Abstract
Several different additions to the basic deterministic Turing machine model are often considered. These additions add computational power to the model and so allow us to compute certain problems more efficiently. Often these are important problems with seemingly no efficient solution in the basic model. The question then becomes whether the efficiency the additional power provides is really due to the new model or whether the added efficiency could have been attained without the additional resources.
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Notes
- 1.
By “natural” we mean a problem whose definition has intrinsic independent interest, and one that does not arise by a complexity-theoretic construction.
- 2.
It should be apparent that we have been confusing “problem” with “language.” Recall that we are free to do so because we identify a decision problem with the set of its yes-instances – those instances for which the answer to the question is “yes.” Also, we are relying on the fact that there are polynomial-time encodings of the standard data structures into strings over the two-letter alphabet.
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Homer, S., Selman, A.L. (2011). Nondeterminism and NP-Completeness. In: Computability and Complexity Theory. Texts in Computer Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0682-2_6
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DOI: https://doi.org/10.1007/978-1-4614-0682-2_6
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