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Are there any significant problems in computer science that can only be solved in double exponential time ? And if they exist then to which class of problems do they belong ?
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Every twelve years, the population doubles, and the exponent becomes an integer based on n=t/12. To model the population at any arbitrary year, we rewrite the exponential function in terms of the doubling time. f(t)=300\cdot 2^{(t/T)}, where T is the doubling time.
Law of Exponents: The first law states that to multiply two exponential functions with the same base, we simply add the exponents. The second law states that to divide two exponential functions with the same base, we subtract the exponents.
The doubling time of a population exhibiting exponential growth is the time required for a population to double. Implicit in this definition is the fact that, no matter when you start measuring, the population will always take the same amount of time to double.
From Wikipedia:
In computational complexity theory, some algorithms take double-exponential time:
Each decision procedure for Presburger arithmetic provably requires at least double-exponential time
Computing a Gröbner basis over a field. In the worst case, a Gröbner basis may have a number of elements which is doubly exponential in the number of variables.
Finding a complete set of associative-commutative unifiers
Satisfying CTL+ (which is, in fact, 2-EXPTIME-complete)
Quantifier elimination on real closed fields takes a doubly-exponential time (see Cylindrical algebraic decomposition).
Calculating the complement of a regular expression
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