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Unambiguity in Automata Theory
[chapter]
2015
Lecture Notes in Computer Science
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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
2007
Theoretical Computer Science
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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]
2021
arXiv
pre-print
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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
2006
Theoretical Computer Science
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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
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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]
2022
arXiv
pre-print
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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]
2009
Lecture Notes in Computer Science
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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]
2006
Lecture Notes in Computer Science
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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
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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]
2022
arXiv
pre-print
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2021 pre-print arXiv:2103.01012v3 fatcat:63xjmans6zc4zmhmscvefowumiOther Versions
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
2012
Theoretical Computer Science
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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]
2021
arXiv
pre-print
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2021 pre-print arXiv:2104.02438v1 fatcat:ozivgs46yjb3dbf23crxn2l2yi
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]
2020
arXiv
pre-print
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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]
2012
arXiv
pre-print
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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
2009
Theoretical Computer Science
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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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