30,729 research outputs found
Unprovability of the Logical Characterization of Bisimulation
We quickly review labelled Markov processes (LMP) and provide a
counterexample showing that in general measurable spaces, event bisimilarity
and state bisimilarity differ in LMP. This shows that the logic in Desharnais
[*] does not characterize state bisimulation in non-analytic measurable spaces.
Furthermore we show that, under current foundations of Mathematics, such
logical characterization is unprovable for spaces that are projections of a
coanalytic set. Underlying this construction there is a proof that stationary
Markov processes over general measurable spaces do not have semi-pullbacks.
([*] J. Desharnais, Labelled Markov Processes. School of Computer Science.
McGill University, Montr\'eal (1999))Comment: Extended introduction and comments; extra section on semi-pullbacks;
11 pages Some background details added; extra example on the non-locality of
state bisimilarity; 14 page
Towards a quantum evolutionary scheme: violating Bell's inequalities in language
We show the presence of genuine quantum structures in human language. The
neo-Darwinian evolutionary scheme is founded on a probability structure that
satisfies the Kolmogorovian axioms, and as a consequence cannot incorporate
quantum-like evolutionary change. In earlier research we revealed quantum
structures in processes taking place in conceptual space. We argue that the
presence of quantum structures in language and the earlier detected quantum
structures in conceptual change make the neo-Darwinian evolutionary scheme
strictly too limited for Evolutionary Epistemology. We sketch how we believe
that evolution in a more general way should be implemented in epistemology and
conceptual change, but also in biology, and how this view would lead to another
relation between both biology and epistemology.Comment: 20 pages, no figures, this version of the paper is equal to the
foregoing. The paper has meanwhile been published in another book series than
the one tentatively mentioned in the comments given with the foregoing
versio
Bisimilarity is not Borel
We prove that the relation of bisimilarity between countable labelled
transition systems is -complete (hence not Borel), by reducing the
set of non-wellorders over the natural numbers continuously to it.
This has an impact on the theory of probabilistic and nondeterministic
processes over uncountable spaces, since logical characterizations of
bisimilarity (as, for instance, those based on the unique structure theorem for
analytic spaces) require a countable logic whose formulas have measurable
semantics. Our reduction shows that such a logic does not exist in the case of
image-infinite processes.Comment: 20 pages, 1 figure; proof of Sigma_1^1 completeness added with
extended comments. I acknowledge careful reading by the referees. Major
changes in Introduction, Conclusion, and motivation for NLMP. Proof for Lemma
22 added, simpler proofs for Lemma 17 and Theorem 30. Added references. Part
of this work was presented at Dagstuhl Seminar 12411 on Coalgebraic Logic
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
Multi-variate quickest detection of significant change process
The paper deals with a mathematical model of a surveillance system based on a net of sensors. The signals acquired by each node of the net are Markovian process, have two different transition probabilities, which depends on the presence or absence of a intruder nearby. The detection of the transition probability change at one node should be confirmed by a detection of similar change at some other sensors. Based on a simple game the model of a fusion center is then constructed. The aggregate function defined on the net is the background of the definition of a non-cooperative stopping game which is a model of the multivariate disorder detectionvoting stopping rule, majority voting rule, monotone voting strategy, change-point problems, quickest detection, sequential detection, simple game
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