Filters








472 Hits in 3.3 sec

A Kleene Theorem for Weighted Tree Automata over Distributive Multioperator Monoids

Zoltán Fülöp, Andreas Maletti, Heiko Vogler
2007 Theory of Computing Systems  
As a consequence of this, Kleene's theorem for weighted tree automata over arbitrary, i.e., not necessarily commutative, semirings is derived.  ...  Kleene's theorem on the equivalence of recognizability and rationality for formal tree series over distributive multioperator monoids is proved.  ...  Weighted tree automata over M-monoids In this section we dene the concept of weighted tree automata with variables over some M-monoid.  ... 
doi:10.1007/s00224-007-9091-9 fatcat:jv476kwubbgvjjc6xqxwnlibsq

Weighted Automata and Expressions over Pre-Rational Monoids [article]

Nicolas Baudru, Louis-Marie Dando, Nathan Lhote, Benjamin Monmege, Pierre-Alain Reynier, Jean-Marc Talbot
2021 arXiv   pre-print
As a corollary, we obtain a class of expressions equivalent to weighted two-way automata, as well as one for tree-walking automata.  ...  Our main result is thus a generalisation of the Kleene theorem for pre-rational monoids and rationally additive semirings.  ...  We prove in Section 5 a Kleene-like theorem stating that weighted automata and weighted expressions define the same series. 4.  ... 
arXiv:2110.12395v1 fatcat:zrv75vhvfnawfm7depmqwew6dq

Page 5646 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
Summary: “In this paper we propose a notion of weak bisimula- tion for a class of weighted automata with unobservable transitions where weights are taken from an idempotent semiring.  ...  The proposed bisimulation is a natural extension of Milner’s well- known weak bisimulation for untimed automata (i.e., weighted automata over the Boolean semiring).  ... 

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

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.  ...  Our proof will be a reduction to the result of Schützenberger, i.e. to the Kleene Theorem for formal power series over free monoids.  ...  We will generalize the results mentioned above and show that a Kleene Theorem holds true if the underlying semiring is a principal ideal domain or a locally finite semifield.  ... 
doi:10.1007/978-3-642-24897-9_5 fatcat:ytxbohsbtjbplcrs6z4ymdtgci

Relation-Algebraic Verification of Prim's Minimum Spanning Tree Algorithm [chapter]

Walter Guttmann
2016 Lecture Notes in Computer Science  
We formally prove the correctness of Prim's algorithm for computing minimum spanning trees.  ...  Only a small part needs additional operations, for which we introduce a new algebraic structure.  ...  I thank Peter Höfner and Bernhard Möller for discussing alternative approaches to minimum spanning trees in Kleene algebras.  ... 
doi:10.1007/978-3-319-46750-4_4 fatcat:7mcpqvvxgzerzfbyenz7usw4lu

Page 9201 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
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  ...  {For the entire collection see MR 2004j:68011.} 2004k:68097 68Q45 68W0S5 92D15 Mohri, Mehryar (1-ATT3; Florham Park, NJ) Edit-distance of weighted automata: general definitions and algorithms.  ... 

Publication List of Zoltán Ésik

2017 Acta Cybernetica  
Journal of Automata, Languages and Combinatorics, 6(4):427-436, 2001. [64] ZoltánÉsik and Werner Kuich. A Kleene theorem for Lindenmayerian al- gebraic power series.  ...  A variety theorem for trees and theories. Publ. Math. Debrecen, 54:711-762, 1999. [72] ZoltánÉsik and Michael Bertol. Nonfinite axiomatizability of the equational theory of shuffle.  ... 
doi:10.14232/actacyb.23.1.2017.23 fatcat:tpgf7t2sgfdsriwvebwyce3lr4

A Kleene Theorem for Nominal Automata

Paul Brunet, Alexandra Silva, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
In this paper, we present a Kleene theorem for nominal automata by providing a syntax to denote regular nominal languages.  ...  Nominal automata are a widely studied class of automata designed to recognise languages over infinite alphabets.  ...  I C A L P 2 0 1 9 107:6 A Kleene Theorem for Nominal Automata Proof. Let Σ, ∆ be two tractable alphabets, and Σ := (Σ ∪ {ε}) × (Γ ∪ {ε}).  ... 
doi:10.4230/lipics.icalp.2019.107 dblp:conf/icalp/Brunet019 fatcat:n77xp2w4lff6hcmvt3oqzsbhpa

Page 3869 of Mathematical Reviews Vol. , Issue 83i [page]

1983 Mathematical Reviews  
The regular L-fuzzy events over X are characterized by a Kleene theorem in strict analogy to the usual case. In a more general setting the theorem was proved by E. S.  ...  Authors’ summary: “We present several parallel algorithms for the problem of finding shortest paths from a specified vertex (called the source) to all others in a weighted directed graph.  ... 

Weighted Specifications over Nested Words [chapter]

Benedikt Bollig, Paul Gastin, Benjamin Monmege
2013 Lecture Notes in Computer Science  
These can be used for XML documents or recursive programs: for instance, counting how often a given entry occurs in an XML document, or computing the memory required for a recursive program execution.  ...  We introduce weighted automata walking in nested words, possibly dropping/lifting (reusable) pebbles during the traversal.  ...  We extend results over words stated in [12] , namely a Kleene-Schützenberger theorem showing correspondence between weighted expressions with pebbles and layered weighted automata with pebbles (i.e.,  ... 
doi:10.1007/978-3-642-37075-5_25 fatcat:ft275yydpzb7tobz3oguetgyvm

An Algebraic Approach to Energy Problems II — The Algebra of Energy Functions

Zoltán Ésik, Uli Fahrenberg, Axel Legay, Karin Quaas
2017 Acta Cybernetica  
An (extended) energy function is a mapping f : [0, ∞] ⊥ → [0, ∞] ⊥ , for which ⊥f = ⊥ and yf ≥ xf + y − x ( * )  ...  This permits to solve energy problems in energy automata in a generic, algebraic way.  ...  For completeness we also mention a Kleene theorem for the Büchi automata introduced above, which is a direct consequence of the Kleene theorem for Conway semiring-semimodule pairs, cf. [29, 32] .  ... 
doi:10.14232/actacyb.23.1.2017.14 fatcat:5m5vr6phhfb4lhpaghgb42nn2e

Two modes of recognition: algebra, coalgebra, and languages [article]

Tomasz Brengos, Marco Peressotti
2019 arXiv   pre-print
We instantiate our framework on classical non-deterministic automata, tree automata, fuzzy automata and weighted automata.  ...  Moreover, we state a Kleene-like theorem characterising the regular morphisms category in terms of the smallest subcategory closed under certain operations.  ...  This result is known under the name of Kleene theorem for regular languages.  ... 
arXiv:1906.05573v1 fatcat:mhmaw32q7feptnlritfetni33u

Stone Relation Algebras [chapter]

Walter Guttmann
2017 Lecture Notes in Computer Science  
Many theorems of relation algebras generalise with no or small changes. Weighted graphs represented as matrices over extended real numbers form an instance.  ...  We study a generalisation of relation algebras in which the underlying Boolean algebra structure is replaced with a Stone algebra.  ...  I thank Georg Struth and the anonymous referees for pointing out related work and for other helpful comments.  ... 
doi:10.1007/978-3-319-57418-9_8 fatcat:shgrhxozrze2xnkhxh7z3ienia

A Probabilistic Kleene Theorem [chapter]

Benedikt Bollig, Paul Gastin, Benjamin Monmege, Marc Zeitoun
2012 Lecture Notes in Computer Science  
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.  ...  This allows them to derive algebraic expressions and a corresponding Kleene Theorem, as well as full axiomatizations for many of those (and even for weighted automata over arbitrary semirings).  ... 
doi:10.1007/978-3-642-33386-6_31 fatcat:m4lnnln4gngxjmtqnsfs3yblz4
« Previous Showing results 1 — 15 out of 472 results