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Paper Abstract and Keywords
Presentation 2013-09-03 11:20
Oracle Pushdown Automata, Nondeterministic Reducibilities, and the Hierarchy over the Family of Context-Free Languages -- (Preliminary Version) --
Tomoyuki Yamakami (Univ. of Fukui) COMP2013-27
Abstract (in Japanese) (See Japanese page) 
(in English) We impose various oracle mechanisms on nondeterministic pushdown automata, which naturally induce nondeterministic reducibilities among formal languages in a theory of context-free languages. In particular, we examine a notion of nondeterministic many-one CFL-reducibility and conduct a ground work to formulate a coherent framework for further expositions. Two more powerful reducibilities--bounded truth-table and Turing CFL-reducibilities--are also discussed in comparison. The Turing CFL-reducibility, in particular, makes it possible to induce a useful hierarchy (the CFL hierarchy) built over the family CFL of context-free languages.
For each level of this hierarchy, basic structural properties are proven and three alternative characterizations are presented. The first and second levels of the hierarchy are proven to be different. The rest of the hierarchy is also infinite unless the polynomial hierarchy over NP collapses. This follows from a characterization of the Boolean hierarchy over the k-th level of the polynomial hierarchy in terms of the Boolean hierarchy over the k+1-st level of the CFL hierarchy. We argue that the CFL hierarchy coincides with a hierarchy over CFL built by applications of many-one CFL-reductions.
Moreover, we exhibit a relativized world where BPCFL--a bounded-error probabilistic version of CFL--is not located within the second level of the CFL hierarchy.
Keyword (in Japanese) (See Japanese page) 
(in English) regular language / context-free language / pushdown automaton / oracle / many-one reducibility / Turing reducibility / truth-table reducibility / CFL hierarchy  
Reference Info. IEICE Tech. Rep., vol. 113, no. 198, COMP2013-27, pp. 17-24, Sept. 2013.
Paper # COMP2013-27 
Date of Issue 2013-08-27 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF COMP2013-27

Conference Information
Committee COMP  
Conference Date 2013-09-03 - 2013-09-03 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2013-09-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Oracle Pushdown Automata, Nondeterministic Reducibilities, and the Hierarchy over the Family of Context-Free Languages 
Sub Title (in English) (Preliminary Version) 
Keyword(1) regular language  
Keyword(2) context-free language  
Keyword(3) pushdown automaton  
Keyword(4) oracle  
Keyword(5) many-one reducibility  
Keyword(6) Turing reducibility  
Keyword(7) truth-table reducibility  
Keyword(8) CFL hierarchy  
1st Author's Name Tomoyuki Yamakami  
1st Author's Affiliation University of Fukui (Univ. of Fukui)
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Speaker Author-1 
Date Time 2013-09-03 11:20:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2013-27 
Volume (vol) vol.113 
Number (no) no.198 
Page pp.17-24 
#Pages 8 
Date of Issue 2013-08-27 (COMP) 

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