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Languages polylog-time reducible to dot-depth 1/2

Christian Glaßer
2007 Journal of computer and system sciences (Print)  
We construct languages of arbitrary dot-depth that are reducible to languages of dot-depth 1/2. (3) Unbalanced star-free leaf languages can be much stronger than balanced ones.  ...  We study (i) regular languages that are polylog-time reducible to languages of dot-depth 1/2 and (ii) regular languages that are polylog-time decidable.  ...  Wagner for exciting discussions about leaf languages and reducibility notions for star-free languages. In particular, Example 13 was discussed in this group. I thank David A.  ... 
doi:10.1016/j.jcss.2006.09.004 fatcat:2pwxmb63yrbcrh75ixflfjm7ea

A Generalized Quantifier Concept in Computational Complexity Theory [article]

Heribert Vollmer
1998 arXiv   pre-print
A notion of generalized quantifier in computational complexity theory is explored and used to give a unified treatment of leaf language definability, oracle separations, type 2 operators, and circuits  ...  Relations to Lindstroem quantifiers are pointed out.  ...  For helpful discussions I am grateful to J. Makowsky (Haifa) and H. Schmitz (Würzburg).  ... 
arXiv:cs/9809115v1 fatcat:wata5tgjonclpk5cyfycpnmyha

On Small Hard Leaf Languages [chapter]

Falk Unger
2005 Lecture Notes in Computer Science  
We then use seeds to show that leaf languages A with N P ⊆ BLeaf P (A) cannot be polylog-sparse (i.e. censusA ∈ O(log O(1) )), unless P H collapses.  ...  This paper deals with balanced leaf language complexity classes, introduced independently in [1] and [14] .  ...  Acknowledgements I would like to thank Gerd Wechsung for supervising my Diploma Thesis on leaf languages and Harry Buhrman for hints on this paper.  ... 
doi:10.1007/11549345_67 fatcat:q2mbj7yiazfinmubwf2heyx3wq

Finite Automata with Generalized Acceptance Criteria

Timo Peichl, Heribert Vollmer
2001 Discrete Mathematics & Theoretical Computer Science  
We study leaf languages either taken from one of the classes of the Chomsky hierarchy, or taken from a time- or space-bounded complexity class.  ...  International audience We examine the power of nondeterministic finite automata with acceptance of an input word defined by a leaf language, i.e., a condition on the sequence of leaves in the automaton's  ...  We are grateful to Klaus W. Wagner (Würzburg) and Ulrich Hertrampf (Stuttgart) for helpful discussions. We also acknowledge helpful comments by the anonymous referees.  ... 
doi:10.46298/dmtcs.287 fatcat:2rekpamiwzhh5psqvohuduc77i

Finite Automata with Generalized Acceptance Criteria [chapter]

Timo Peichl, Heribert Vollmer
1999 Lecture Notes in Computer Science  
We study leaf languages either taken from one of the classes of the Chomsky hierarchy, or taken from a time-or space-bounded complexity class.  ...  We examine the power of nondeterministic finite automata with acceptance of an input word defined by a leaf language, i. e., a condition on the sequence of leaves in the automaton's computation tree.  ...  We are grateful to Klaus W. Wagner (Würzburg) and Ulrich Hertrampf (Stuttgart) for helpful discussions. We also acknowledge helpful comments by the anonymous referees.  ... 
doi:10.1007/3-540-48523-6_57 fatcat:olsevkclxfdf5mymazrt7vqyru

Logspace and Logtime Leaf Languages

Birgit Jenner, Pierre McKenzie, Denis Thérien
1996 Information and Computation  
We show that logspace leaf languages yield a much ner classi cation scheme for complexity classes than polynomial time leaf languages, capturing also many classes within P.  ...  In contrast, logtime leaf languages basically behave like logtime reducibilities. Both cases are more subtle to handle than the polynomial time case.  ...  Thanks also go to the two anonymous referees for their very detailed and valuable comments. One of the referees provided the proof of the non-closure-under-padding results of Proposition 2.2.  ... 
doi:10.1006/inco.1996.0071 fatcat:sn5ihls7vng57dcdv3xuwslti4

On Word and Frontier Languages of Unsafe Higher-Order Grammars

Kazuyuki Asada, Naoki Kobayashi, Marc Herbstritt
2016 International Colloquium on Automata, Languages and Programming  
We use intersection types for transforming an order-(n+1) word grammar to a corresponding order-n tree grammar.  ...  We show that the class of unsafe order-(n+1) word languages coincides with the class of frontier languages of unsafe order-n tree languages.  ...  We would like to thank Takeshi Tsukada for helpful discussions and thank Pawel Parys for information about the related work [4] .  ... 
doi:10.4230/lipics.icalp.2016.111 dblp:conf/icalp/Asada016 fatcat:shjoj5j7vbh6ta4l7uskuzh374

The Gessel Correspondence and the Partial γ-Positivity of the Eulerian Polynomials on Multiset Stirling Permutations [article]

William Y.C. Chen, Amy M. Fu, Sherry H.F. Yan
2021 arXiv   pre-print
Pondering upon the grammatical labeling of 0-1-2 increasing plane trees, we came to the realization that the grammatical labels play a role as records of chopped off leaves of the original increasing binary  ...  to Ma-Ma-Yeh in connection with certain statistics of Stirling permutations.  ...  First, we need to translate the defining property of an unbalanced y-leaf into the language of Stirling permutations.  ... 
arXiv:2111.04098v1 fatcat:fuuhtq6osvcf5oypycb2y7pkse

A reducibility for the dot-depth hierarchy

Victor L. Selivanov, Klaus W. Wagner
2005 Theoretical Computer Science  
We prove some basic facts on the corresponding degree structure and discuss relationships of the reducibility to complexity theory (via the leaf-language approach).  ...  In this paper we propose a reducibility having similar relationship to the Brzozowski's dot-depth hierarchy and some its refinements.  ...  We are also grateful to Erich Grädel, Wolfgang Thomas (Aachen) and Denis Thérien (Montreal) for useful remarks and bibliographical hints.  ... 
doi:10.1016/j.tcs.2005.07.020 fatcat:zvp4cowd4nch3jcmhs2tv5wfca

Machines that Can Output Empty Words

Christian Glaßer, Stephen Travers
2007 Theory of Computing Systems  
A central aspect is that it allows us to prove strong gap theorems: For any class C that is definable in the e-model, either coUP ⊆ C or C ⊆ NP.  ...  We propose the e-model for leaf languages which generalizes the known balanced and unbalanced concepts.  ...  With Theorem 5.10 we give such a characterization for the class of languages corresponding to 1NP.  ... 
doi:10.1007/s00224-007-9087-5 fatcat:ztduhoeczjbo5e4eqkloyfoga4

Machines that Can Output Empty Words [chapter]

Christian Glaßer, Stephen Travers
2006 Lecture Notes in Computer Science  
A central aspect is that it allows us to prove strong gap theorems: For any class C that is definable in the e-model, either coUP ⊆ C or C ⊆ NP.  ...  We propose the e-model for leaf languages which generalizes the known balanced and unbalanced concepts.  ...  With Theorem 5.10 we give such a characterization for the class of languages corresponding to 1NP.  ... 
doi:10.1007/11821069_38 fatcat:aziyx7bfpzgo3if4oor673jrji

Page 8387 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
Summary: “Under the assumption that the polynomial-time hier- archy does not collapse we show for a regular language L that the unbalanced polynomial-time leaf language class determined by L equals NP  ...  Summary: “If one builds a topological model, analogous to that of J. R.  ... 

Soft computational techniques to identify cotton leaf damage

Rafael Faria Caldeira, Wesley Esdras Santiago, Bárbara Teruel
2021 Australian Journal of Crop Science  
Then they analyzed with a neuro-fuzzy classifier trained to discriminate the three types of regions (soil, healthy leaf, and lesioned leaf).  ...  The algorithm developed was able to recognize the three classes. It generated a great amount of information on recognition of background which was more consistent than leaf damage areas.  ...  Acknowledgements The authors would like to thank the Brazilian National Council for Scientific and Technological Development (CNPq) for the grant (process 140719/2017-2) awarded to the research worker  ... 
doi:10.21475/ajcs.21.15.08.p3256 fatcat:gvn2rlvkojf2bflms7tmbksboa

Hierarchies and reducibilities on regular languages related to modulo counting

Victor L. Selivanov
2008 RAIRO - Theoretical Informatics and Applications  
For any discussed reducibility we try to give motivations and open questions, in a hope to convince the reader that the study of these reducibilities is interesting for automata theory and computational  ...  As an application, we characterize the regular languages whose balanced leaf-language classes are contained in the polynomial hierarchy.  ...  I am grateful to Klaus Wagner for hosting the stays, and also to him and Christian Glaßer for many useful discussions and for the help with making pictures.  ... 
doi:10.1051/ita:2007063 fatcat:n7kjjgxllzdijp4gu5ub3nbkva

Checking Data Structure Properties Orders of Magnitude Faster [chapter]

Emmanouil Koukoutos, Viktor Kuncak
2014 Lecture Notes in Computer Science  
Then, it applies a program transformation that changes recursively computed properties into data structure fields, ensuring that properties are evaluated no more than once on a given data structure node  ...  We present a set of techniques that improve the efficiency of run-time checks by orders of magnitude, often recovering the original asymptotic behavior of operations.  ...  This sealed abstract class Tree case class Leaf() extends Tree case class Node(left : Tree, value : Int, right: Tree) extends Tree def insert(t: Tree, e : Int) : idea has been applied to partially evaluate  ... 
doi:10.1007/978-3-319-11164-3_22 fatcat:wv4qua2dyfb67kht2ko452cx6u
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