460 research outputs found
What is known about the Value 1 Problem for Probabilistic Automata?
The value 1 problem is a decision problem for probabilistic automata over
finite words: are there words accepted by the automaton with arbitrarily high
probability? Although undecidable, this problem attracted a lot of attention
over the last few years. The aim of this paper is to review and relate the
results pertaining to the value 1 problem. In particular, several algorithms
have been proposed to partially solve this problem. We show the relations
between them, leading to the following conclusion: the Markov Monoid Algorithm
is the most correct algorithm known to (partially) solve the value 1 problem
On the Spectrum of Hecke Type Operators related to some Fractal Groups
We give the first example of a connected 4-regular graph whose Laplace
operator's spectrum is a Cantor set, as well as several other computations of
spectra following a common ``finite approximation'' method. These spectra are
simple transforms of the Julia sets associated to some quadratic maps. The
graphs involved are Schreier graphs of fractal groups of intermediate growth,
and are also ``substitutional graphs''. We also formulate our results in terms
of Hecke type operators related to some irreducible quasi-regular
representations of fractal groups and in terms of the Markovian operator
associated to noncommutative dynamical systems via which these fractal groups
were originally defined. In the computations we performed, the self-similarity
of the groups is reflected in the self-similarity of some operators; they are
approximated by finite counterparts whose spectrum is computed by an ad hoc
factorization process.Comment: 1 color figure, 2 color diagrams, many figure
Schema-Guided Induction of Monadic Queries
International audienceThe induction of monadic node selecting queries from partially annotated XML-trees is a key task in Web information extraction. We show how to integrate schema guidance into an RPNI-based learning algorithm, in which monadic queries are represented by pruning node selecting tree transducers. We present experimental results on schema guidance by the DTD of HTML
Freeness of automaton groups vs boundary dynamics
We prove that the boundary dynamics of the (semi)group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group. We specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to the existence of a finite Schreier graph in the boundary of the enriched dual pointed at some essentially non-trivial point. From these results we derive some consequences from the algebraic, algorithmic and dynamical points of view
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
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