113 research outputs found

    Advances and applications of automata on words and trees : abstracts collection

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    From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

    Advances and applications of automata on words and trees : executive summary

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    Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail

    On determinism versus nondeterminism for restarting automata

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    AbstractA restarting automaton processes a given word by executing a sequence of local simplifications until a simple word is obtained that the automaton then accepts. Such a computation is expressed as a sequence of cycles. A nondeterministic restarting automaton M is called correctness preserving, if, for each cycle u⊢Mcv, the string v belongs to the characteristic language LC(M) of M, if the string u does. Our first result states that for each type of restarting automaton X∈{R,RW,RWW,RL,RLW,RLWW}, if M is a nondeterministic X-automaton that is correctness preserving, then there exists a deterministic X-automaton M1 such that the characteristic languages LC(M1) and LC(M) coincide. When a restarting automaton M executes a cycle that transforms a string from the language LC(M) into a string not belonging to LC(M), then this can be interpreted as an error of M. By counting the number of cycles it may take M to detect this error, we obtain a measure for the influence that errors have on computations. Accordingly, this measure is called error detection distance. It turns out, however, that an X-automaton with bounded error detection distance is equivalent to a correctness preserving X-automaton, and therewith to a deterministic X-automaton. This means that nondeterminism increases the expressive power of X-automata only in combination with an unbounded error detection distance

    10501 Abstracts Collection -- Advances and Applications of Automata on Words and Trees

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    From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 ``Advances and Applications of Automata on Words and Trees\u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

    Random growth models with polygonal shapes

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    We consider discrete-time random perturbations of monotone cellular automata (CA) in two dimensions. Under general conditions, we prove the existence of half-space velocities, and then establish the validity of the Wulff construction for asymptotic shapes arising from finite initial seeds. Such a shape converges to the polygonal invariant shape of the corresponding deterministic model as the perturbation decreases. In many cases, exact stability is observed. That is, for small perturbations, the shapes of the deterministic and random processes agree exactly. We give a complete characterization of such cases, and show that they are prevalent among threshold growth CA with box neighborhood. We also design a nontrivial family of CA in which the shape is exactly computable for all values of its probability parameter.Comment: Published at http://dx.doi.org/10.1214/009117905000000512 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Clearing Restarting Automata

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    Restartovací automaty byly navrženy jako model pro redukční analýzu, která představuje lingvisticky motivovanou metodu pro kontrolu korektnosti věty. Cílem práce je studovat omezenější modely restartovacích automatů, které smí vymazat podřetězec nebo jej nahradit speciálním pomocným symbolem, jenom na základě omezeného lokálního kontextu tohoto podřetězce. Tyto restartovací automaty se nazývají clearing restarting automata. V práci jsou taktéž zkoumány uzávěrové vlastnosti těchto automatů, jejich vztah k Chomskeho hierarchii a možnosti učení těchto automatů na základě pozitivních a negativních příkladů.Restarting automata were introduced as a model for analysis by reduction which is a linguistically motivated method for checking correctness of a sentence. The goal of the thesis is to study more restricted models of restarting automata which based on a limited context can either delete a substring of the current content of its tape or replace a substring by a special symbol, which cannot be overwritten anymore, but it can be deleted later. Such restarting automata are called clearing restarting automata. The thesis investigates the properties of clearing restarting automata, their relation to Chomsky hierarchy and possibilities for machine learning of such automata from positive and negative samples.Department of Software and Computer Science EducationKatedra softwaru a výuky informatikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

    Sampling Correctors

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    In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported to have, in order to allow one to make "on-the-fly" corrections to samples drawn from probability distributions. These algorithms then act as filters between the noisy data and the end user. We show connections between sampling correctors, distribution learning algorithms, and distribution property testing algorithms. We show that these connections can be utilized to expand the applicability of known distribution learning and property testing algorithms as well as to achieve improved algorithms for those tasks. As a first step, we show how to design sampling correctors using proper learning algorithms. We then focus on the question of whether algorithms for sampling correctors can be more efficient in terms of sample complexity than learning algorithms for the analogous families of distributions. When correcting monotonicity, we show that this is indeed the case when also granted query access to the cumulative distribution function. We also obtain sampling correctors for monotonicity without this stronger type of access, provided that the distribution be originally very close to monotone (namely, at a distance O(1/log2n)O(1/\log^2 n)). In addition to that, we consider a restricted error model that aims at capturing "missing data" corruptions. In this model, we show that distributions that are close to monotone have sampling correctors that are significantly more efficient than achievable by the learning approach. We also consider the question of whether an additional source of independent random bits is required by sampling correctors to implement the correction process

    Probabilistic modal {\mu}-calculus with independent product

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    The probabilistic modal {\mu}-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS's). Two equivalent semantics have been studied for this logic, both assigning to each state a value in the interval [0,1] representing the probability that the property expressed by the formula holds at the state. One semantics is denotational and the other is a game semantics, specified in terms of two-player stochastic parity games. A shortcoming of the probabilistic modal {\mu}-calculus is the lack of expressiveness required to encode other important temporal logics for PLTS's such as Probabilistic Computation Tree Logic (PCTL). To address this limitation we extend the logic with a new pair of operators: independent product and coproduct. The resulting logic, called probabilistic modal {\mu}-calculus with independent product, can encode many properties of interest and subsumes the qualitative fragment of PCTL. The main contribution of this paper is the definition of an appropriate game semantics for this extended probabilistic {\mu}-calculus. This relies on the definition of a new class of games which generalize standard two-player stochastic (parity) games by allowing a play to be split into concurrent subplays, each continuing their evolution independently. Our main technical result is the equivalence of the two semantics. The proof is carried out in ZFC set theory extended with Martin's Axiom at an uncountable cardinal
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