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On relativizing auxiliary pushdown machines

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Abstract

We consider relativizing the constructions of Cook in [4] characterizing space-bounded auxiliary pushdown automata in terms of timebounded computers. LetS(n) ≥ logn be a measurable space bound. LetDT A[NTA] be the class of setsS such that there exists a machineM such thatM with oracleA recognizes the setS andM is a deterministic [nondeterministic] oracle Turing machine acceptor that runs in time 2cS(n) for some constantc. LetDB A i [NB Ai ] be the class of setsS such that there exists a machineM such thatM with oracleA recognizes the setS andM is a deterministic [non-deterministic] oracle Turing machine acceptor with auxiliary pushdown that runs in spaceS(n) and never queries the oracle about strings longer than:S(n) ifi = 1, 2cS(n) for some constantc, ifi = 2, + ∞ ifi = 3.

Then we prove the following results:

These contrast with Cook's (unrelativized) result:DT = NB = DB.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 93106, Santa Barbara, California, USA

    Dana Angluin

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  1. Dana Angluin
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Additional information

This research was supported by the National Science Foundation under Grant MCS77-11360. Current address of author: Department of Computer Science, Yale University, New Haven, Connecticut 06520.

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Angluin, D. On relativizing auxiliary pushdown machines. Math. Systems Theory 13, 283–299 (1979). https://doi.org/10.1007/BF01744301

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  • DOI: https://doi.org/10.1007/BF01744301

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