Rational and Recognisable Power Series

Sakarovitch, Jacques

doi:10.1007/978-3-642-01492-5_4

Cited by 66 publications

(66 citation statements)

References 42 publications

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“…The supports of recognizable series are well-studied objects, see [3,9] for recent overviews. It is well known that there are recognizable series S such that supp(S) is not a recognizable language.…”

Section: Overview Main Results and Discussionmentioning

confidence: 99%

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The Support of a Recognizable Series over a Zero-sum Free, Commutative Semiring is Recognizable

Kirsten¹

2011

Acta Cybern

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Section: Overview Main Results and Discussionmentioning

confidence: 99%

“…However, for large classes of semirings, it is known that the support of a recognizable series is always recognizable, see [3,5,9] for recent overviews. These classes include all positive semirings (semirings which are both zero-divisor free and zero-sum free), all finite, and more generally, all locally finite semirings.…”

Section: Introductionmentioning

confidence: 99%

The Support of a Recognizable Series over a Zero-sum Free, Commutative Semiring is Recognizable

Kirsten¹

2011

Acta Cybern

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“…Hence, we cannot apply directly the theory of rational series over graded monoids as developped e.g. in [28]. Instead, we will use the theory of rational series over a continuous semiring S (see e.g., [27,III.5]).…”

Section: Series Over a Partial Monoidmentioning

confidence: 99%

Adding Pebbles to Weighted Automata

Gastin

Monmege

2012

Implementation and Application of Automata

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Abstract. We extend weighted automata and weighted rational expressions with 2-way moves and (reusable) pebbles. We show with examples from natural language modeling and quantitative model-checking that weighted expressions and automata with pebbles are more expressive and allow much more natural and intuitive specifications than classical ones. We extend Kleene-Schützenberger theorem showing that weighted expressions and automata with pebbles have the same expressive power. We focus on an efficient translation from expressions to automata. We also prove that the evaluation problem for weighted automata can be done very efficiently if the number of (reusable) pebbles is low.

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“…Naturally, this fundamental result has been generalized to various settings and in particular to quantitative extensions of classical languages, called formal power series [24,23,4].…”

Section: Introductionmentioning

confidence: 99%

A Probabilistic Kleene Theorem

Bollig

Gastin

Monmege

et al. 2012

Automated Technology for Verification and Analysis

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Abstract. We provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. We provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a star operator. We prove that probabilistic expressions and probabilistic automata are expressively equivalent. Our result actually extends to two-way probabilistic automata with pebbles and corresponding expressions.

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Rational and Recognisable Power Series

Cited by 66 publications

References 42 publications

The Support of a Recognizable Series over a Zero-sum Free, Commutative Semiring is Recognizable

The Support of a Recognizable Series over a Zero-sum Free, Commutative Semiring is Recognizable

Adding Pebbles to Weighted Automata

A Probabilistic Kleene Theorem

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