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

Christian Pech
2003 Lecture Notes in Computer Science  
We sketch the proof of a Kleene-type 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 .  ... 
doi:10.1007/978-3-540-45077-1_36 fatcat:tvhukjpiqrddtiiwmjysidoiui

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]

Ina Fichtner, Christian Mathissen
2011 Lecture Notes in Computer Science  
Using these results we prove a Kleene-Schützenberger 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.  ... 
doi:10.1007/978-3-642-24897-9_5 fatcat:ytxbohsbtjbplcrs6z4ymdtgci

Schützenberger's theorem on formal power series follows from Kleene's theorem

Dietrich Kuske
2008 Theoretical Computer Science  
We derive Schützenberger's characterisation of the set of recognizable formal power series as a formal corollary from 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.  ... 
doi:10.1016/j.tcs.2008.04.041 fatcat:nz5dcvsq25bfrn7lzibw5m542u

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]

Morten Kühnrich, Stefan Schwoon, Jiří Srba, Stefan Kiefer
2009 arXiv   pre-print
We demonstrate how the reachability problem 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.  ... 
arXiv:0901.0501v2 fatcat:vtk63shp3fc6tbiejtk3i2demy

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

Clarence A. Ellis
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.  ... 
doi:10.1016/s0019-9958(71)90673-5 fatcat:2h4345tqwfbpdprpuerxgozpse

Probabilistic Tree Automata

Clarence A. Ellis
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.  ... 
doi:10.1145/800161.805165 dblp:conf/stoc/Ellis70 fatcat:34ac7v3dpvforcnjsh63zqolyu

SEA: A Symbolic Environment for Automata Theory [chapter]

Philippe Andary, Pascal Caron, Jean-Marc Champarnaud, Gérard Duchamp, Marianne Flouret, Éric Laugerotte
2001 Lecture Notes in Computer Science  
We here present the system SEA which integrates manipulations over boolean and multiplicity 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  ... 
doi:10.1007/3-540-45526-4_2 fatcat:aes6lyg6lze3tn4ox4i72csbde

Adding Pebbles to Weighted Automata [chapter]

Paul Gastin, Benjamin Monmege
2012 Lecture Notes in Computer Science  
Schützenberger proved the equivalence between 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.  ... 
doi:10.1007/978-3-642-31606-7_4 fatcat:e6lk5p6zavfxpi7juwjijeqes4

Resource-Aware Automata and Games for Optimal Synthesis

Corina Cîrstea
2019 Electronic Proceedings in Theoretical Computer Science  
amount of initial resources, respectively 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.  ... 
doi:10.4204/eptcs.305.4 fatcat:7rvy2nbqcffa5phv6lwjdy3pjy

Weighted Specifications over Nested Words [chapter]

Benedikt Bollig, Paul Gastin, Benjamin Monmege
2013 Lecture Notes in Computer Science  
We introduce 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.  ... 
doi:10.1007/978-3-642-37075-5_25 fatcat:ft275yydpzb7tobz3oguetgyvm
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