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Weighted Automata and Expressions over Pre-Rational Monoids
[article]
2021
arXiv
pre-print
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In the present work, we aim at combining both research directions 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 ...
arXiv:2110.12395v1
fatcat:zrv75vhvfnawfm7depmqwew6dq
Weighted Automata and Expressions over Pre-Rational Monoids
2022
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In the present work, we aim at combining both research directions 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 ...
doi:10.4230/lipics.csl.2022.6
fatcat:kgvwm7wtwrg5vm7wq2gsli3rvm
Implementation Concepts in Vaucanson 2
[chapter]
2013
Lecture Notes in Computer Science
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Vaucanson is an open source C ++ platform dedicated to the computation with finite 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 ...
doi:10.1007/978-3-642-39274-0_12
fatcat:fnjphcqlnfa4hfwzktsurgrbvm
A Type System for Weighted Automata and Rational Expressions
[chapter]
2014
Lecture Notes in Computer Science
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We present a type system for 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. ...
doi:10.1007/978-3-319-08846-4_12
fatcat:wchuvxcyejgoxptg4rtpyqwkzm
Introducing VAUCANSON
2004
Theoretical Computer Science
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shows how VAUCANSON allows to program algorithms on 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 ...
doi:10.1016/j.tcs.2004.07.007
fatcat:bakboytqufda5mgl5qq43pavo4
Derived-Term Automata of Multitape Expressions with Composition
2017
Scientific Annals of Computer Science
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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. ...
doi:10.7561/sacs.2017.2.137
fatcat:vmxawevesfbjrfp6gjckqvv2iq
Syntactic Monoids in a Category
2015
Conference on Algebra and Coalgebra in Computer Science
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Assuming that D is a commutative variety of algebras, we prove that the syntactic D-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. ...
doi:10.4230/lipics.calco.2015.1
dblp:conf/calco/AdamekMU15
fatcat:cvyl4vu5qnhmnfqrh3upjfxto4
Detectability of labeled weighted automata over monoids
[article]
2022
arXiv
pre-print
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In this paper, we for the first time obtain characterization of four fundamental notions of detectability for general labeled 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. ...
arXiv:2006.14164v7
fatcat:zrp4dihvazhrjolcfkfqbcpbjy
Generic Partition Refinement and Weighted Tree Automata
[article]
2019
arXiv
pre-print
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2019 pre-print arXiv:1811.08850v2 fatcat:3k5dhn3pmvfdzj4zafv5w3mpw4Other Versions
In the present work, we refine the run time analysis of our algorithm to cover additional instances, notably 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. ...
arXiv:1811.08850v3
fatcat:k5bpbbcjljde5fxehpnsodcmna
Syntactic Monoids in a Category
[article]
2015
arXiv
pre-print
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Assuming that D is an entropic variety of algebras, we prove that the syntactic D-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. ...
arXiv:1504.02694v2
fatcat:2cgebp2atzhh7jg367iqdkuk3e
Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2104.02438v1 fatcat:ozivgs46yjb3dbf23crxn2l2yi
Using this theory, we give a decision procedure for equivalence of 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 ...
arXiv:2104.02438v2
fatcat:z2x4rcx7xnedlcyilfa2aaaqwe
Page 5102 of Mathematical Reviews Vol. , Issue 2000g
[page]
2000
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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. ...
From Generic Partition Refinement to Weighted Tree Automata Minimization
[article]
2020
arXiv
pre-print
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2020 pre-print arXiv:2004.01250v2 fatcat:uz62a3gw5reydfdqbrdrswhgomOther Versions
In the present work, we refine the run time analysis of our algorithm to cover additional instances, notably 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. ...
arXiv:2004.01250v4
fatcat:4yooh6jlgjhinauj4gcvu7wtaq
A Probabilistic Kleene Theorem
[chapter]
2012
Lecture Notes in Computer Science
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We prove that probabilistic 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. ...
doi:10.1007/978-3-642-33386-6_31
fatcat:m4lnnln4gngxjmtqnsfs3yblz4
Subject index volumes 1–200
1999
Theoretical Computer Science
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Cardelli 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 ...
doi:10.1016/s0304-3975(98)00319-3
fatcat:s22ud3iiqjht7lfbtc3zctk7zm
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