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A Kleene Theorem for Weighted Tree Automata over Distributive Multioperator Monoids

2007
*
Theory of Computing Systems
*

As

doi:10.1007/s00224-007-9091-9
fatcat:jv476kwubbgvjjc6xqxwnlibsq
*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. ...##
###
Weighted Automata and Expressions over Pre-Rational Monoids
[article]

2021
*
arXiv
*
pre-print

As

arXiv:2110.12395v1
fatcat:zrv75vhvfnawfm7depmqwew6dq
*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. ...##
###
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]

2003
*
Lecture Notes in Computer Science
*

We sketch the proof of

doi:10.1007/978-3-540-45077-1_36
fatcat:tvhukjpiqrddtiiwmjysidoiui
*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*. ...##
###
Rational Transformations and a Kleene Theorem for Power Series over Rational Monoids
[chapter]

2011
*
Lecture Notes in Computer Science
*

Using these results we prove

doi:10.1007/978-3-642-24897-9_5
fatcat:ytxbohsbtjbplcrs6z4ymdtgci
*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. ...##
###
Relation-Algebraic Verification of Prim's Minimum Spanning Tree Algorithm
[chapter]

2016
*
Lecture Notes in Computer Science
*

We formally prove the correctness of Prim's algorithm

doi:10.1007/978-3-319-46750-4_4
fatcat:7mcpqvvxgzerzfbyenz7usw4lu
*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. ...##
###
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

doi:10.14232/actacyb.23.1.2017.23
fatcat:tpgf7t2sgfdsriwvebwyce3lr4
*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. ...##
###
A Kleene Theorem for Nominal Automata

2019
*
International Colloquium on Automata, Languages and Programming
*

In this paper, we present

doi:10.4230/lipics.icalp.2019.107
dblp:conf/icalp/Brunet019
fatcat:n77xp2w4lff6hcmvt3oqzsbhpa
*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}). ...##
###
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]

2013
*
Lecture Notes in Computer Science
*

These can be used

doi:10.1007/978-3-642-37075-5_25
fatcat:ft275yydpzb7tobz3oguetgyvm
*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., ...##
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An Algebraic Approach to Energy Problems II — The Algebra of Energy Functions

2017
*
Acta Cybernetica
*

An (extended) energy function is

doi:10.14232/actacyb.23.1.2017.14
fatcat:5m5vr6phhfb4lhpaghgb42nn2e
*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] . ...##
###
Two modes of recognition: algebra, coalgebra, and languages
[article]

2019
*
arXiv
*
pre-print

We instantiate our framework on classical non-deterministic

arXiv:1906.05573v1
fatcat:mhmaw32q7feptnlritfetni33u
*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. ...##
###
Stone Relation Algebras
[chapter]

2017
*
Lecture Notes in Computer Science
*

Many

doi:10.1007/978-3-319-57418-9_8
fatcat:shgrhxozrze2xnkhxh7z3ienia
*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. ...##
###
A Probabilistic Kleene Theorem
[chapter]

2012
*
Lecture Notes in Computer Science
*

We provide

doi:10.1007/978-3-642-33386-6_31
fatcat:m4lnnln4gngxjmtqnsfs3yblz4
*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). ...
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