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Unambiguity in Automata Theory
[chapter]

2015
*
Lecture Notes in Computer Science
*

In this paper, we will investigate the nature of

doi:10.1007/978-3-319-19225-3_1
fatcat:wncinjdfmfc6ne4u4pkfy7gjoe
*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. ...##
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On a zeta function associated with automata and codes

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

doi:10.1016/j.tcs.2007.04.004
fatcat:dqrgwdisbvfrjmx6xlyagtzgsa
*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 . ...##
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Weighted Automata and Expressions over Pre-Rational Monoids
[article]

2021
*
arXiv
*
pre-print

As a corollary, we obtain a class of expressions equivalent to weighted two-way

arXiv:2110.12395v1
fatcat:zrv75vhvfnawfm7depmqwew6dq
*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] . ...##
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Codes, unambiguous automata and sofic systems

2006
*
Theoretical Computer Science
*

We study the relationship between codes and

doi:10.1016/j.tcs.2006.01.043
fatcat:lygvobxrcfevbb7bhvqkc2qgm4
*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. ...##
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Page 4677 of Mathematical Reviews Vol. , Issue 83k
[page]

1983
*
Mathematical Reviews
*

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*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. ...##
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Ambiguity through the lens of measure theory
[article]

2022
*
arXiv
*
pre-print

In this paper, we establish a strong link between the ambiguity for finite

arXiv:2011.10534v4
fatcat:7udbeo5nfzasbi3n4ujzl3m5ba
*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*. ...##
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Synchronization of Regular Automata
[chapter]

2009
*
Lecture Notes in Computer Science
*

Functional graph grammars are finite devices which generate the class of regular

doi:10.1007/978-3-642-03816-7_2
fatcat:l5ozq5azcvbwpeqghgfo5uswji
*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*. ...##
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Complete Codes in a Sofic Shift
[chapter]

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

doi:10.1007/11672142_9
fatcat:uzq2i4knwrhztcglyt6pw2qdbq
*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. ...##
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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. ...##
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Unambiguously coded shifts
[article]

2022
*
arXiv
*
pre-print

We give several constructions which allow

arXiv:2103.01012v4
fatcat:fwqtpunyszbz5jef65ua64ptei
*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. ...##
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Weighted automata and multi-valued logics over arbitrary bounded lattices

2012
*
Theoretical Computer Science
*

We show that L-weighted

doi:10.1016/j.tcs.2011.11.008
fatcat:hfmvkyxq3jab3pnwhxcaqfxa3q
*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. ...##
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Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
[article]

2021
*
arXiv
*
pre-print

As a special case, we can decide, with the same complexity, language equivalence for

arXiv:2104.02438v2
fatcat:z2x4rcx7xnedlcyilfa2aaaqwe
*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. ...##
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Preservation of normality by unambiguous transducers
[article]

2020
*
arXiv
*
pre-print

We consider finite state non-deterministic but

arXiv:2006.00891v3
fatcat:j7o6pohyjfcbhnx7kuvn7c7zwu
*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 . ...##
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Regular Ideal Languages and Their Boolean Combinations
[article]

2012
*
arXiv
*
pre-print

Right ideals over finite

arXiv:1102.5013v3
fatcat:dtsq7y76ofccvdmtckl5y5asw4
*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*. ...##
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Completing codes in a sofic shift

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

doi:10.1016/j.tcs.2009.07.023
fatcat:mbrdjpmpmrf5ngq3r4lqyu5zyu
*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. ...
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