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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
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

Nicolas Baudru, Louis-Marie Dando, Nathan Lhote, Benjamin Monmege, Pierre-Alain Reynier, Jean-Marc Talbot, Florin Manea, Alex Simpson
2022
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]

Akim Demaille, Alexandre Duret-Lutz, Sylvain Lombardy, Jacques Sakarovitch
2013 Lecture Notes in Computer Science  
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]

Akim Demaille, Alexandre Duret-Lutz, Sylvain Lombardy, Luca Saiu, Jacques Sakarovitch
2014 Lecture Notes in Computer Science  
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

Sylvain Lombardy, Yann Régis-Gianas, Jacques Sakarovitch
2004 Theoretical Computer Science  
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

Akim Demaille
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.  ... 
doi:10.7561/sacs.2017.2.137 fatcat:vmxawevesfbjrfp6gjckqvv2iq

Syntactic Monoids in a Category

Jiri Adamek, Stefan Milius, Henning Urbat, Marc Herbstritt
2015 Conference on Algebra and Coalgebra in Computer Science  
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]

Kuize Zhang
2022 arXiv   pre-print
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]

Hans-Peter Deifel, Stefan Milius, Lutz Schröder, Thorsten Wißmann
2019 arXiv   pre-print
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]

Jiri Adamek, Stefan Milius, Henning Urbat
2015 arXiv   pre-print
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]

Mikołaj Bojańczyk, Bartek Klin, Joshua Moerman
2021 arXiv   pre-print
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  
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]

Thorsten Wißmann, Hans-Peter Deifel, Stefan Milius, Lutz Schröder
2020 arXiv   pre-print
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]

Benedikt Bollig, Paul Gastin, Benjamin Monmege, Marc Zeitoun
2012 Lecture Notes in Computer Science  
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  
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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