect
sampling algorithm for the invariant measure of an ergodic PCA. Our algorithm
does not assume any monotonicity property of the local rule. It is based on a
bounding process which is shown to be also a PCA. Last, we focus on the PCA
Majority, whose asymptotic behavior is unknown, and perform numerical
experiments using the perfect sampling procedure
On deciding stability of multiclass queueing networks under buffer priority scheduling policies
One of the basic properties of a queueing network is stability. Roughly
speaking, it is the property that the total number of jobs in the network
remains bounded as a function of time. One of the key questions related to the
stability issue is how to determine the exact conditions under which a given
queueing network operating under a given scheduling policy remains stable.
While there was much initial progress in addressing this question, most of the
results obtained were partial at best and so the complete characterization of
stable queueing networks is still lacking. In this paper, we resolve this open
problem, albeit in a somewhat unexpected way. We show that characterizing
stable queueing networks is an algorithmically undecidable problem for the case
of nonpreemptive static buffer priority scheduling policies and deterministic
interarrival and service times. Thus, no constructive characterization of
stable queueing networks operating under this class of policies is possible.
The result is established for queueing networks with finite and infinite buffer
sizes and possibly zero service times, although we conjecture that it also
holds in the case of models with only infinite buffers and nonzero service
times. Our approach extends an earlier related work [Math. Oper. Res. 27 (2002)
272--293] and uses the so-called counter machine device as a reduction tool.Comment: Published in at http://dx.doi.org/10.1214/09-AAP597 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Qualitative Analysis of Partially-observable Markov Decision Processes
We study observation-based strategies for partially-observable Markov
decision processes (POMDPs) with omega-regular objectives. An observation-based
strategy relies on partial information about the history of a play, namely, on
the past sequence of observations. We consider the qualitative analysis
problem: given a POMDP with an omega-regular objective, whether there is an
observation-based strategy to achieve the objective with probability~1
(almost-sure winning), or with positive probability (positive winning). Our
main results are twofold. First, we present a complete picture of the
computational complexity of the qualitative analysis of POMDP s with parity
objectives (a canonical form to express omega-regular objectives) and its
subclasses. Our contribution consists in establishing several upper and lower
bounds that were not known in literature. Second, we present optimal bounds
(matching upper and lower bounds) on the memory required by pure and randomized
observation-based strategies for the qualitative analysis of POMDP s with
parity objectives and its subclasses
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