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    On the sizes of DPDAs, PDAs, LBAs

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    1503.08847v3.pdf
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    Genre
    Journal Article
    Date
    2016-07-25
    Author
    Beigel, R
    Gasarch, W
    Subject
    Pushdown Automata
    Context free languages
    Linear Bounded Automata
    Length of description of languages
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5706
    
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    DOI
    10.1016/j.tcs.2015.08.028
    Abstract
    © 2015. There are languages A such that there is a Pushdown Automata (PDA) that recognizes A which is much smaller than any Deterministic Pushdown Automata (DPDA) that recognizes A. There are languages A such that there is a Linear Bounded Automata (Linear Space Turing Machine, henceforth LBA) that recognizes A which is much smaller than any PDA that recognizes A. There are languages A such that both A and A are recognizable by a PDA, but the PDA for A is much smaller than the PDA for A. There are languages A1, A2 such that A1, A2, A1∩A2 are recognizable by a PDA, but the PDA for A1 and A2 are much smaller than the PDA for A1∩A2. We investigate these phenomena and show that, in all these cases, the size difference is captured by a function whose Turing degree is on the second level of the arithmetic hierarchy.Our theorems lead to infinitely-many-n results. For example: for-infinitely-many-n there exists a language An recognized by a DPDA such that there is a small PDA for An, but any DPDA for An is very large. We look at cases where we can get all-but-a-finite-number-of-n results, though with much smaller size differences.
    Citation to related work
    Elsevier BV
    Has part
    Theoretical Computer Science
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    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5688
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