On the complexity of some computational problems in the Turing model
نویسنده
چکیده
In the areas of algorithmic number theory and cryptology, algorithms are usually described and analyzed in some randomized random access machine model. In this work the complexity of various computational problems is studied in the multitape Turing model of computation. It is shown that “up to logarithmic factors” key results also hold in the multitape Turing model. Specific problems which are considered are linear algebra computations, factorization of integers and computations of discrete logarithms in various classes of groups.
منابع مشابه
Some improvements in fuzzy turing machines
In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy s...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملOn the computational complexity of finding a minimal basis for the guess and determine attack
Guess-and-determine attack is one of the general attacks on stream ciphers. It is a common cryptanalysis tool for evaluating security of stream ciphers. The effectiveness of this attack is based on the number of unknown bits which will be guessed by the attacker to break the cryptosystem. In this work, we present a relation between the minimum numbers of the guessed bits and uniquely restricted...
متن کاملA MULTI-OBJECTIVE OPTIMIZATION MODEL FOR PROJECT PORTFOLIO SELECTION CONSIDERING AGGREGATE COMPLEXITY: A CASE STUDY
Existing project selection models do not consider the complexity of projects as a selection criterion, while their complexity may prolong the project duration and even result in its failure. In addition, existing models cannot formulate the aggregate complexity of the selected projects. The aggregated complexity is not always equal to summation of complexity of projects because of possible syne...
متن کاملMechanical Computing: The Computational Complexity of Physical Devices
Computing Machine Models To gage the computational power of a family of mechanical computers, we will use a widely known abstract computational model known as the Turing machine, defined in this section. The Turing machine. The Turing machine model formulated by Alan Turing (1937) was the first complete mathematical model of an abstract computing machine that possessed universal computing power...
متن کامل