Limit, logic, and computation
نویسندگان
چکیده
منابع مشابه
Limit, logic, and computation.
We introduce "ultrafilter limits" into the classical Turing model of computation and develop a paradigm for interpreting the problem of distinguishing the class P from NP as a logical problem of decidability. We use P(NP) to denote decision problems which can be solved on a (nondeterministic) Turing machine in polynomial time. The concept is that in an appropriate limit it may be possible to pr...
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The theory of addition in the domains of natural (N), integer (Z), rational (Q), real (R) and complex (C) numbers is decidable; so is the theory of multiplication in all those domains. By Gödel’s Incompleteness Theorem the theory of addition and multiplication is undecidable in the domains of N, Z and Q; though Tarski proved that this theory is decidable in the domains of R and C. The theory of...
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The goal of these lectures is to describe a “structural” theory of quantum computation. Quantum programs can be reasoned about at many different levels. They can be reasoned about numerically and algebraically, which involves specific calculations with complex numbers and vector space notation. Programs can also be reasoned about symbolically, by expressing them in a formal language and formula...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1998
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.95.1.95