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 ADR is trading at a value lower than what it is worth, one can purchase the ADR and expect to make money as its value converges on the original.

Since the left-hand side of this equation is a series of non-negative numbers, and that it converges to

Since a series of complex numbers converges if and only if both its real and imaginary parts converge, we may assume with equal generality that.

Since, the inequality could be satisfied for sufficiently small m. The sum of series first converges to the value of φ ( t ) with arbitrary high accuracy if m is small enough, and left part of the strong inequality is satisfied.

Since the sinc function is continuous, this approximation converges to the actual integral

Since the final integral becomes arbitrarily small if only a is large enough, γ ( s, x ) converges uniformly for x → ∞ on the strip towards a holomorphic function, which must be Γ ( s ) because of the identity theorem.

Since AICc converges to AIC as n gets large, AICc generally should be employed regardless.

Since converges absolutely, for some real number T. The sequence is clearly nondecreasing, so for all n. Thus for all n,

Since fly cutters are one sided and not balanced, they should be used at the slowest speed available, and fed very slowly to avoid binding.

Since the international adoption of the MKS standard in the 1940s and the SI standard in the 1960s, the technical use of CGS units has gradually declined worldwide, in the United States more slowly than elsewhere.

Since the 1980s the term " new religions " or " new religious movements " has slowly entered into Evangelical usage, alongside the word " cult ".

Since the liberalization of the telecommunications market, OTE has been slowly losing market share to " alternative ", competing telecom operators, such as Vivodi, Q-Telecom, Tellas and Forthnet.

Since the 1991 coup, tourism has recovered slowly.

Since then differences between the Hasidim and their opponents have slowly diminished and both groups are now considered part of Haredi Judaism.

Since the polymer only dissolves very slowly in the chemical part of the etching, it builds up on the sidewalls and protects them from etching.

Since the control signals change only slowly compared to the original speech waveform, the bandwidth required to transmit speech can be reduced.

Since digital circuits are made from analog components, digital circuits calculate more slowly than low-precision analog circuits that use a similar amount of space and power.

Since the retreat of the most recent glaciation the South East of England, like the Netherlands, has been steadily slowly sinking through historic time due to forebulge sinking.

Since it is always positioned on the macula, there is no way to make it move laterally, but it can be made to rotate, by viewing a white surface through a rotating polarizer, or by slowly tilting one's head to one side.

Since the demise of Group C ( where Japan and Germany both had successful series of their own ) Japan has largely gone its own way in sports car racing ; the Super GT series is for very highly modified production-based cars ; although prototypes are slowly returning to Japanese racing in the Japan Le Mans Challenge many of these ' prototypes ' are little more than rebodied Formula 3 cars ( although there has been a long Japanese tradition of such hybrids ; a Grand Champion series ran for many years with rebodied Formula 2 and Formula 3000 cars, rather similar to the second incarnation of Can-Am ).

Since then, the nature of the events themselves has evolved relatively slowly.

Since plains can cause a river to flow very slowly, the Tisza used to follow a path with many curves and turns, which led to many large floods in the area.

Since the 16th Century, due to Castilian influences, the name has slowly evolved to taken on the form Guadiana, a cognitive variation that developed from many Moorish-Arab river place-names using the prefix guad ( such as the rivers Guadalquivir, Guadalete, Guadalajara or Guadarrama ).

Since this time, AIDS deaths have continued to decline, but much more slowly, and not as completely in black Americans as in other population segments.

" Since then, the site has been allowed to deteriorate, though the University of Connecticut has been slowly finding uses for and fixing up many of the buildings.

Since the war, Mont Vernon has slowly become a suburban community.

Since that point, the town continued to slowly grow into a prosperous community.

Since the area was so far away from the center of Warwick, the area that became Coventry grew very slowly.

Since that time, the federal government has slowly devolved legislative jurisdiction to the territories.

Since the summit has been barren of soil cover, red spruce have been slowly ascending back towards the top in a process known as ecological succession.

Since Fredrik Reinfeldt became party leader, the party has slowly started to move further towards the political center and also adopted pragmatic views.

Since most double stars are true binary stars rather than mere optical doubles ( as William Herschel had been the first to discover ), they orbit around one another's barycenter and slowly change position over the years.

Since byte code is interpreted it executes more slowly than compiled machine code, unless it is actually compiled to machine code, which could be performed before the execution – making the program loading slow – or during the execution.