Algorithmic complexity

Its virtue is its ability to assign a measure of complexity to an individual string, without having to resort to ensembles or probabilities. Its main drawback is that it is typically very hard to calculate exactly. Nonetheless it can be estimated for most systems relatively easily. 

Suppose a state s is encoded as a binary string of 10 O s and 10 I s , s = 10101010. While the number of raw bits defining s is huge, its algorithmic complexity is actually very small because it can be reproduced exactly by the following short program print 10 10 times . On the other hand, a completely 

We make three additional comments concerning algorithmic complexity, as defined by equation 12.9. First, while Ku(s) clearly depends on the universal computer [/ that is chosen to run the program V, because of the ability of universal computers to simulate one another, the difference between algorithmic complexities computed for universal computers U and U2 will be bounded by the 0 ) size of the prefix code allowing any program V that is executed on U to be executed 

This finite difference obviously becomes increasingly less important in the limit of very long strings. For purposes of mathematical analysis, Ku(s) can be treated as being effectively independent of U. 

The final comment is that algorithmic complexity is really a better measure of the degree of randomness in a system rather than its complexity. For example, 

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Algorithmic Complexity Dynamic Measures complexity of given string vice ensemble Hard to compute complexity equated with randomness... 

Another way of looking at it is that Shannon information is a formal equivalent of thermodynamic entroi)y, or the degree of disorder in a physical system. As such it essentially measures how much information is missing about the individual constituents of a system. In contrast, a measure of complexity ought to (1) refer to individual states and not ensembles, and (2) reflect how mnc h is known about a system vice what is not. One approach that satisfies both of these requirements is algorithmic complexity theory. 

One possible measure of algorithmic complexity is program size. Such a measure is related to the inherent simplicity or complexity of a method. This measure is static it is independent of the size or structure of the particular input data. Some other possible measures are dynamic they measure the amount of a resource used by the method as a function of the size of the input data. Typical dynamic measures are running time and storage space. 

Until the late 80 s, the software development was very much curtailed by the limitations of hardware, where the size of the memory was the most critical factor. Today, about a decade later, the most critical aspect for large scale parallel MD simulation is not the hardware, but the software. Coping with increased problem and algorithmic complexity, as well as, varying hardware platforms is a daunting task. Adding the requirement of optimal use of hardware resources makes the development or modification of an efficient and portable parallel MD simulation software a formidable challenge. 

The same advantageous algorithmic complexity characterizes the so-called population localization method of Pipek and Mezey [21], where the functional of the form... 

It is also important that the method used to simulate multi-protein systems be fast. Most of the models used in simulating multi-protein systems are based on continuous intermolecular potentials like the Lennard-Jones potential. Simulations based on continuous potentials proceed by solving Newton equations at a uniformly spaced time intervals. They have an algorithm complexity of C>(Mog N), where IVis the number of particles in the system. The big-(9 notation describes how the performance or complexity (referring to the number of operations) required to mn an algorithm depends on the number of particles in the system. Therefore, the required computational time for continuous MD simulations increases dramatically with the number of beads in the system, limiting their application to relatively small systems. 

Discontinuous molecular dynamics (DMD) simulations can be used to investigate large systems efficiently with moderate computational resources. DMD simulations were designed to be applicable to systems that interact via discontinuous potentials (square-well/square-shoulder and hard-sphere). They proceed by analytically calculating the next collision time. Several papers [26-28] describe the details of DMD simulations. The algorithm complexity of DMD simulations is O (Mog N). (One paper by Paul [29] even claims a realization of the DMD method... 

L M Burdina et al, Tikhomirova microwave radiometry in algorithm complex diagnosis of breast diseases . Modem Oncology, 2005 6(1) 8-9 (in Russian). 

We model an adversary that has gained execute access on a single computer within the mission network. From their perch inside the network, the adversary launches an algorithmic-complexity attack by sending a continuous stream of specially crafted packets to the computer hosting the Radar-Sensor Service. 

In our setup, it might be possible for an adversary to exploit a vulnerability in the host operating system. In addition, VMware Workstation itself might be vulnerable to attack. For example, it is possible that VMware workstation contains an algorithmic-complexity vulnerability that would allow an adversary to violate Workstation s performance-isolation property. 

Crosby, S.A., Wallach, D.S. Denial of service via algorithmic complexity attacks. In USENIX Security Symposium (2003)... 

Weimer, F. Algorithmic complexity attacks and the finux networking code (May 2003), http //www. enyo. de/fw/security/notes/linux-dst- cache-dos. html... 

The qualitative increase stems from the need to perform particle tracking, a task which has no equivalent in one dimension, since particles never leave the element in which they are initially located as they are carried by the velocity field. The generic term particle tracking actually involves a number of nontrivial individual subtasks, which must be tackled efficiently if CONNFFESSIT is to be viable. The key to practicable micro/macro computations is the invention of efficient schemes of reduced algorithmic complexity. 

The security of this chiral-energy encipherment therefore relies both on the algorithmic complexity of the mapping M and the tremendous... 

The grand canonical ensemble, with its algorithmic complexity and convergence problems, is the least used. The canonical ensemble is the easiest to... 

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