We can run the algorithm a constant number of times and take a majority vote to achieve any desired probability of correctness less than 1, using the Chernoff bound.

This can help in proving correctness, simplifying an algorithm, assisting in modifying code without breaking it, or optimizing code by means of memoization, common subexpression elimination or parallelization.

Informally, the " P vs. NP " question asks whether every optimization problem whose answers can be efficiently verified for correctness / optimality can be solved optimally with an efficient algorithm.

The correctness of the algorithm can be shown by induction.

In theoretical computer science, correctness of an algorithm is asserted when it is said that the algorithm is correct with respect to a specification.

Functional correctness refers to the input-output behaviour of the algorithm ( i. e., for each input it produces the correct output ).

A distinction is made between total correctness, which additionally requires that the algorithm terminates, and partial correctness, which simply requires that if an answer is returned it will be correct.

A termination proof is a type of mathematical proof that plays a critical role in formal verification because total correctness of an algorithm depends on termination.

In particular it is not expected to be a correctness assertion for a given program implementing the algorithm on a given machine.

In response to some of these variants, and to other feedback, the paper " PRIMES is in P " was updated with a new formulation of the AKS algorithm and of its proof of correctness.

Its correctness follows from the more general correctness of the Davis-Putnam algorithm, and its polynomial time bound is clear since each resolution step increases the number of clauses in the instance, which is upper bounded by a quadratic function of the number of variables.

The participants could not rely on a computer to verify the correctness of their programs, while the markers had to read every line of the program and try to understand the underlying algorithm.

If this is the case, then we can run the algorithm a polynomial number of times and take a majority vote to achieve any desired probability of correctness less than 1, using the Chernoff bound.

Votes consist of a rating of the correctness & completeness of the full set of data for an item ( not just the most recent changes ), as assessed by users who have been automatically determined, by an undisclosed algorithm, to be experienced & reliable enough to be allowed to cast votes.

To prove theorem 1 we will construct a decoding algorithm and prove its correctness.

The correctness of Varro's calculation has not been proven scientifically but is still used worldwide.

From this it follows that correctness of drawing depends solely upon the principal rays ; and is independent of the sharpness or curvature of the image field.

Furthermore, by breaking the system up into smaller components, the complexity of individual components is reduced, opening up the possibility of using techniques such as automated theorem proving to prove the correctness of crucial software subsystems.

Not surprisingly, it is impractical for generalized correctness, which probably cannot even be defined, much less proven.

It is heavily utilized by the Database and Storage engines ( see above ) both to guarantee the correct execution of concurrent transactions, and ( different mechanisms ) the correctness of other DBMS processes.

Often, when possible without harming correctness, the serializability property is compromised for better performance.

* Locking is the most common transaction concurrency control method in DBMSs, used to provide both serializability and recoverability for correctness.

It is heavily utilized by the Database and Storage engines ( see above ) both to guarantee the correct execution of concurrent transactions, and ( different mechanisms ) the correctness of other DBMS processes.

Often, when possible without harming correctness, the serializability property is compromised for better performance.

* Locking is the most common transaction concurrency control method in DBMSs, used to provide both serializability and recoverability for correctness.

Eiffel's most important contribution to software engineering is design by contract ( DbC ), in which assertions, preconditions, postconditions, and class invariants are employed to help ensure program correctness without sacrificing efficiency.

Different opinions arise only from the application of these preconceptions to particular cases, and it is then that the darkness of ignorance, which blindly maintains the correctness of its own opinion, must be dispelled.

Whatever strategy is used ( simple or mutual ), the level of protection strongly depends on the correctness of the implementation of the web browser and the server software and the actual cryptographic algorithms supported.

The correctness of decisions is measured by two major criteria:

The Department of Safeguards is responsible for carrying out this mission, through technical measures designed to verify the correctness and completeness of states ' nuclear declarations.

One school is sometimes called exclusive legal positivism, and it is associated with the view that the legal validity of a norm can never depend on its moral correctness.

It is in this sense that St Paul's words are taken by the Fathers of the fourth and fifth centuries like St Hilary of Poitiers, St Ambrose, and St Augustine, and there seems no reason to doubt the correctness of their interpretation.

A distinction may be made here between etic and emic viewpoints – the purely descriptive ( etic ) approach which simply considers any system that is actually used, and the emic view which takes account of language users ' perceptions of correctness, which are analogous in some ways to a moral sense of right and wrong.

While censorious political correctness threatened Punch and Judy performances in the UK and other English speaking countries for a time, the show is having one of its cyclical recurrences and can now be seen not only in England, Wales, and Ireland, but also in Canada, the United States ( including Puerto Rico ), Australia, New Zealand and South Africa.

The goal of a type system is to verify and usually enforce a certain level of correctness in programs written in that language by detecting certain incorrect operations.

Political correctness ( adjectivally, politically correct ; both forms commonly abbreviated to PC ) is a term which denotes language, ideas, policies, and behavior seen as seeking to minimize social and institutional offense in occupational, gender, racial, cultural, sexual orientation, certain other religions, beliefs or ideologies, disability, and age-related contexts, and, as purported by the term, doing so to an excessive extent.

Proponents of the view that differences in IQ test scores between blacks and whites are ( primarily or largely ) genetically determined state that criticism of these views is based on political correctness.

In the United Kingdom, " political correctness gone mad " is a catchphrase associated with the conservative Daily Mail newspaper.

Discussion of political correctness, to the extent that it uses the term and accepts the existence of political correctness as a significant force, is almost invariably critical.

When sitting in review of a decision, the Court will only look at the method in which the decision was arrived at, whereas in an administrative appeal the correctness of the decision itself will be examined, usually by a higher body in the agency.

His focus of technical correctness over flair meant that his style of play was usually less suited to the shorter form of the game, at which he had less success.

To ensure correctness, a DBMS usually guarantees that only serializable transaction schedules are generated, unless serializability is intentionally relaxed to increase performance, but only in cases where application correctness is not harmed.

The resulting summary does not reflect a correct result for any ( usually needed for correctness ) precedence order between the two transactions ( if one is executed before the other ), but rather some random result, depending on the timing of the updates, and whether certain update results have been included in the summary or not.

The tenured faculty also usually can control appointments which contributes to political correctness and groupthink.

A fact checker is the person who checks factual assertions in non-fictional text, usually intended for publication in a periodical, to determine their veracity and correctness.