Since algorithms are platform-independent ( i. e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system ), there are significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms.

Since the reference model given for traffic policing in the network is the GCRA, this algorithm is normally used for shaping as well, and single and dual leaky bucket implementations may be used as appropriate.

Since the desired effect is computational difficulty, in theory one would choose an algorithm and desired difficulty level, thus decide the key length accordingly.

The proof of this fact relies on an algorithm which, given the first n digits of Ω, solves Turing's halting problem for programs of length up to n. Since the halting problem is undecidable, Ω can not be computed.

Since the invention of the MIDI system in the early 1980s, for example, some people have worked on programs which map MIDI notes to an algorithm and then can either output sounds or music through the computer's sound card or write an audio file for other programs to play.

Since the algorithm ensures that the remainders decrease steadily with every step, r < sub > k − 1 </ sub > is less than its predecessor r < sub > k − 2 </ sub >.

Since the remainders decrease with every step but can never be negative, a remainder r < sub > N </ sub > must eventually equal zero, at which point the algorithm stops.

Since the last remainder is zero, the algorithm ends with 21 as the greatest common divisor of 1071 and 462.

Since the inverse DFT is the same as the DFT, but with the opposite sign in the exponent and a 1 / N factor, any FFT algorithm can easily be adapted for it.

Since 1968, however, the lowest published count for power-of-two was long achieved by the split-radix FFT algorithm, which requires real multiplications and additions for.

Since NC contains NL, it is also unknown whether a space-efficient algorithm for computing the GCD exists, even for nondeterministic Turing machines.

Since the late 1990s, bzip2, a file compression utility based on a block-sorting algorithm, has gained some popularity as a gzip replacement.

Since a paper describing the algorithm had been published in August 1977, prior to the December 1977 filing date of the patent application, regulations in much of the rest of the world precluded patents elsewhere and only the US patent was granted.

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.

Since PHP 5. 3, it implements the algorithm from Bacon's above mentioned paper.

Since IBM's implementation, several other groups have implemented Shor's algorithm using photonic qubits, emphasizing that entanglement was observed.

Since the parsing algorithm makes intelligent use of layout ( indentation ), there is rarely a need for bracketing statements and no statement terminators are required.

Since any algorithm for multiplying two n × n-matrices has to process all 2 × n < sup > 2 </ sup >- entries, there is an asymptotic lower bound of operations.

Since the eigenvalues of this matrix coincide with the roots of the polynomial, one can use any eigenvalue algorithm to find the roots of the polynomial.

Since the minimax algorithm and its variants are inherently depth-first, a strategy such as iterative deepening is usually used in conjunction with alpha-beta so that a reasonably good move can be returned even if the algorithm is interrupted before it has finished execution.

Since the finalisation of MPEG-1 Audio and MPEG-2 Audio ( in 1992 and 1994 ), the original MUSICAM algorithm is not used anymore.

Since drawing proceeds from back to front with closer objects simply overwriting farther ones, the process is known as employing the Painter's algorithm.

Since the only known way to solve that problem is to factor the modulus, it is generally regarded that the difficulty of integer factorization provides a conditional security proof for the Blum Blum Shub algorithm.

Since a D & C algorithm eventually reduces each problem or sub-problem instance to a large number of base instances, these often dominate the overall cost of the algorithm, especially when the splitting / joining overhead is low.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Since the work is done by hand, the only limitation, it is said, `` is that of human conception ''.

Since two of these could be trustees of the college, actually it would be necessary to have the consent of only one elected official to impose a levy of millions of dollars of tax revenue.

Since the Santo Spirito hospital had taken only men, he had had no experience in the study of female anatomy ; ;

Since the provision of skywave service requires adequate freedom from interference, only class 1, stations are capable of rendering skywave service.

Since it requires only five players, it would seem to fall into the category of chamber music -- yet it calls for a double bass, an instrument generally regarded as symphonic.

Since the same method of shaping and fitting the dogs and notches is used throughout, we will only describe the construction of one locking bar.

Since the writer had not noticed this characteristic in married students scattered throughout the various sections previous to this experiment, nor, as a matter of fact, in those who were continuing in `` single sections '', he can only conclude that there must have been something `` contagious '' within the specific group which caused this to occur.

Since this book is concerned only incidentally with railroad rates, it will not attempt to analyze the methods by which the staff of the Interstate Commerce Commission has estimated out-of-pocket costs and apportioned residue costs.

Since the company under review is supplying what we are here regarding as only one kind of service, we might suppose that the problem of total cost apportionment would be very simple ; ;

Since then, many Protestant denominations have made separate pronouncements, in which they not only approved birth control, but declared it at times to be a religious duty.

Since the 1946 disaster there have been 15 tsunami in the Pacific, but only one was of any consequence.

Since the A.L.A.M. holdings embraced only about twenty-five per cent of motor vehicle patents, the denial of rights to independent companies did not retard technical progress in unlicensed sectors of the industry.

Since Mrs. Calhoun remembered only that the marriage had been in the spring, he started to plod through several months.

Since 1949, the only National League club that got off to a hot start and made a runaway of the race was the '55 Dodger team.

Since P was never asserted as the only sufficient condition for Q, other factors could account for Q ( while P was false ).

Since the minting of coins was a prerogative accorded in Islamic practice only to a sovereign, it can be considered that Osmanli became independent of the Mongol Khans.

Since her adulteress mother was his own sister, Afonso V had not only ambition, but the family honour to protect.

Since the difference between the U. S. and International acre is only about a quarter of the size of an A4 sheet of paper ( 0. 016 square metres, 160 square centimetres or 24. 8 square inches ), it is usually not important which one is being discussed.

Since she was Raymond's only child, they became rulers of Toulouse at Raymond's death in 1247.

Since there are only seven hotel chains in the game, placing a tile that would create an eighth chain is not permitted.

Since the implementation of the Statute of Westminster 1931 in each of the Commonwealth realms ( on successive dates from 1931 onwards ), the Act of Settlement cannot be altered in any realm except by that realm's own parliament and, by convention, only with the consent of all the other realms, as it touches on the succession to the shared throne.

Since this office was a stepping stone to higher office and the Senate, it helped to ensure that only wealthy individuals ( mostly landowners ) would win election to high office.

Since the aircraft normally approached these speeds only in a dive, pilots would report the aircraft attempting to nose over into the ground.