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An Effective Extension of the Wagner Hierarchy to Blind Counter Automata [article]

Olivier Finkel
2010 arXiv   pre-print
The extension of the Wagner hierarchy to blind counter automata accepting infinite words with a Muller acceptance condition is effective. We determine precisely this hierarchy.  ...  Thanks to Jean-Pierre Ressayre and Jacques Duparc for many helpful discussions about Wadge and Wagner Hierarchies.  ...  Thanks also to the anonymous referees for useful comments on the preliminary version of this paper. In particular the remark 19 is due to one of them.  ... 
arXiv:1005.5635v1 fatcat:q7o65legm5ffzkwctcdrw6pqwq

An Effective Extension of the Wagner Hierarchy to Blind Counter Automata [chapter]

Olivier Finkel
2001 Lecture Notes in Computer Science  
The extension of the Wagner hierarchy to blind counter automata accepting infinite words with a Muller acceptance condition is effective. We determine precisely this hierarchy.  ...  Thanks to Jean-Pierre Ressayre and Jacques Duparc for many helpful discussions about Wadge and Wagner Hierarchies.  ...  Thanks also to the anonymous referees for useful comments on the preliminary version of this paper. In particular the remark 19 is due to one of them.  ... 
doi:10.1007/3-540-44802-0_26 fatcat:dg647pp3urgmdo6n4eyiwfcdju

A game theoretical approach to the algebraic counterpart of the Wagner hierarchy : Part I

Jérémie Cabessa, Jacques Duparc
2009 RAIRO - Theoretical Informatics and Applications  
Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy.  ...  The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a well-founded and decidable partial ordering of width 2 and height  ...  The authors wish to express their deep gratitude to Jean-Eric Pin for his very significant contribution to this paper, in particular as the PhD supervisor of the first author.  ... 
doi:10.1051/ita/2009004 fatcat:vnyqwj35wnbgpon7oz2a6sw5ti

A Game Theoretical Approach to The Algebraic Counterpart of The Wagner Hierarchy : Part II

Jérémie Cabessa, Jacques Duparc
2009 RAIRO - Theoretical Informatics and Applications  
The algebraic counterpart of the Wagner hierarchy consists of a well-founded and decidable classification of finite pointed ω-semigroups of width 2 and height ω ω .  ...  This paper completes the description of this algebraic hierarchy.  ...  Acknowledgement The authors wish to express their profound gratitude to Jean-Eric Pin for his helpful participation in this whole work, and also to Victor Selivanov for helpful and interesting discussions  ... 
doi:10.1051/ita/2009007 fatcat:dmiokw3azrf33pajgeh6i4iame

The Boolean Hierarchy over Level 1/2 of the Straubing-Therien Hierarchy [article]

Heinz Schmitz, Klaus W. Wagner
1998 arXiv   pre-print
From this criterion we can conclude that this boolean hierarchy is proper and that its classes are decidable.In finite model theory the latter implies the decidability of the classes of the boolean hierarchy  ...  We give a membership criterion for the single classes of the boolean hierarchy over L(1/2).  ...  In the last section we state a result of this type relating the boolean hierarchy over level 1/2 of the Straubing-Thérien hierarchy to the boolean hierarchy over NP.  ... 
arXiv:cs/9809118v1 fatcat:gez5cgx7efgjhevgwqthywniq4

A Tentative Approach for the Wadge-Wagner Hierarchy of Regular Tree Languages of Index [0, 2] [chapter]

Jacques Duparc, Kevin Fournier
2015 Lecture Notes in Computer Science  
We provide a hierarchy of tree languages recognised by nondeterministic parity tree automata with priorities in {0, 1, 2}, whose length exceeds the first fixed point of the ε operation (that itself enumerates  ...  the fixed points of x → ω x ).  ...  In particular, the Wadge hierarchy tremendously refines the Borel and the projective hierarchies.  ... 
doi:10.1007/978-3-319-19225-3_7 fatcat:z6d2m2dhorgfzfxx2c2sx2v2si

The Boolean Hierarchy of NP-Partitions [chapter]

Sven Kosub, Klaus W. Wagner
2000 Lecture Notes in Computer Science  
doi:10.1007/3-540-46541-3_13 fatcat:zavukibf7rhj3dehc6yw6cfcpm

The boolean hierarchy of NP-partitions

Sven Kosub, Klaus W. Wagner
2008 Information and Computation  
Whereas the structure of the latter hierarchy is rather simple the structure of the boolean hierarchy of k-partitions over NP for k ≥ 3 turns out to be much more complicated.  ...  We introduce the boolean hierarchy of k-partitions over NP for k ≥ 3 as a generalization of the boolean hierarchy of sets (i.e., 2-partitions) over NP.  ...  We also thank the anonymous referees for their helpful comments.  ... 
doi:10.1016/j.ic.2007.06.003 fatcat:nqaggmcrm5elxklgdllobixrwa

A reducibility for the dot-depth hierarchy

Victor L. Selivanov, Klaus W. Wagner
2005 Theoretical Computer Science  
Hierarchies considered in computability theory and in complexity theory are related to some reducibilities in the sense that levels of the hierarchies are downward closed and have complete sets.  ...  In this paper we propose a reducibility having similar relationship to the Brzozowski's dot-depth hierarchy and some its refinements.  ...  Last not least we thank the anonymous referees for their very helpful comments.  ... 
doi:10.1016/j.tcs.2005.07.020 fatcat:zvp4cowd4nch3jcmhs2tv5wfca

Bounding queries in the analytic polynomial-time hierarchy

Herbert Baier, Klaus W. Wagner
1998 Theoretical Computer Science  
In a previous paper the present authors (Baier and Wagner, 1996) investigated an S-V-hierarchy over P using word quantifiers as well as two types of set quantifiers, the so-called analytic polynomial-time  ...  examine a hierarchy which extends the analytic polynomial-time hierarchy by considering restrictions on the number of oracle queries.  ...  We call this hierarchy the bounded analytic polynomial-time hierarchy.  ... 
doi:10.1016/s0304-3975(98)00057-7 fatcat:tyizpbbtcvh5nnc5gatw66zapq

Enumeration of the adjunctive hierarchy of hereditarily finite sets

G. Audrito, A. I. Tomescu, S. Wagner
2014 Journal of Logic and Computation  
Determining the cardinality a_n of each level of this hierarchy, problem crucial in establishing whether the natural adjunctive hierarchy leads to an efficient encoding by numbers, was left open.  ...  In 2008, Kirby proposed an adjunctive hierarchy of hereditarily finite sets, based on the fact that they can also be seen as built up from the empty set by repeated adjunction, that is, by the addition  ...  The second author is partially supported by the Academy of Finland under grant 250345 (CoECGR), and by the European Science Foundation, activity "Games for Design and Verification".  ... 
doi:10.1093/logcom/exu062 fatcat:ncsj3cew7nhrzmze4jewklc2ju

Unambiguous Languages Exhaust the Index Hierarchy

Michal Skrzypczak, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
The notion of complexity is the canonical one, called the (parity or Rabin-Mostowski) index hierarchy.  ...  The technical core of the article is a definition of the canonical signatures together with a parity game that compares signatures of a given pair of parity games (of the same index).  ...  In other words, L does not belong to the level (i, k) of the index hierarchy.  ... 
doi:10.4230/lipics.icalp.2018.140 dblp:conf/icalp/Skrzypczak18 fatcat:qzseclwponc67kuwvcbg5yd36u

The difference and truth-table hierarchies for NP

Johannes Köbler, Uwe Schöning, Klaus W. Wagner
1987 RAIRO - Theoretical Informatics and Applications  
DÉFINITION To prove the relationships between the Boolean NP-hierarchy, the différence hierarchy and the Boolean hierarchy we need the following définition.  ...  hierarchy are the same.  ... 
doi:10.1051/ita/1987210404191 fatcat:u6ragzrbbndktbjjnoveibir74

The Quantifier Alternation Hierarchy of Synchronous Relations

Diego Figueira, Varun Ramanathan, Pascal Weil, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
Our results reveal the connections between this hierarchy and the well-known hierarchy of first-order defined languages of finite words.  ...  Here, we study the quantifier alternation hierarchy of this logic. We show that it collapses at level Σ3 and that all levels below admit decidable characterizations.  ...  The quantifier alternation hierarchy within FO[<] forms a strict infinite hierarchy, and it has been the object of intense study (see [17, 18] for an overview).  ... 
doi:10.4230/lipics.mfcs.2019.29 dblp:conf/mfcs/FigueiraRW19 fatcat:mzz6br3utncjrgpuzz4af3qrfm

The Complexity of Separation for Levels in Concatenation Hierarchies

Thomas Place, Marc Zeitoun, Michael Wagner
2018 Foundations of Software Technology and Theoretical Computer Science  
Moreover, using specific transfer results [15] , this can be pushed to the levels 3/2 and 2 for the two most famous finitely based hierarchies: the dot-depth [1] and the Straubing-Thérien hierarchy [21  ...  Dot-depth two is a class belonging to a famous concatenation hierarchy which stratifies the star-free languages: the dot-depth [1]. A specific concatenation hierarchy is built in a generic way.  ...  The Straubing-Thérien hierarchy In this final section, we consider one of the most famous concatenation hierarchies: the Straubing-Thérien hierarchy [21, 22] .  ... 
doi:10.4230/lipics.fsttcs.2018.47 dblp:conf/fsttcs/PlaceZ18 fatcat:wbhnpdtok5f37pwghrju7v4l2m
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