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

2021
*
arXiv
*
pre-print

In the present work, we aim at combining both research directions

arXiv:2110.12395v1
fatcat:zrv75vhvfnawfm7depmqwew6dq
*and*consider*weighted*extensions of*automata**and**expressions**over*a class of*monoids*that we call*pre*-*rational*, generalising both the free ... The Kleene theorem establishes a fundamental link between*automata**and**expressions**over*the free*monoid*. Numerous generalisations of this result exist in the literature. ... A Kleene-Like Theorem Our main result is the following Kleene-like theorem, stating the constructive equivalence between*expressions**and**automata**over*a*pre*-*rational**monoid**and**weighted**over*a*rationally*...##
###
Weighted Automata and Expressions over Pre-Rational Monoids

2022

In the present work, we aim at combining both research directions

doi:10.4230/lipics.csl.2022.6
fatcat:kgvwm7wtwrg5vm7wq2gsli3rvm
*and*consider*weighted*extensions of*automata**and**expressions**over*a class of*monoids*that we call*pre*-*rational*, generalising both the free ... The Kleene theorem establishes a fundamental link between*automata**and**expressions**over*the free*monoid*. ... A Kleene-Like Theorem Our main result is the following Kleene-like theorem, stating the constructive equivalence between*expressions**and**automata**over*a*pre*-*rational**monoid**and**weighted**over*a*rationally*...##
###
Implementation Concepts in Vaucanson 2
[chapter]

2013
*
Lecture Notes in Computer Science
*

Vaucanson is an open source C ++ platform dedicated to the computation with finite

doi:10.1007/978-3-642-39274-0_12
fatcat:fnjphcqlnfa4hfwzktsurgrbvm
*weighted**automata*. It is generic: it allows to write algorithms that apply on a wide set of mathematical objects. ... Initiated ten years ago, several shortcomings were discovered along the years, especially problems related to code complexity*and*obfuscation as well as performance issues. ... For instance, if M is a free*monoid**over*a finite alphabet A, the*weighted*automaton is an automaton*over*finite words; if M is a product A * × B * of two free*monoids*(A*and*B are finite alphabets), then ...##
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A Type System for Weighted Automata and Rational Expressions
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present a type system for

doi:10.1007/978-3-319-08846-4_12
fatcat:wchuvxcyejgoxptg4rtpyqwkzm
*automata**and**rational**expressions*,*expressive*enough to encompass*weighted**automata**and*transducers in a single coherent formalism. ... The system allows to*express*useful properties about the applicability of operations including binary heterogeneous functions*over**automata*. ... Acknowledgements We wish to thank the anonymous reviewers for their helpful*and*constructive suggestions. ...##
###
Introducing VAUCANSON

2004
*
Theoretical Computer Science
*

shows how VAUCANSON allows to program algorithms on

doi:10.1016/j.tcs.2004.07.007
fatcat:bakboytqufda5mgl5qq43pavo4
*automata*in a way which is very close to the mathematical*expression*of the algorithm*and*finally explains the main choices of the programming design ... This paper reports on a new software platform called VAUCANSON*and*dedicated to the computation with*automata**and*transducers. ... From*automata*to*expressions**and*back Almost all systems computing with*automata*implement Kleene's Theorem, that is compute a*rational*(regular)*expression*equivalent to a given automaton*and*conversely ...##
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Derived-Term Automata of Multitape Expressions with Composition

2017
*
Scientific Annals of Computer Science
*

*Rational*

*expressions*are powerful tools to define

*automata*, but often restricted to single-tape

*automata*. ... Series A (formal power) series

*over*M with

*weights*(or multiplicities) in K is a map from M to K. The

*weight*of m ∈ M in a series s is denoted s(m). ... To ensure semantic soundness, we need M to be graded

*monoid*

*and*K to be a strong topological semiring. We will need a property of star based on the following result. ...

##
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Syntactic Monoids in a Category

2015
*
Conference on Algebra and Coalgebra in Computer Science
*

Assuming that D is a commutative variety of algebras, we prove that the syntactic D-

doi:10.4230/lipics.calco.2015.1
dblp:conf/calco/AdamekMU15
fatcat:cvyl4vu5qnhmnfqrh3upjfxto4
*monoid*of a language L can be constructed as a quotient of a free D-*monoid*modulo the syntactic congruence of L,*and*... This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic*monoids*of Rabin*and*Scott (D " sets), the syntactic semirings of Polák (D ... More generally,*automata*in D " ModpSq with X " ΨX 0*and*Y " S are S-*weighted**automata*. ...##
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Detectability of labeled weighted automata over monoids
[article]

2022
*
arXiv
*
pre-print

In this paper, we for the first time obtain characterization of four fundamental notions of detectability for general labeled

arXiv:2006.14164v7
fatcat:zrp4dihvazhrjolcfkfqbcpbjy
*weighted**automata**over**monoids*(denoted by 𝒜^𝔐 for short), where the four ... Thirdly, we prove that for a labeled*weighted*automaton*over**monoid*(ℚ^k,+) (denoted by 𝒜^ℚ^k), its concurrent composition, observer,*and*detector can be computed in NP, 2-EXPTIME,*and*2-EXPTIME, respectively ...*and*labeled*weighted**automata**over**monoids*. ...##
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Generic Partition Refinement and Weighted Tree Automata
[article]

2019
*
arXiv
*
pre-print

In the present work, we refine the run time analysis of our algorithm to cover additional instances, notably

arXiv:1811.08850v3
fatcat:k5bpbbcjljde5fxehpnsodcmna
*weighted**automata**and*, more generally,*weighted*tree*automata*. ... For*weights*in a cancellative*monoid*we match,*and*for non-cancellative*monoids*such as (the additive*monoid*of) the tropical semiring even substantially improve, the asymptotic run time of the best known ... On*weighted*tree*automata*with n states, k transitions*and*rank r*over*a cancellative*monoid*, our algorithm runs in time O((rk +n)·log(k +n))·r. ...##
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Syntactic Monoids in a Category
[article]

2015
*
arXiv
*
pre-print

Assuming that D is an entropic variety of algebras, we prove that the syntactic D-

arXiv:1504.02694v2
fatcat:2cgebp2atzhh7jg367iqdkuk3e
*monoid*of a language L can be constructed as a quotient of a free D-*monoid*modulo the syntactic congruence of L,*and*that ... This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic*monoids*of Rabin*and*Scott (D = sets), the syntactic semirings of Polak (D ... More generally,*automata*in D " ModpSq with X " ΨX 0*and*Y " S are S-*weighted**automata*. ...##
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Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
[article]

2021
*
arXiv
*
pre-print

Using this theory, we give a decision procedure for equivalence of

arXiv:2104.02438v2
fatcat:z2x4rcx7xnedlcyilfa2aaaqwe
*weighted*register*automata*, which are the common generalization of*weighted**automata**and*register*automata*for infinite alphabets. ... atoms,*and*not just equality; (b) the complexity is exponentially better;*and*(c) we allow*automata*with guessing. ... The algorithm is a simple reduction to equivalence of*weighted**automata*: a nondeterministic automaton can be viewed as a*weighted*automaton*over*the field of*rational*numbers, such that the*weight*of a ...##
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Page 5102 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

A

*pre*- vious characterization, valid when the semiring of coefficients is the field of*rational*numbers, is generalized to arbitrary commu- tative semirings. ... An e-free substitution is a*monoid*morphism y from X* to the power set of Y* such that y(.x) is finite*and*does not include e for any given x € XY. ...##
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From Generic Partition Refinement to Weighted Tree Automata Minimization
[article]

2020
*
arXiv
*
pre-print

In the present work, we refine the run time analysis of our algorithm to cover additional instances, notably

arXiv:2004.01250v4
fatcat:4yooh6jlgjhinauj4gcvu7wtaq
*weighted**automata**and*, more generally,*weighted*tree*automata*. ... For*weights*in a cancellative*monoid*we match,*and*for non-cancellative*monoids*such as (the additive*monoid*of) the tropical semiring even substantially improve, the asymptotic run time of the best known ...*over*non-cancellative*monoids*. ...##
###
A Probabilistic Kleene Theorem
[chapter]

2012
*
Lecture Notes in Computer Science
*

We prove that probabilistic

doi:10.1007/978-3-642-33386-6_31
fatcat:m4lnnln4gngxjmtqnsfs3yblz4
*expressions**and*probabilistic*automata*are*expressively*equivalent. ... 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. ... Introduction Kleene's Theorem states the equivalence of*rational**and*recognizable languages in the free*monoids*. ...##
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Subject index volumes 1–200

1999
*
Theoretical Computer Science
*

Cardelli

doi:10.1016/s0304-3975(98)00319-3
fatcat:s22ud3iiqjht7lfbtc3zctk7zm
*and*-, 3299 Weibel, Baunwall, Bertelsen*and*-, 952*weight*function, 1205, 2492 sequence, 1735*weight*-balanced trees, 240 well founded decomposition, mechanism of -, 595 well-balanced trees, 1735 ...*expression*, 807 2300,2630,33 lo,3799 sets, 1838 continuous semantics for -, 474 unambiguous modeling -, 2630 reduction of*monoids*, 987 semantics for -, 474 reductions of*monoids*, 987 theory ...
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