A few years later, in his seminal 1971 paper " The Complexity of Theorem Proving Procedures ", Cook formalized the notions of polynomial-time reduction ( a. k. a. Cook reduction ) and NP-completeness, and proved the existence of an NP-complete problem by showing that the Boolean satisfiability problem ( usually known as SAT ) is NP-complete.

Cook recounted his move to the University of Toronto in 1970 and the reception of his work on NP-completeness, leading up to his A. M. Turing Award.

Also in the 1970s, beginning with the work of and, researchers began finding mathematical justification for the perceived difficulty of the clique problem in the theory of NP-completeness and related intractability results.

For this reason finding Hamiltonian cycles and longest cycles in outerplanar graphs may be solved in linear time, in contrast to the NP-completeness of these problems for arbitrary graphs.

The first three of these problems are all important in practical applications ; the independent set decision problem is not, but is necessary in order to apply the theory of NP-completeness to problems related to independent sets.

The concept of NP-completeness was developed in the late 1960s and early 1970s in parallel by researchers in the US and the USSR.

The theoretical interest in NP-completeness was also enhanced by the work of Theodore P. Baker, John Gill, and Robert Solovay who showed that solving NP-problems in Oracle machine models requires exponential time.

He has also written highly-cited research papers on the NP-completeness of approximately solving certain optimization problems, on open shop scheduling, on parallel algorithms for matrix multiplication and their application in graph theory, and on improved exponential time exact algorithms for the subset sum problem, among his many other research results.

Michael Randolph Garey is a computer science researcher, and co-author ( with David S. Johnson ) of Computers and Intractability: A Guide to the Theory of NP-completeness.

Karp's reduction also implies the NP-completeness of the feedback vertex set problem on undirected graphs, where the problem stays NP-hard on graphs of maximum degree four.

This demonstration drove interest in the study of NP-completeness and the P = NP problem.

ASR-complete is, by analogy to NP-completeness in complexity theory, a term to indicate that the difficulty of a computational problem is equivalent to solving the central Automatic Speech Recognition problem, i. e. recognize and understanding spoken language.

Note that unlike NP-completeness, this term is typically used more informally.

Yet it is not only Europe the play refers to.

He mentions the beats only once '', when he refers to their having revived through mere power and abandonment and the unwillingness to, commit death in life some idea of a decent equivalent between verbal expression and actual experience,, but the entire narrative, is written in the tiresome vocabulary `` of '' that lost `` and '' dying cause, `` and in the '' `` sprung syntax that is supposed to supplant, our mother, tongue.

For example, when the film is only four minutes old, Neitzbohr refers to a small, Victorian piano stool as `` Wilhelmina '', and we are thereupon subjected to a flashback that informs us that this very piano stool was once used by an epileptic governess whose name, of course, was Doris ( the English equivalent, when passed through middle-Gaelic derivations, of Wilhelmina ).

' Compositae ', an older but still valid name, means composite and refers to the characteristic inflorescence, a special type of pseudanthium found in only a few other angiosperm families.

For example, the word " Amerika " in German has a one-to-one equivalence to its meaning in modern English: it may denote North America, South America, or both, and in some instances refers to the United States only.

Likewise, the Esperanto word Ameriko refers only to the continent.

In his writings, Ambrose refers only to the performance of psalms, in which solo singing of psalm verses alternated with a congregational refrain called an antiphon.

However, the temple of Ares to which he refers had only been moved from Acharnes and re-sited in the Agora in Augustus's time, and statues known to derive from Alcamenes ' statue show the god in a breastplate, so the identification of Alcamenes ' Ares with the Ares Borghese is not secure.

Wace usually only refers to li roi (" the king ") without naming him, and someone has taken an early mention of Uther's epithet Pendragon as the name of his brother.

Allotropy refers only to different forms of an element within the same phase ( i. e. different solid, liquid or gas forms ); the changes of state between solid, liquid and gas in themselves are not considered allotropy.

The term " Islamic " refers not only to the religion, but to any form of art created in an Islamic culture or in an Islamic context.

The term " last rites " refers to administration to a dying person not only of this sacrament but also of Penance and Holy Communion, the last of which, when administered in such circumstances, is known as " Viaticum ", a word whose original meaning in Latin was " provision for the journey ".

The LAFTA agreement had important limitations: it only refers to goods, not to services, and it does not include a coordination of policies.

Likewise, " architecture " refers not only to the design of safe, functional buildings, but also to elements of creation and innovation which aim at elegant solutions to construction problems, to the use of space, and to the attempt to evoke an emotional response in the builders, owners, viewers and users of the building.

The bookkeeping process refers primarily to recording the financial effects of financial transactions only.

Sometimes the word country is used to refer both to sovereign states and to other political entities, while other times it refers only to states.

Esoteric Christianity is a term which refers to an ensemble of spiritual currents which regard Christianity as a mystery religion, and profess the existence and possession of certain esoteric doctrines or practices, hidden from the public but accessible only to a narrow circle of " enlightened ", " initiated ", or highly educated people.

In recent usage, especially in the context of environmental policy, the term " climate change " often refers only to changes in modern climate, including the rise in average surface temperature known as global warming.

Though nowadays most cardinals are also bishops, the term Cardinal bishops only refers to the cardinals that are titular bishops of one of the " suburbicarian " sees.

The more general term computer generated imagery encompasses both static scenes and dynamic images, while computer animation only refers to moving images.

However, U. S. law permits " blended " whisky to contain up to 80 % un-aged grain neutral spirits ( with an age statement on the label that refers only to the " straight " part of the blend ), while Canadian law requires that all of the spirits in a Canadian whisky be aged for at least three years.

) The notation " h / 2 " refers to the M < sub > 2 </ sub > C type structure described above, which is only an approximate description of the actual structures.

The only early Arab historian who mentions the Druze is the 11th century Christian scholar Yahya of Antioch, who clearly refers to the heretical group created by ad-Darazī rather than the followers of Hamza ibn ' Alī.

Dharma refers not only to the sayings of the Buddha, but also to the later traditions of interpretation and addition that the various schools of Buddhism have developed to help explain and to expand upon the Buddha's teachings.

For instance, the problem of integer factorization is suspected to require more than a polynomial function of the length of the input as run-time if the input is given in binary, but it only needs linear runtime if the input is presented in unary.

In this way, the program need only ask for a ScrollBar and, at run-time, it will be given the correct concrete element.

This would leave only a minimum of such bindings to change at run-time.

These are modules that may act not only during run-time but also compile time, thus making it possible to alter the language.

As such, many prototype-based systems encourage the alteration of prototypes during run-time, whereas only very few class-based object-oriented systems ( such as the dynamic object-oriented system, Common Lisp, Smalltalk, Objective-C, Python, Perl, or Ruby ) allow classes to be altered during the execution of a program.

In the long term, benchmarks, using real-life examples, provide the only real hope of resolving such conflicts-at least in terms of run-time efficiency.

For example, some parts of the executable may be reachable only through indirect branches, whose value is known only at run-time.

In addition, it can in some cases offer better performance than static compilation, as many optimizations are only feasible at run-time:

However, historically, if the type of a value is known only at run-time ; these languages are dynamically typed.

In C ++ 11 a special semantic-glyph "&&" exists, to denote the use / access of the expression's address for the compiler only, i. e. the address cannot be retrieved using the "&"– address-of – operator during the run-time of the program ( see the use of move semantics ).

The fact that the compiler and compiler subroutines are available at run-time ( a requirement for incremental compilation ) gives it the ability to support a far wider range of extensions than would be possible using only a macro facility.

Delegation has the advantage that it can take place at run-time and affect only a subset of entities of some type and can even be removed at run-time.

SOM prevents these issues by providing only late binding, to allow the run-time linker to re-build the table on the fly.

In number theory, Dixon's factorization method ( also Dixon's random squares method or Dixon's algorithm ) is a general-purpose integer factorization algorithm ; it is the prototypical factor base method, and the only factor base method for which a run-time bound not reliant on conjectures about the smoothness properties of values of a polynomial is known.

* RSTS / E ( synchronous only, emulated by the RSX run-time system )

Another disadvantage is that some utilities can no longer identify run-time library dependencies, as only the statically linked extractor stub is visible.

This model, analogous to the familiar model of client web browsers downloading a website piecemeal as-needed at run-time, permits simple, efficient distribution and maintenance of applications and relies only on the ubiquitous web server and the Yoix interpreter.

Such constraints could include not only constraints imposed by the chosen architecture but also any non-functional – technological or environmental – constraints, such as transaction throughput, response time, run-time platform, development environment, or those inherent in the programming language.