If they don't then for the algorithm to be effective it must provide a set of rules for extracting a square root.

If a polynomial time algorithm calls as a subroutine polynomially many polynomial time algorithms, the resulting algorithm is still polynomial time.

If a " weak " character is followed by another " weak " character, the algorithm will look at the first neighbouring " strong " character.

If the algorithm is symmetric, the key must be known to the recipient and sender and to no one else.

If the algorithm is an asymmetric one, the enciphering key is different from, but closely related to, the deciphering key.

If one key cannot be deduced from the other, the asymmetric key algorithm has the public / private key property and one of the keys may be made public without loss of confidentiality.

If a suitably sized quantum computer capable of running Grover's algorithm reliably becomes available, it would reduce a 128-bit key down to 64-bit security, roughly a DES equivalent.

If a naive rendering algorithm is used without any filtering, high frequencies in the image function will cause ugly aliasing to be present in the final image.

If implemented using remainders of Euclidean division rather than subtractions, Euclid's algorithm computes the GCD of large numbers efficiently: it never requires more division steps than five times the number of digits ( base 10 ) of the smaller integer.

If a is smaller than b, the first step of the algorithm swaps the numbers.

If the arguments are both greater than zero then the algorithm can be written in more elementary terms as follows:

If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.

If a large, b-bit number is the product of two primes that are roughly the same size, then no algorithm has been published that can factor in polynomial time, i. e., that can factor it in time O ( b < sup > k </ sup >) for some constant k. There are published algorithms that are faster than O (( 1 + ε )< sup > b </ sup >) for all positive ε, i. e., sub-exponential.

If the true function is simple, then an " inflexible " learning algorithm with high bias and low variance will be able to learn it from a small amount of data.

If the desired output values are often incorrect ( because of human error or sensor errors ), then the learning algorithm should not attempt to find a function that exactly matches the training examples.

* Robustness: If the model, cost function and learning algorithm are selected appropriately the resulting ANN can be extremely robust.

If using efficient sorting such as mergesort or heapsort this is an O ( n log n ) average and worst-case algorithm.

The algorithm for deciding this is conceptually simple: it constructs ( the description of ) a new program t taking an argument n which ( 1 ) first executes program a on input i ( both a and i being hard-coded into the definition of t ), and ( 2 ) then returns the square of n. If a ( i ) runs forever, then t will never get to step ( 2 ), regardless of n. Then clearly, t is a function for computing squares if and only if step ( 1 ) terminates.

If we apply the run-length encoding ( RLE ) data compression algorithm to the above hypothetical scan line, we get the following:

If not, is there an algorithm to determine how many are required?

If the user wanted to see a font at another size, the Font Manager would find the closest match and apply a basic scaling algorithm.

If a particle visits every point on its trajectory then the motion is an algorithm for each point.

If two processes attempt to enter a critical section at the same time, the algorithm will allow only one process in, based on whose turn it is.

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If you are unable to sign the request, because of illness or other good cause, another person who stands in close personal or business relationship to you may sign the request on your behalf, stating the reason why you are unable to sign.

If he died before she did, she would never be unable to resist opening it.

If an opponent tries to anticipate the stroke, he may move in the wrong direction and may be unable to change his body momentum in time to reach the shuttlecock.

If one die is unable to be moved, but such a move is made possible by the moving of the other die, that move is compulsory.

If it was instead hilly, wooded, marshy, or urban, armour would be vulnerable to infantry in close-quarters combat and unable to break out at full speed.

If he had been a bit more trustworthy, if his character was somewhat better, the CCP would have been unable to beat him ".

If the user is unable to identify what is being demonstrated in a reasonable fashion, the map may be regarded as useless.

If enough magma is ejected, the emptied chamber is unable to support the weight of the volcanic edifice above it.

To avoid debates about the possibility of in-vitro fertilization, artificial insemination, or cloning, the original Darwin Awards book applied the following " deserted island " test to potential winners: If the person were unable to reproduce when stranded on a deserted island with a fertile member of the opposite sex, he or she would be considered sterile.

" If you bind me so that I am unable to release myself, then you will be standing by in such a way that I should have to wait a long time before I got any help from you.

If for any reason there are complications, the village midwife will forward the ‘ patient ’ to the ‘ nurse ’, and if she is unable to help then they are forwarded to the Primary Health Center.

If the photon energy is too low, the electron is unable to escape the material.

If there is no covering fire, the tank may be destroyed easily as it unable to move to protect itself.

# If a vessel on port tack is unable to determine the tack of the other boat, she should be prepared to give way ( Rule 12 )

If the mass of the core exceeds the Chandrasekhar limit, electron degeneracy pressure will be unable to support its weight against the force of gravity, and the core will undergo sudden, catastrophic collapse to form a neutron star or ( in the case of cores that exceed the Tolman-Oppenheimer-Volkoff limit ), a black hole.

If the government has a large majority, then they are very unlikely to lose enough votes to be unable to pass legislation.

If the embalmer is unable to do so, or if the family requests otherwise, the funeral home can perform a closed casket service.

** If the router was unable to establish a successful TCP session, then it ends up in the Active state.

If the defensive player is in the backcourt but unable to position himself for a non-defensive shot, he may need to hit the ball off of the back wall.

If a user thread or a fiber performs a system call that blocks, the other user threads and fibers in the process are unable to run until the system call returns.

If a conference committee is unable to reach an agreement, it may be discharged, and a new conference committee may be appointed.

If the president is not present, dies, resigns, or is otherwise unable to fulfill his or her duties, the vice president will generally serve as president.

If however both tubes were completely blocked, so that sperm and egg were physically unable to meet, then fertilization of the egg would naturally be impossible, and neither normal pregnancy nor ectopic pregnancy could occur.