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Experiments in Complexity of Probabilistic and Ultrametric Automata
"... Abstract. We try to compare the complexity of deterministic, nondeterministic, probabilistic and ultrametric finite automata for the same language. We do not claim to have final upper and lower bounds. Rather these results can be considered as experiments to find advantages of one type of automata ..."
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Abstract. We try to compare the complexity of deterministic, nondeterministic, probabilistic and ultrametric finite automata for the same language. We do not claim to have final upper and lower bounds. Rather these results can be considered as experiments to find advantages of one type of automata
Advantages of Ultrametric Counter Automata?
"... Abstract. Ultrametric algorithms are similar to probabilistic algorithms but they describe the degree of indeterminism by padic numbers instead of real numbers. No wonder that only very few examples of advantages for ultrametric algorithms over probabilistic ones have been published up to now, and ..."
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, and all they are slightly artificial. This paper considers ultrametric and probabilistic onecounter automata with two oneway input tapes. A language is found which is recognizable by ultrametric but not by probabilistic automata of this type. 1
Ultrametric automata and Turing machines ∗
"... We introduce a notion of ultrametric automata and Turing machines using padic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of probabilistic automata but complexity of probabilistic automata and complexity of ultrametric ..."
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We introduce a notion of ultrametric automata and Turing machines using padic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of probabilistic automata but complexity of probabilistic automata and complexity
Ultrametric Automata with One Head Versus Multihead Nondeterministic Automata?
"... Abstract. The idea of using padic numbers in Turing machines and finite automata to describe random branching of the process of computation was recently introduced. In the last two years some advantages of ultrametric algorithms for finite automata and Turing machines were explored. In this paper ..."
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Abstract. The idea of using padic numbers in Turing machines and finite automata to describe random branching of the process of computation was recently introduced. In the last two years some advantages of ultrametric algorithms for finite automata and Turing machines were explored. In this paper
Ultrametric Subsets with . . .
"... It is shown that for every ε ∈ (0, 1), every compact metric space (X, d) has a compact subset S ⊆ X that embeds into an ultrametric space with distortion O(1/ε), and dimH(S) � (1 − ε) dimH(X), where dimH(·) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via ..."
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It is shown that for every ε ∈ (0, 1), every compact metric space (X, d) has a compact subset S ⊆ X that embeds into an ultrametric space with distortion O(1/ε), and dimH(S) � (1 − ε) dimH(X), where dimH(·) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via
Ultrametric Subsets with Large . . .
"... It is shown that for every ε ∈ (0, 1), every compact metric space (X, d) has a compact subset S ⊆ X that embeds into an ultrametric space with distortion O(1/ε), and dimH(S) � (1 − ε) dimH(X), where dimH(·) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via a ..."
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It is shown that for every ε ∈ (0, 1), every compact metric space (X, d) has a compact subset S ⊆ X that embeds into an ultrametric space with distortion O(1/ε), and dimH(S) � (1 − ε) dimH(X), where dimH(·) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via
Combinatorial stochastic processes
"... This is a collection of expository articles about various topics at the interface between enumerative combinatorics and stochastic processes. These articles expand on a course of lectures given at the École d’Été de Probabilités de St. Flour in July 2002. The articles are called ’chapters ’ and numb ..."
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Cited by 219 (15 self)
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This is a collection of expository articles about various topics at the interface between enumerative combinatorics and stochastic processes. These articles expand on a course of lectures given at the École d’Été de Probabilités de St. Flour in July 2002. The articles are called ’chapters ’ and numbered according to the order of these chapters in a printed volume to appear in Springer Lecture Notes in Mathematics. Each chapter is fairly selfcontained, so readers with adequate background can start reading any chapter, with occasional consultation of earlier chapters as necessary. Following this Chapter 0, there are 10 chapters, each divided into sections. Most sections conclude with some Exercises. Those for which I don’t know solutions are called Problems. Acknowledgments Much of the research reviewed here was done jointly with David Aldous. Much credit is due to him, especially for the big picture of continuum approximations to large combinatorial structures. Thanks also to my other collaborators in this work, especially Jean Bertoin, Michael Camarri, Steven
Active Learning of Classes of Recursive Functions by Ultrametric Algorithms
, 2013
"... We study active learning of classes of recursive functions by asking value queries about the target function f, where f is from the target class. That is, the query is a natural number x, and the answer to the query is f(x). The complexity measure in this paper is the worstcase number of queries as ..."
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asked. We prove that for some classes of recursive functions ultrametric active learning algorithms can achieve the learning goal by asking significantly fewer queries than deterministic, probabilistic, and even nondeterministic active learning algorithms. This is the first ever example of a problem
Results 1  10
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