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Unambiguity in Automata Theory [chapter]

Thomas Colcombet
2015 Lecture Notes in Computer Science  
In this paper, we will investigate the nature of unambiguity in automata theory, presenting the cases of standard finite words up to infinite trees, as well as data-words and tropical automata.  ...  One possible way (among others) to relax this notion is to consider unambiguous machines: non-deterministic machines that have at most one accepting run on each input.  ...  Acknowledgment I am really grateful to Jean-Éric Pin, Gabriele Puppis and Michał Skrypczak for their precious help and their discussions on the topic.  ... 
doi:10.1007/978-3-319-19225-3_1 fatcat:wncinjdfmfc6ne4u4pkfy7gjoe

On a zeta function associated with automata and codes

Sylvain Lavallée, Christophe Reutenauer
2007 Theoretical Computer Science  
The zeta function of a finite automaton A is exp{ ∞ n=1 a n z n n }, where a n is the number of bi-infinite paths in A labelled by a bi-infinite word of period n.  ...  Let A be an unambiguous automaton. One associates with it two dynamical systems. Let X (resp. Y ) be the set of bi-infinite paths in A (resp. of bi-infinite words which are labels of such paths).  ...  A bi-infinite word is an element of A Z .  ... 
doi:10.1016/j.tcs.2007.04.004 fatcat:dqrgwdisbvfrjmx6xlyagtzgsa

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.  ...  The presence of idempotent elements in these pre-rational monoids leads in the weighted setting to consider infinite sums.  ...  These expressions have also been extended to run on infinite words [7] .  ... 
arXiv:2110.12395v1 fatcat:zrv75vhvfnawfm7depmqwew6dq

Codes, unambiguous automata and sofic systems

Marie-Pierre Béal, Dominique Perrin
2006 Theoretical Computer Science  
We study the relationship between codes and unambiguous automata inside a sofic system.  ...  We show that a recognizable set is a code in a sofic system if and only if a particular automaton associated to the set and the shift is unambiguous.  ...  Acknowledgments We would like to thank Christophe Reutenauer and the anonymous referees for useful comments on an earlier version.  ... 
doi:10.1016/j.tcs.2006.01.043 fatcat:lygvobxrcfevbb7bhvqkc2qgm4

Page 4677 of Mathematical Reviews Vol. , Issue 83k [page]

1983 Mathematical Reviews  
re of ld 8 3S o mae raa ~~ —= bi Te ad -_ 4677 68D whether a nondeterministic finite transducer (ndft) is single-valued; (2) whether an ndft is unambiguous; (3) whether two single-valued transducers are  ...  Wiodzimierz 83k:68045 Determinancy of sinking automata on infinite trees and inequalities between various Rabin’s pair indices. Inform. Process. Lett. 15 (1982), no. 4, 159-163.  ... 

Ambiguity through the lens of measure theory [article]

Olivier Carton
2022 arXiv   pre-print
In this paper, we establish a strong link between the ambiguity for finite words of a B\"uchi automaton and the ambiguity for infinite words of the same automaton.  ...  More precisely, we show that such an automaton is unambiguous, in the sense that no finite word labels two runs with the same starting state and the same ending state if and only if for each state, the  ...  The polynomial time algorithm for the containment of unambiguous automata accepting finite words in [21] is based on a clever counting argument which cannot easily be adapted to infinite words.  ... 
arXiv:2011.10534v4 fatcat:7udbeo5nfzasbi3n4ujzl3m5ba

Synchronization of Regular Automata [chapter]

Didier Caucal
2009 Lecture Notes in Computer Science  
Functional graph grammars are finite devices which generate the class of regular automata.  ...  When the synchronizing automaton is unambiguous, the class of its synchronized languages forms an effective boolean algebra lying between the classes of regular languages and unambiguous context-free languages  ...  Thus R and ≺R≻ are bi-synchronized, and ≺R≻ is unambiguous when R is unambiguous.  ... 
doi:10.1007/978-3-642-03816-7_2 fatcat:l5ozq5azcvbwpeqghgfo5uswji

Complete Codes in a Sofic Shift [chapter]

Marie-Pierre Béal, Dominique Perrin
2006 Lecture Notes in Computer Science  
We define a code in a sofic shift as a set of blocks of symbols of the shift such that any block of the shift has at most one decomposition in code words.  ...  It is maximal if it is not strictly included in another one. Such a code is complete in the sofic shift if any block of the shift occurs within some concatenation of code words.  ...  We denote by A * the set of finite words, by A + the set of nonempty finite words, and by A Z the set of bi-infinite words on A.  ... 
doi:10.1007/11672142_9 fatcat:uzq2i4knwrhztcglyt6pw2qdbq

Page 2817 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
Summary: “In this paper we are interested in the bi-infinite words and mainly in the bi-infinite power of languages of finite words.  ...  Summary: “We present a simple parallel algorithm recognizing unambiguous context-free languages on a CREW PRAM in time log” n with only n> processors.  ... 

Unambiguously coded shifts [article]

Marie-Pierre Béal and Dominique Perrin and Antonio Restivo
2022 arXiv   pre-print
We give several constructions which allow one to represent a coded system as a strongly unambiguous one.  ...  An automaton is strongly unambiguous if the labelling of bi-infinite paths is injective, that is, it has at most one bi-infinite path with a given bi-infinite label.  ...  It is not strongly unambiguous because there are two bi-infinite paths labeled with letters b.  ... 
arXiv:2103.01012v4 fatcat:fwqtpunyszbz5jef65ua64ptei

Weighted automata and multi-valued logics over arbitrary bounded lattices

Manfred Droste, Heiko Vogler
2012 Theoretical Computer Science  
We show that L-weighted automata, L-rational series, and L-valued monadic second order logic have the same expressive power, for any bounded lattice L and for finite and infinite words.  ...  This extends classical results of Kleene, Büchi-Elgot-Trakhtenbrot, and others to arbitrary bounded lattices, without any distributivity assumption that is fundamental in the theory of weighted automata  ...  Therefore here we also define Büchi and Muller automata acting on infinite words and with weights in a given bounded lattice L.  ... 
doi:10.1016/j.tcs.2011.11.008 fatcat:hfmvkyxq3jab3pnwhxcaqfxa3q

Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata [article]

Mikołaj Bojańczyk, Bartek Klin, Joshua Moerman
2021 arXiv   pre-print
As a special case, we can decide, with the same complexity, language equivalence for unambiguous register automata, which improves previous results in three ways: (a) we allow for order comparisons on  ...  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.  ...  For unambiguous automata, the number of accepting runs is either zero or one, and hence two unambiguous automata accept the same words if and only if the corresponding weighted automata are equivalent.  ... 
arXiv:2104.02438v2 fatcat:z2x4rcx7xnedlcyilfa2aaaqwe

Preservation of normality by unambiguous transducers [article]

Olivier Carton
2020 arXiv   pre-print
We consider finite state non-deterministic but unambiguous transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality of sequences of symbols.  ...  We provide an algorithm that decides in cubic time whether a unambiguous transducer preserves normality.  ...  By definition, deterministic automata are unambiguous but they are not the only ones as it is shown by Figure 1 .  ... 
arXiv:2006.00891v3 fatcat:j7o6pohyjfcbhnx7kuvn7c7zwu

Regular Ideal Languages and Their Boolean Combinations [article]

Franz Jahn, Manfred Kufleitner, Alexander Lauser
2012 arXiv   pre-print
Right ideals over finite words resemble the open sets in the Cantor topology over infinite words.  ...  In the main part of this paper we consider the following deterministic one-way automaton models: unions of flip automata, weak automata, and Staiger-Wagner automata.  ...  Introduction The Cantor topology over infinite words is an important concept for classifying languages over infinite words.  ... 
arXiv:1102.5013v3 fatcat:dtsq7y76ofccvdmtckl5y5asw4

Completing codes in a sofic shift

Marie-Pierre Béal, Dominique Perrin
2009 Theoretical Computer Science  
We define a code in a sofic shift as a set of blocks of symbols of the shift such that any block of the shift has at most one decomposition into code words.  ...  It is maximal if it is not strictly included in another one. Such a code is complete in the sofic shift if any block of the shift occurs within some concatenation of code words.  ...  We denote by A * the set of finite words, by A + the set of nonempty finite words, and by A Z the set of bi-infinite words on A.  ... 
doi:10.1016/j.tcs.2009.07.023 fatcat:mbrdjpmpmrf5ngq3r4lqyu5zyu
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