POWER CIRCUITS, EXPONENTIAL ALGEBRA, AND TIME COMPLEXITY
نویسندگان
چکیده
منابع مشابه
Power Circuits, Exponential Algebra, and Time Complexity
Motivated by algorithmic problems from combinatorial group theory we study computational properties of integers equipped with binary operations +, −, z = x2, z = x2 (the former two are partial) and predicates < and =. Notice that in this case very large numbers, which are obtained as n towers of exponentiation in the base 2 can be realized as n applications of the operation x2, so working with ...
متن کاملOn Parameterized Exponential Time Complexity
In this paper we study the notion of parameterized exponential time complexity. We show that a parameterized problem can be solved in parameterized 2o(f (k))p(n) time if and only if it is solvable in time O(2δf (k)q(n)) for any constant δ > 0, where p and q are polynomials. We then illustrate how this equivalence can be used to show that special instances of parameterized NP-hard problems are a...
متن کاملPolynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits
We present an interactive probabilistic proof protocol that certifies in (logN )O (1) arithmetic and Boolean operations for the verifier the determinant, for example, of an N × N matrix over a field whose entries a(i, j) are given by a single (logN )O (1)-depth arithmetic circuit, which contains (logN )O (1) field constants and which is polynomial time uniform, for example, which has size (logN...
متن کاملA note on parameterized exponential time complexity
In this paper we define the notion of an f(k)-uniform parameterized exponential time scheme. We show that a problem can be solved in parameterized O(2p(n)) time if and only if it has an f(k)-uniform parameterized exponential time scheme (p is a polynomial). We then illustrate how our formulation can be used to show that special instances of parameterized NPhard problems are as difficult as the ...
متن کاملDigital Algebra and Circuits
Digital numbers D are the world’s most popular data representation: nearly all texts, sounds and images are coded somewhere in time and space by binary sequences. The mathematical construction of the fixed-point D ' Z2 and floating-point D′ ' Q2 digital numbers is a dual to the classical constructions of the real numbers R. The domain D′ contains the binary integers N and Z, as well as Q. The a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2012
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196712500476