On the Optimality of the Binary Algorithm for the Jacobi Symbol
نویسنده
چکیده
We establish lower bounds on the complexity of computing the following number-theoretic functions and relations from piecewise linear primitives: (i) the Legendre and Jacobi symbols, (ii) pseudoprimality, and (iii) modular exponentiation. As a corollary to the lower bound obtained for (i), an algorithm of Shallit and Sorenson is optimal (up to a multiplicative constant).
منابع مشابه
A BINARY LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION
This paper proposes an effective algorithm based on the level set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary level set method (BLSM) is used instead. In the BLSM, the level set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jac...
متن کاملDegree of Optimality as a Measure of Distance of Power System Operation from Optimal Operation
This paper presents an algorithm based on inter-solutions of having scheduled electricity generation resources and the fuzzy logic as a sublimation tool of outcomes obtained from the schedule inter-solutions. The goal of the algorithm is to bridge the conflicts between minimal cost and other aspects of generation. In the past, the optimal scheduling of electricity generation resources has been ...
متن کاملOptimality of the flexible job shop scheduling system based on Gravitational Search Algorithm
The Flexible Job Shop Scheduling Problem (FJSP) is one of the most general and difficult of all traditional scheduling problems. The Flexible Job Shop Problem (FJSP) is an extension of the classical job shop scheduling problem which allows an operation to be processed by any machine from a given set. The problem is to assign each operation to a machine and to order the operations on the machine...
متن کاملOptimality of the flexible job shop scheduling system based on Gravitational Search Algorithm
The Flexible Job Shop Scheduling Problem (FJSP) is one of the most general and difficult of all traditional scheduling problems. The Flexible Job Shop Problem (FJSP) is an extension of the classical job shop scheduling problem which allows an operation to be processed by any machine from a given set. The problem is to assign each operation to a machine and to order the operations on the machine...
متن کاملBQIABC: A new Quantum-Inspired Artificial Bee Colony Algorithm for Binary Optimization Problems
Artificial bee colony (ABC) algorithm is a swarm intelligence optimization algorithm inspired by the intelligent behavior of honey bees when searching for food sources. The various versions of the ABC algorithm have been widely used to solve continuous and discrete optimization problems in different fields. In this paper a new binary version of the ABC algorithm inspired by quantum computing, c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Fundam. Inform.
دوره 76 شماره
صفحات -
تاریخ انتشار 2007