Fine hierarchies and m-reducibilities in theoretical computer science

Selivanov, Victor L.

doi:10.1016/j.tcs.2008.06.031

Cited by 24 publications

(30 citation statements)

References 131 publications

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“…The argument is based on a uniform construction of an inseparable pair in each class Σ n . It should be noted that the separation property of the class (1, 2) was proved earlier by Selivanov [15], who also gave a hint [16] how this result can be generalized for all classes Π n in the index hierarchy of deterministic automata on infinite words.…”

Section: Introductionmentioning

confidence: 69%

“…Recall that the separation property for the class Π 2 was proved earlier by Selivanov [15], who also gave 7 a hint [16] on how this result can be generalized for all classes Π n .…”

Section: Lemma 8 Let E = {I K} Where K Is Even and Letmentioning

confidence: 77%

“…7 More precisely, that author considered the reduction property for the dual classes Σ m . See a comment after Proposition 3.5 in [16].…”

Section: Contractionsmentioning

confidence: 99%

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On the Separation Question for Tree Languages

Arnold¹,

Michalewski

Niwiński

2013

Theory Comput Syst

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We show that the separation property fails for the classes Σ n of the RabinMostowski index hierarchy of alternating automata on infinite trees. This extends our previous result (obtained with Szczepan Hummel) on the failure of the separation property for the class Σ 2 (i.e., for co-Büchi sets). The non-separation result is also adapted to the analogous classes induced by weak alternating automata.To prove our main result, we first consider the Rabin-Mostowski index hierarchy of deterministic automata on infinite words, for which we give a complete answer (generalizing previous results of Selivanov): the separation property holds for Π n and fails for Σ n -classes. The construction invented for words turns out to be useful for trees via a suitable game.It remains open if the separation property holds for all classes Π n of the index hierarchy for tree automata. To give a positive answer it would be enough to show the reduction property of the dual classes-a method well-known in descriptive set theory. We show that it cannot work here, because the reduction property fails for all classes in the index hierarchy.

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Section: Introductionmentioning

confidence: 69%

“…Recall that the separation property for the class Π 2 was proved earlier by Selivanov [15], who also gave 7 a hint [16] on how this result can be generalized for all classes Π n .…”

Section: Lemma 8 Let E = {I K} Where K Is Even and Letmentioning

confidence: 77%

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On the Separation Question for Tree Languages

Arnold¹,

Michalewski

Niwiński

2013

Theory Comput Syst

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“…As is usual in classical DST, we put emphasis on the "ininitary version" of hierarchy theory where people are concerned with transfinite (along with finite) levels of hierarchies. The "finitary" version where people concentrate on the finite levels of hierarchies has a special flavor and is relevant to several fields of Logic and Computation Theory; it was systematized in [Se06,Se08a,Se12]. We extend some well known facts about classical hierarchies in Polish spaces to natural classes of cb 0 -spaces.…”

Section: Introductionmentioning

confidence: 99%

Towards a descriptive theory of cb₀-spaces

Selivanov

2016

Math. Struct. Comp. Sci.

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The paper tries to extend results of the classical Descriptive Set Theory to as many countably based T0-spaces (cb0-spaces) as possible. Along with extending some central facts about Borel, Luzin and Hausdorff hierarchies of sets we consider also the more general case of k-partitions. In particular, we investigate the difference hierarchy of k-partitions and the fine hierarchy closely related to the Wadge hierarchy.

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“…The latter being a huge refinement of the Borel hierarchy. The standard work here can be found in [10,28,38,40,42,43,44,45,47].…”

Section: Introductionmentioning

confidence: 99%