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Kleene's Theorem for Weighted Tree-Automata
[chapter]

2003
*
Lecture Notes in Computer Science
*

We sketch the proof of a Kleene-type

doi:10.1007/978-3-540-45077-1_36
fatcat:tvhukjpiqrddtiiwmjysidoiui
*theorem**for*formal*tree*-series over commutative semirings. ... That is,*for*a suitable set of rational operations we show that the proper rational formal*tree*-series coincide with the recognizable ones. ... On the level of*weighted**tree*-languages we can prove a Kleene-type*theorem*. ...##
###
Page 5631 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

*Theorem*4.2.1 of Section 4.2

*for*e-

*automata*, Section 5.1

*for*regular expressions, and Section 5.3

*for*an algorithmic proof of

*Kleene’s*

*Theorem*. ... This centres on

*Kleene’s*

*Theorem*, the first major re- sult proved about finite

*automata*. ...

##
###
Page 6034 of Mathematical Reviews Vol. , Issue 88k
[page]

1988
*
Mathematical Reviews
*

Summary: “Using regular

*tree*grammars*weighted*over a semiring, we establish*Kleene’s**theorem*in the context of formal*tree*power series.” 88k:68053 68Q50 20M05 68Q10 68T15 Diekert, Volker (D-MUTU-D) On ... Wolfgang Thomas (D-AACH-I) 68 COMPUTER SCIENCE 88k:68052 68Q50 03D05 68Q45 Alexandrakis, Athanasios (GR-THESS); Bozapalidis, Symeon (GR-THESS)*Weighted*grammars and*Kleene’s**theorem*. Inform. Process. ...##
###
Rational Transformations and a Kleene Theorem for Power Series over Rational Monoids
[chapter]

2011
*
Lecture Notes in Computer Science
*

Using these results we prove a Kleene-Schützenberger

doi:10.1007/978-3-642-24897-9_5
fatcat:ytxbohsbtjbplcrs6z4ymdtgci
*Theorem**for*formal power series over rational monoids. It extends a result of Sakarovitch. ... The first is the characterisation of*weighted**automata*in terms of rational expressions, a quantitative version of*Kleene's*result, which was shown by Schützenberger already in 1961 [19] . ... Recognizable and Rational Series In this section we recall some basics*for*monoids, semirings and from the theory of*weighted**automata*. ...##
###
Schützenberger's theorem on formal power series follows from Kleene's theorem

2008
*
Theoretical Computer Science
*

We derive Schützenberger's characterisation of the set of recognizable formal power series as a formal corollary from

doi:10.1016/j.tcs.2008.04.041
fatcat:nz5dcvsq25bfrn7lzibw5m542u
*Kleene's*characterisation of the set of regular languages. ...*Kleene's*and Schützenberger's*theorems*have been extended to other structures like infinite words [10, 5, 7] ,*trees*[12, 3, 9, 16, 2, 6] , sp-pomsets [13, 15] , and pictures [4, 14] using direct ... Introduction Schützenberger's*theorem*[17, 8] shows that the behaviors of*weighted*finite*automata*over an arbitrary semiring are precisely the rational formal power series. ...##
###
Page 6323 of Mathematical Reviews Vol. , Issue 93k
[page]

1993
*
Mathematical Reviews
*

A generalization of

*Kleene’s**theorem*is given that states the equality of the w-rational sets introduced in this paper and the sets accepted by Biichi’s*tree**automata*. ... Then it is proved that Nerode’s*theorem*cannot be extended to w-*tree**automata*. ...##
###
Interprocedural Dataflow Analysis over Weight Domains with Infinite Descending Chains
[article]

2009
*
arXiv
*
pre-print

We demonstrate how the reachability problem

arXiv:0901.0501v2
fatcat:vtk63shp3fc6tbiejtk3i2demy
*for**weighted*pushdown*automata*can be reduced to solving equations in the framework mentioned above and we describe a few applications to demonstrate its usability ... We study generalized fixed-point equations over idempotent semirings and provide an efficient algorithm*for*the detection whether a sequence of*Kleene's*iterations stabilizes after a finite number of steps ...*For*this purpose, so-called*weighted**automata*are employed. Definition 7 (*Weighted*W-Automaton). Let W = (P, Γ, ∆, S) be a pushdown system over a bounded semiring S. ...##
###
Page 9201 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

We give several basic constructions, including determinization, state minimization, and an analog of

*Kleene’s**theorem*. ... We also show that a basic result of the theory of Boolean decision diagrams (BDDs), namely that minimal ordered BDDs are unique, is a special case of the Myhill-Nerode*theorem**for*a class of*automata*on ...##
###
Page 5191 of Mathematical Reviews Vol. , Issue 84m
[page]

1984
*
Mathematical Reviews
*

The object of the

*theorem*, which extends*Kleene’s*first recursion*theorem*(the one referring to continuous functionals), is the determination of the least fixed points of a monotonic functional.” ... the coding used*for*the*trees*.” ...##
###
Probabilistic tree automata

1971
*
Information and Control
*

*Tree*

*Automata*which characterize Probabilistic Context Free Languages. ... It is quite natural to assign probabilities (or frequencies) to the sentences of a language to try to get some quantitative measure of "efficiency" of translators and grammars

*for*the language. ... The corresponding

*theorem*

*for*context free P grammars will later be proved using Probabilistic

*Tree*

*Automata*. ...

##
###
Probabilistic Tree Automata

1970
*
Proceedings of the second annual ACM symposium on Theory of computing - STOC '70
*

*Tree*

*Automata*which characterize Probabilistic Context Free Languages. ... It is quite natural to assign probabilities (or frequencies) to the sentences of a language to try to get some quantitative measure of "efficiency" of translators and grammars

*for*the language. ... The corresponding

*theorem*

*for*context free P grammars will later be proved using Probabilistic

*Tree*

*Automata*. ...

##
###
SEA: A Symbolic Environment for Automata Theory
[chapter]

2001
*
Lecture Notes in Computer Science
*

We here present the system SEA which integrates manipulations over boolean and multiplicity

doi:10.1007/3-540-45526-4_2
fatcat:aes6lyg6lze3tn4ox4i72csbde
*automata*. The system provides also self development facilities. ? Corresponding ... Sch utzenberger's classical*theorem*17, 8] asserts that rationnal series are exactly recognizable series. This is then an extension of*Kleene's*classical result 11] . ... Here,*for*each word w = a 1 a p 2 A , the coe cient hSjwi is the sum of the*weights*of paths labeled by a 1 a p , this*weight*being obtained by the product of input, output and edges*weights*of the path ...##
###
Adding Pebbles to Weighted Automata
[chapter]

2012
*
Lecture Notes in Computer Science
*

Schützenberger proved the equivalence between

doi:10.1007/978-3-642-31606-7_4
fatcat:e6lk5p6zavfxpi7juwjijeqes4
*weighted**automata*and*weighted*regular expressions, extending*Kleene's**theorem*. ... of*Kleene's**theorem*. ... Acknowledgements The authors would like to thank Benedikt Bollig and Jacques Sakarovitch*for*helpful discussions. ...##
###
Resource-Aware Automata and Games for Optimal Synthesis

2019
*
Electronic Proceedings in Theoretical Computer Science
*

amount of initial resources, respectively

doi:10.4204/eptcs.305.4
fatcat:7rvy2nbqcffa5phv6lwjdy3pjy
*for*winning a game with minimum initial resources. ... We consider quantitative notions of parity automaton and parity game aimed at modelling resource-aware behaviour, and study (memory-full) strategies*for*exhibiting accepting runs that require a minimum ... The existence of the nested fixpoint follows again by*Kleene's**theorem*. ...##
###
Weighted Specifications over Nested Words
[chapter]

2013
*
Lecture Notes in Computer Science
*

We introduce

doi:10.1007/978-3-642-37075-5_25
fatcat:ft275yydpzb7tobz3oguetgyvm
*weighted**automata*walking in nested words, possibly dropping/lifting (reusable) pebbles during the traversal. ... We prove that the evaluation problem*for*such*automata*can be done very efficiently if the number of pebble names is small, and we also consider the emptiness problem. ... In [18] , Sakarovitch gives a survey about different constructions establishing Schützenberger's*theorem*, namely*Kleene's**theorem**for**weighted*one-way*automata*over finite words. ...
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