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On Unambiguous Regular Tree Languages of Index (0,2)

Jacques Duparc, Kevin Fournier, Szczepan Hummel
unpublished
We show that in case of infinite tree languages, the unambiguous ones are topologically far more complicated than the deterministic ones.  ...  height of the Wadge hierarchy of deterministic tree languages as uncovered by Filip Murlak. 3.  ...  C S L 2 0 1 5 On Unambiguous Regular Tree Languages of Index (0,2) C S L 2 0 1 5  ... 
fatcat:hc4y2fqtgfcmbit2ey6lqgckeu

Holographic four-point functions in the (2, 0) theory

Leonardo Rastelli, Xinan Zhou
2018 Journal of High Energy Physics  
By an extension of the position space approach developed in [1, 2] for the AdS_5× S^5 background, we compute four-point correlators of one-half BPS operators for identical weights k=2, 3, 4.  ...  We revisit the calculation of holographic correlators for eleven-dimensional supergravity on AdS_7× S^4.  ...  Acknowledgments We thank Eric Perlmutter for helpful discussions on the W n four-point functions. Our work is supported in part by NSF Grant PHY-1620628.  ... 
doi:10.1007/jhep06(2018)087 fatcat:tu2ejkp5xvemdbd2fcmgfdtqtq

Unambiguous Buchi is weak [article]

Henryk Michalewski, Michał Skrzypczak
2016 arXiv   pre-print
Moreover, there are no known upper bounds on the descriptive complexity of unambiguous languages among all regular tree languages.  ...  The assumptions of the presented theorem are syntactic (we require one automaton to be both unambiguous and of particular parity index).  ...  Additionally, there are no upper bounds on the descriptive complexity (e.g. the parity index) or topological complexity of unambiguous languages among all regular tree languages.  ... 
arXiv:1401.4025v3 fatcat:slhkcuppjzcwfmb3evsdqsifyu

Unambiguous Büchi Is Weak [chapter]

Henryk Michalewski, Michał Skrzypczak
2016 Lecture Notes in Computer Science  
A non-deterministic automaton on infinite trees is unambiguous if it has at most one accepting run on every tree.  ...  For a given unambiguous parity automaton A of index (i, 2j) we construct an alternating automaton Transformation(A) which accepts the same language, but is simpler in terms of alternating hierarchy of  ...  Additionally, there are no upper bounds on the descriptive complexity (e.g. the parity index) or topological complexity of unambiguous languages among all regular tree languages.  ... 
doi:10.1007/978-3-662-53132-7_26 fatcat:jixzi2z4yrgwljes6to5c2m57y

Unambiguous Tree Languages Are Topologically Harder Than Deterministic Ones

Szczepan Hummel
2012 Electronic Proceedings in Theoretical Computer Science  
The paper gives an example of a tree language G that is recognised by an unambiguous parity automaton and is analytic-complete as a set in Cantor space.  ...  This already shows that the unambiguous languages are topologically more complex than the deterministic ones, that are all coanalytic.  ...  Theorem 1.3 Each regular language of infinite trees is in ∆ 1 2 . Proof (sketch): For a fixed branch α of an infinite tree, the set of runs for which the parity condition on α holds, is Borel.  ... 
doi:10.4204/eptcs.96.19 fatcat:slw6awzc5rcbrozg4hk7ywneqm

On Recognizable Tree Languages Beyond the Borel Hierarchy [article]

Olivier Finkel
2009 arXiv   pre-print
On the other hand, we prove that a tree language accepted by an unambiguous Büchi tree automaton must be Borel. Then we consider the game tree languages W_(i,k), for Mostowski-Rabin indices (i, k).  ...  We prove that the D_ω^n(Σ^1_1)-complete tree languages L_n are Wadge reducible to the game tree language W_(i, k) for k-i ≥ 2.  ...  We thank the anonymous referees for their very helpful comments which have led to a great improvement of our paper.  ... 
arXiv:0909.0393v1 fatcat:zcnorxtnkbdxvh6ph5ckpoe3ua

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

Unambiguous Languages Exhaust the Index Hierarchy

Michal Skrzypczak, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
It is known that not every regular language of infinite trees is unambiguous. Except that, very little is known about which regular tree languages are unambiguous.  ...  This paper answers the question whether unambiguous languages are of bounded complexity among all regular tree languages.  ...  Clearly each deterministic automaton is unambiguous but the converse is not true. Due to [6] we know that there are regular tree languages that are ambiguous (i.e. not unambiguous). Games.  ... 
doi:10.4230/lipics.icalp.2018.140 dblp:conf/icalp/Skrzypczak18 fatcat:qzseclwponc67kuwvcbg5yd36u

Attribute Grammars for Scalable Query Processing on XML Streams [chapter]

Christoph Koch, Stefanie Scherzinger
2004 Lecture Notes in Computer Science  
XSAGs are the first scalable query language for XML streams (running strictly in linear time with bounded memory consumption independent of the size of the stream) that allows for actual data transformations  ...  Moreover, the XSAG formalism provides a strong intuition for which queries can or cannot be processed scalably on streams.  ...  of the paper.  ... 
doi:10.1007/978-3-540-24607-7_15 fatcat:pg36w4s7znhslda4dv77noeh34

Attribute grammars for scalable query processing on XML streams

Christoph Koch, Stefanie Scherzinger
2006 The VLDB journal  
XSAGs are the first scalable query language for XML streams (running strictly in linear time with bounded memory consumption independent of the size of the stream) that allows for actual data transformations  ...  Moreover, the XSAG formalism provides a strong intuition for which queries can or cannot be processed scalably on streams.  ...  of the paper.  ... 
doi:10.1007/s00778-005-0169-1 fatcat:7ujg4q7oczfqtp34zmbtd7pbau

Ambiguity Hierarchy of Regular Infinite Tree Languages [article]

Alexander Rabinovich, Doron Tiferet
2021 arXiv   pre-print
Over finite words every regular language is accepted by a deterministic automaton. Over finite trees every regular language is accepted by an unambiguous automaton.  ...  The degree of ambiguity of a regular language is defined in a natural way.  ...  On the other hand, Skrzypczak [Skr18] proved that unambiguous languages climb up the whole index hierarchy and are topologically as complex as arbitrary regular tree languages.  ... 
arXiv:2009.02985v3 fatcat:zuxog3db4fbmlciqcs4rihqkci

N-Ary Queries by Tree Automata [chapter]

Joachim Niehren, Laurent Planque, Jean-Marc Talbot, Sophie Tison
2005 Lecture Notes in Computer Science  
We investigate the subclass of run-based n-ary queries by unambiguous tree automata.  ...  We investigate n-ary node selection queries in trees by successful runs of tree automata.  ...  Sets of models become languages of annotated trees. Let B = {0, 1} be the set of Booleans.  ... 
doi:10.1007/11601524_14 fatcat:et24hmhegncwhanlsg2byydnha

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.  ...  Moreover, different monoids can be considered: for instance, two-way automata, and even tree-walking automata, can be described by expressions using the free inverse monoid.  ...  The proof is by induction on rational languages, denoted by unambiguous regular expressions [4] .  ... 
arXiv:2110.12395v1 fatcat:zrv75vhvfnawfm7depmqwew6dq

Page 483 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
Ritchie [The C pro- gramming language, Prentice-Hall, Englewood Cliffs, NJ, 1978]. The result related to that algorithm is an unambiguous decompo- sition of trees into smaller ones.  ...  We give two sufficient conditions for induc- tive inferrability of an indexed family from positive data which do not depend on the indexing of the family.  ... 

Unambiguous languages exhaust the index hierarchy [article]

Michał Skrzypczak
2018 arXiv   pre-print
It is known that not every regular language of infinite trees is unambiguous. Except that, very little is known about which regular tree languages are unambiguous.  ...  This paper answers the question whether unambiguous languages are of bounded complexity among all regular tree languages.  ...  The author would like to thank Szczepan Hummel, Damian Niwiński, and Igor Walukiewicz for fruitful and inspiring discussions on the topic.  ... 
arXiv:1803.06163v4 fatcat:sfu2jgfujfaa7gzgbq7er4qik4
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