727 research outputs found
Topological Complexity of omega-Powers : Extended Abstract
This is an extended abstract presenting new results on the topological
complexity of omega-powers (which are included in a paper "Classical and
effective descriptive complexities of omega-powers" available from
arXiv:0708.4176) and reflecting also some open questions which were discussed
during the Dagstuhl seminar on "Topological and Game-Theoretic Aspects of
Infinite Computations" 29.06.08 - 04.07.08
There Exist some Omega-Powers of Any Borel Rank
Omega-powers of finitary languages are languages of infinite words
(omega-languages) in the form V^omega, where V is a finitary language over a
finite alphabet X. They appear very naturally in the characterizaton of regular
or context-free omega-languages. Since the set of infinite words over a finite
alphabet X can be equipped with the usual Cantor topology, the question of the
topological complexity of omega-powers of finitary languages naturally arises
and has been posed by Niwinski (1990), Simonnet (1992) and Staiger (1997). It
has been recently proved that for each integer n > 0, there exist some
omega-powers of context free languages which are Pi^0_n-complete Borel sets,
that there exists a context free language L such that L^omega is analytic but
not Borel, and that there exists a finitary language V such that V^omega is a
Borel set of infinite rank. But it was still unknown which could be the
possible infinite Borel ranks of omega-powers. We fill this gap here, proving
the following very surprising result which shows that omega-powers exhibit a
great topological complexity: for each non-null countable ordinal alpha, there
exist some Sigma^0_alpha-complete omega-powers, and some Pi^0_alpha-complete
omega-powers.Comment: To appear in the Proceedings of the 16th EACSL Annual Conference on
Computer Science and Logic, CSL 2007, Lausanne, Switzerland, September 11-15,
2007, Lecture Notes in Computer Science, (c) Springer, 200
Casimir Effect and Global Theory of Boundary Conditions
The consistency of quantum field theories defined on domains with external
borders imposes very restrictive constraints on the type of boundary conditions
that the fields can satisfy. We analyse the global geometrical and topological
properties of the space of all possible boundary conditions for scalar quantum
field theories. The variation of the Casimir energy under the change of
boundary conditions reveals the existence of singularities generically
associated to boundary conditions which either involve topology changes of the
underlying physical space or edge states with unbounded below classical energy.
The effect can be understood in terms of a new type of Maslov index associated
to the non-trivial topology of the space of boundary conditions. We also
analyze the global aspects of the renormalization group flow, T-duality and the
conformal invariance of the corresponding fixed points.Comment: 11 page
Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
We investigated quantum critical behaviours in the non-equilibrium steady
state of a spin chain with boundary Markovian noise using the Fisher
information. The latter represents the distance between two infinitesimally
close states, and its superextensive size scaling witnesses a critical
behaviour due to a phase transition, since all the interaction terms are
extensive. Perturbatively in the noise strength, we found superextensive Fisher
information at anisotropy and irrational
irrespective of the order of two non-commuting
limits, i.e. the thermodynamic limit and the limit of sending
to an irrational number via a sequence of rational
approximants. From this result we argue the existence of a non-equilibrium
quantum phase transition with a critical phase . From the
non-superextensivity of the Fisher information of reduced states, we infer that
this non-equilibrium quantum phase transition does not have local order
parameters but has non-local ones, at least at . In the
non-perturbative regime for the noise strength, we numerically computed the
reduced Fisher information which lower bounds the full state Fisher
information, and is superextensive only at . Form the latter
result, we derived local order parameters at in the
non-perturbative case. The existence of critical behaviour witnessed by the
Fisher information in the phase is still an open problem. The
Fisher information also represents the best sensitivity for any estimation of
the control parameter, in our case the anisotropy , and its
superextensivity implies enhanced estimation precision which is also highly
robust in the presence of a critical phase
Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns
Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is
described by means of an infinite hierarchy of its unstable spatiotemporally
periodic solutions. An intrinsic parametrization of the corresponding invariant
set serves as accurate guide to the high-dimensional dynamics, and the periodic
orbit theory yields several global averages characterizing the chaotic
dynamics.Comment: Latex, ioplppt.sty and iopl10.sty, 18 pages, 11 PS-figures,
compressed and encoded with uufiles, 170 k
Geospatial Narratives and their Spatio-Temporal Dynamics: Commonsense Reasoning for High-level Analyses in Geographic Information Systems
The modelling, analysis, and visualisation of dynamic geospatial phenomena
has been identified as a key developmental challenge for next-generation
Geographic Information Systems (GIS). In this context, the envisaged
paradigmatic extensions to contemporary foundational GIS technology raises
fundamental questions concerning the ontological, formal representational, and
(analytical) computational methods that would underlie their spatial
information theoretic underpinnings.
We present the conceptual overview and architecture for the development of
high-level semantic and qualitative analytical capabilities for dynamic
geospatial domains. Building on formal methods in the areas of commonsense
reasoning, qualitative reasoning, spatial and temporal representation and
reasoning, reasoning about actions and change, and computational models of
narrative, we identify concrete theoretical and practical challenges that
accrue in the context of formal reasoning about `space, events, actions, and
change'. With this as a basis, and within the backdrop of an illustrated
scenario involving the spatio-temporal dynamics of urban narratives, we address
specific problems and solutions techniques chiefly involving `qualitative
abstraction', `data integration and spatial consistency', and `practical
geospatial abduction'. From a broad topical viewpoint, we propose that
next-generation dynamic GIS technology demands a transdisciplinary scientific
perspective that brings together Geography, Artificial Intelligence, and
Cognitive Science.
Keywords: artificial intelligence; cognitive systems; human-computer
interaction; geographic information systems; spatio-temporal dynamics;
computational models of narrative; geospatial analysis; geospatial modelling;
ontology; qualitative spatial modelling and reasoning; spatial assistance
systemsComment: ISPRS International Journal of Geo-Information (ISSN 2220-9964);
Special Issue on: Geospatial Monitoring and Modelling of Environmental
Change}. IJGI. Editor: Duccio Rocchini. (pre-print of article in press
When are Stochastic Transition Systems Tameable?
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of
decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness
allows one to lift most good properties from finite Markov chains to
denumerable ones, and therefore to adapt existing verification algorithms to
infinite-state models. Decisive Markov chains however do not encompass
stochastic real-time systems, and general stochastic transition systems (STSs
for short) are needed. In this article, we provide a framework to perform both
the qualitative and the quantitative analysis of STSs. First, we define various
notions of decisiveness (inherited from [1]), notions of fairness and of
attractors for STSs, and make explicit the relationships between them. Then, we
define a notion of abstraction, together with natural concepts of soundness and
completeness, and we give general transfer properties, which will be central to
several verification algorithms on STSs. We further design a generic
construction which will be useful for the analysis of {\omega}-regular
properties, when a finite attractor exists, either in the system (if it is
denumerable), or in a sound denumerable abstraction of the system. We next
provide algorithms for qualitative model-checking, and generic approximation
procedures for quantitative model-checking. Finally, we instantiate our
framework with stochastic timed automata (STA), generalized semi-Markov
processes (GSMPs) and stochastic time Petri nets (STPNs), three models
combining dense-time and probabilities. This allows us to derive decidability
and approximability results for the verification of these models. Some of these
results were known from the literature, but our generic approach permits to
view them in a unified framework, and to obtain them with less effort. We also
derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page
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