15,573 research outputs found
On computing fixpoints in well-structured regular model checking, with applications to lossy channel systems
We prove a general finite convergence theorem for "upward-guarded" fixpoint
expressions over a well-quasi-ordered set. This has immediate applications in
regular model checking of well-structured systems, where a main issue is the
eventual convergence of fixpoint computations. In particular, we are able to
directly obtain several new decidability results on lossy channel systems.Comment: 16 page
Finitely additive beliefs and universal type spaces
The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14
(1967/68) 159--182, 320--334, 486--502] are the prevalent models used to
describe interactive uncertainty. In this paper we examine the existence of a
universal type space when beliefs are described by finitely additive
probability measures. We find that in the category of all type spaces that
satisfy certain measurability conditions (-measurability, for some
fixed regular cardinal ), there is a universal type space (i.e., a
terminal object) to which every type space can be mapped in a unique
beliefs-preserving way. However, by a probabilistic adaption of the elegant
sober-drunk example of Heifetz and Samet [Games Econom. Behav. 22 (1998)
260--273] we show that if all subsets of the spaces are required to be
measurable, then there is no universal type space.Comment: Published at http://dx.doi.org/10.1214/009117905000000576 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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
RankPL: A Qualitative Probabilistic Programming Language
In this paper we introduce RankPL, a modeling language that can be thought of
as a qualitative variant of a probabilistic programming language with a
semantics based on Spohn's ranking theory. Broadly speaking, RankPL can be used
to represent and reason about processes that exhibit uncertainty expressible by
distinguishing "normal" from" surprising" events. RankPL allows (iterated)
revision of rankings over alternative program states and supports various types
of reasoning, including abduction and causal inference. We present the
language, its denotational semantics, and a number of practical examples. We
also discuss an implementation of RankPL that is available for download
Limits on non-local correlations from the structure of the local state space
The outcomes of measurements on entangled quantum systems can be nonlocally
correlated. However, while it is easy to write down toy theories allowing
arbitrary nonlocal correlations, those allowed in quantum mechanics are
limited. Quantum correlations cannot, for example, violate a principle known as
macroscopic locality, which implies that they cannot violate Tsirelson's bound.
This work shows that there is a connection between the strength of nonlocal
correlations in a physical theory, and the structure of the state spaces of
individual systems. This is illustrated by a family of models in which local
state spaces are regular polygons, where a natural analogue of a maximally
entangled state of two systems exists. We characterize the nonlocal
correlations obtainable from such states. The family allows us to study the
transition between classical, quantum, and super-quantum correlations, by
varying only the local state space. We show that the strength of nonlocal
correlations - in particular whether the maximally entangled state violates
Tsirelson's bound or not - depends crucially on a simple geometric property of
the local state space, known as strong self-duality. This result is seen to be
a special case of a general theorem, which states that a broad class of
entangled states in probabilistic theories - including, by extension, all
bipartite classical and quantum states - cannot violate macroscopic locality.
Finally, our results show that there exist models which are locally almost
indistinguishable from quantum mechanics, but can nevertheless generate
maximally nonlocal correlations.Comment: 26 pages, 4 figures. v2: Document structure changed. Main theorem has
been extended. It applies to all quantum states now. v3: new abstrac
Mean-payoff Automaton Expressions
Quantitative languages are an extension of boolean languages that assign to
each word a real number. Mean-payoff automata are finite automata with
numerical weights on transitions that assign to each infinite path the long-run
average of the transition weights. When the mode of branching of the automaton
is deterministic, nondeterministic, or alternating, the corresponding class of
quantitative languages is not robust as it is not closed under the pointwise
operations of max, min, sum, and numerical complement. Nondeterministic and
alternating mean-payoff automata are not decidable either, as the quantitative
generalization of the problems of universality and language inclusion is
undecidable.
We introduce a new class of quantitative languages, defined by mean-payoff
automaton expressions, which is robust and decidable: it is closed under the
four pointwise operations, and we show that all decision problems are decidable
for this class. Mean-payoff automaton expressions subsume deterministic
mean-payoff automata, and we show that they have expressive power incomparable
to nondeterministic and alternating mean-payoff automata. We also present for
the first time an algorithm to compute distance between two quantitative
languages, and in our case the quantitative languages are given as mean-payoff
automaton expressions
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