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Coinductive Counting with Weighted Automata

Journal of Automata, Languages and Combinatorics, 2003
A general methodology is developed to compute the solution of a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite weighted automaton; (2) the automaton is reduced by means of the quantitative notion of stream bisimulation; (3) the reduced automaton is used to compute an ...
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Weighted automata with discounting

Information Processing Letters, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Droste, Manfred   +2 more
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Languages Accepted by Weighted Restarting Automata*

Fundamenta Informaticae, 2021
Weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata. In earlier works we studied the classes of functions and relations that are computed by weighted restarting automata. Here we use them to define classes of formal languages by restricting the weight associated to a given input word ...
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DECOMPOSITION OF WEIGHTED MULTIOPERATOR TREE AUTOMATA

International Journal of Foundations of Computer Science, 2009
Weighted multioperator tree automata (for short: wmta) are finite-state bottom-up tree automata in which the transitions are weighted with an operation taken from some multioperator monoid. A wmta recognizes a tree series which is a mapping from the set of trees to some commutative monoid.
Stüber, Torsten   +2 more
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Quantitative vs. Weighted Automata

2021
Weighted automata are widely researched, but with a variety of different semantics, which mostly fit into either the “quantitative view” or the “algebraic view”. We argue that the two views result with incomparable automata families, each providing a different conceptual generalization of Boolean automata and having different natural extensions.
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Undecidability in Integer Weighted Finite Automata

Fundamenta Informaticae, 1999
It is shown that the universe problem L(Aγ) = A* is undecidable for 4-state finite automata A with integer weight function γ on its transitions. This holds even in the case, where A is acyclic and the weighting γ satisfies the unimodality condition. The language L(Aγ) is defined as the set of words ω for which there exists a path π of A having zero ...
Halava, Vesa, Harju, Tero
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Context-Free Recognition with Weighted Automata

Grammars, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cortes, Corinna, Mohri, Mehryar
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Image compression using weighted finite automata

Computers & Graphics, 1993
We introduce Weighted Finite Automata (WFA) as a tool to define real functions, in particular, the greyness functions of grey-tone images. Mathematical properties and the definition power of WFA have been studied by Culik and Karhumaki. Their generative power is incomparable with Barnsley's Iterative Function Systems.
Karel Culik, Jarkko Kari
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Stochastization of Weighted Automata

2015
Nondeterministic weighted finite automata (WFAs) map input words to real numbers. Each transition of a WFA is labeled by both a letter from some alphabet and a weight. The weight of a run is the sum of the weights on the transitions it traverses, and the weight of a word is the minimal weight of a run on it.
Guy Avni, Orna Kupferman
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Weighted automata

2021
Manfred Droste, Dietrich Kuske
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