A Program-Size Complexity Measure for Mathematical Problems and Conjectures
نویسنده
چکیده
Cristian Calude et al. in [5] have recently introduced the idea of measuring the degree of difficulty of a mathematical problem (even those still given as conjectures) by the length of a program to verify or refute the statement. The method to evaluate and compare problems, in some objective way, will be discussed in this note. For the practitioner, wishing to apply this method using a standard universal register machine language, we provide (for the first time) some “small” core subroutines or library for dealing with array data structures. These can be used to ease the development of full programs to check mathematical problems that require more than a predetermined finite number of variables.
منابع مشابه
Measurement of Complexity and Comprehension of a Program Through a Cognitive Approach
The inherent complexity of the software systems creates problems in the software engineering industry. Numerous techniques have been designed to comprehend the fundamental characteristics of software systems. To understand the software, it is necessary to know about the complexity level of the source code. Cognitive informatics perform an important role for better understanding the complexity o...
متن کاملInverse and Reverse 2-facility Location Problems with Equality Measures on a Network
In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse c...
متن کاملInductive Complexity of the P versus NP Problem
This paper does not propose a solution, not even a new possible attack, to the P versusNP problem. We are asking the simpler question: How “complex” is the P versus NPproblem? Using the inductive complexity measure—a measure based on computationsrun by inductive register machines of various orders—developed in [2], we determine anupper bound on the inductive complexity of second...
متن کاملMathematical Programming Models for Solving Unequal-Sized Facilities Layout Problems - a Generic Search Method
This paper present unequal-sized facilities layout solutions generated by a genetic search program named LADEGA (Layout Design using a Genetic Algorithm). The generalized quadratic assignment problem requiring pre-determined distance and material flow matrices as the input data and the continuous plane model employing a dynamic distance measure and a material flow matrix are discussed. Computa...
متن کاملPotpourri of Conjectures and Open Questions in Nonlinear Analysis and Optimization
We present a collection of fourteen conjectures and open problems in the fields of nonlinear analysis and optimization. These problems can be classified into three groups: problems of pure mathematical interest, problems motivated by scientific computing and applications, and problems whose solutions are known but for which we would like to know better proofs. For each problem we provide a succ...
متن کامل