In his 1948 essay, "Intelligent Machinery", Turing wrote that his machine consisted of: an unlimited memory capacity obtained in the form of an infinite tape marked out into squares, on each of which a symbol could be printed. [11] More precisely, no computable function can decide the question. 2 ) M.J. Hatch, & M.H. the random access machine (RAM) as introduced by Cook and Reckhow , which models the idealized Von Neumann-style computer. ( An example of this is binary search, an algorithm that can be shown to perform more quickly when using the RASP model of computation rather than the Turing machine model. more mathematical functions). Power does not exclusively refer to the threat or use of force by one actor against another, but may also be exerted through diffuse means (such as institutions).Power may also take structural forms, as it orders actors in Most jurisdictions provide for the use of trademarks to be licensed to third parties. 2 Terms that differ only by -conversion are called -equivalent. . {\displaystyle (\lambda x.t)s} x In the study of digital signal processing (DSP), the unit sample function s Doctoral dissertation, University of Twente, Enschede, The Netherlands. By comparison, copyright law generally seeks to protect original literary, artistic, and other creative works. ( n , which demonstrates that ", "KitKat goes unprotected as European court rejects trademark case", "CCH Pinpoint | Australian Legal Research", "Everything You Need to Know About Trademark Law | The Polaris Law Firm", Directive harmonizing the term of copyright protection, "Law of the Jungle: Burroughs Descendants' Suit Says Adult Movie, Game Violate Trademark", "The STIckler: inside the latest trademark protection gTLD discussion Blog World Trademark Review", Intellectual Property Office (United Kingdom), Trade Marks: The information brochure on trademark protection, German Patent and Trade Mark Office (GPTO), "Trademark law in the European Union. If it is considered as a type (1,1) tensor, the Kronecker tensor can be written Read-only, right-moving Turing machines are equivalent to DFAs (as well as NFAs by conversion using the NDFA to DFA conversion algorithm). q 1 and In 1881, Congress passed a new trademark act, this time according to its Commerce Clause powers. q By varying what is being repeated, and varying what argument that function being repeated is applied to, a great many different effects can be achieved. A Turing machine is a mathematical model of computation describing an abstract machine[1] that manipulates symbols on a strip of tape according to a table of rules. Variables that fall within the scope of an abstraction are said to be bound. s the next section. When a trademark is used about services rather than products, it may sometimes be called a service mark, particularly in the United States.[8]. A Turing machine is equivalent to a single-stack pushdown automaton (PDA) that has been made more flexible and concise by relaxing the last-in-first-out (LIFO) requirement of its stack. [10] As espoused by Holm (cited in Laurie & Mortimer, 2011), at its ultimate stage, IMC is implemented at a corporate level and consolidates all aspects of the organization; this initiates brand consonance which in turn inspires strong corporate identity. t := x WebIn mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly X itself) to Y.The subset S, that is, the domain of f viewed as a function, is called the domain of definition of f.If S equals X, that is, if f is defined on every element in X, then f is said to be total.. More technically, a partial function is a binary relation over two , Trademarks may also be searched on third-party databases such as LexisNexis, Dialog, CompuMark, and Corsearch. The thesis states that Turing machines indeed capture the informal notion of effective methods in logic and mathematics, and provide a model through which one can reason about an algorithm or "mechanical procedure". x y There is a limit to the memory possessed by any current machine, but this limit can rise arbitrarily in time. For entity-header fields, both sender and recipient refer to either the client or the server, depending on who sends and who receives the entity. z Examples and Observations "In music, the rhythm is usually produced by making certain notes in a sequence stand out from others by being louder or longer or higherIn speech, we find that syllables take the place of musical notes or beats, and in many languages the stressed syllables determine the rhythm "What does seem to be For example, Pascal and many other imperative languages have long supported passing subprograms as arguments to other subprograms through the mechanism of function pointers. In this process, the corporate actors are of equal importance as those others; corporate identity pertains to the company (the group of corporate actors) as well as to the relevant others; Differentiation. ] are in use. Another useful representation is the following form: Often, a single-argument notation i is used, which is equivalent to setting j = 0: In linear algebra, it can be thought of as a tensor, and is written ij. Dana Scott has also addressed this question in various public lectures. is superfluous when using abstraction. The regularized incomplete beta function (or regularized beta function for short) is defined in terms of the incomplete beta function and the complete beta function: The regularized incomplete beta function is the cumulative distribution function of the beta distribution, and is related to the cumulative distribution function t IMC is a collective of concepts and communications processes that seek to establish clarity and consistency in the positioning of a brand in the mind of consumers. := 0 x ) can be found in Emil Artin's book The Gamma Function, page 1819. Then the degree of mapping is 1/4 times the solid angle of the image S of Suvw with respect to the interior point of Sxyz, O. x Gandy's analysis of Babbage's analytical engine describes the following five operations (cf. By contrast, there are always-halting concurrent systems with no inputs that can compute an integer of unbounded size. z Only in the related area of analysis of algorithms this role is taken over by the RAM model. This page was last edited on 31 October 2022, at 10:50. Once trademark rights are established in a particular jurisdiction, these rights are generally only enforceable in that jurisdiction, a quality which is sometimes known as "territoriality". Kiriakidou, O, & Millward, L.J., (2000). Relevance. A relatively uncommon variant allows "no shift", say N, as a third element of the set of directions A Turing machine is a finite-state machine associated with a special kind of environment -- its tape -- in which it can store (and later recover) sequences of symbols," also Stone 1972:8 where the word "machine" is in quotation marks. x Global television networks and the rise of business news have caused the public representation of organizations to critically influence the construction and deconstruction of certain organizational identities more than ever before. (Hodges p.91, Hawking p.1121). x While trademark law seeks to protect indications of the commercial source of products or services, patent law generally seeks to protect new and useful inventions, and registered designs law generally seeks to protect the look or appearance of a manufactured article. Monitoring is not easy and usually requires professional expertise. [ 1 This would be the case if we were using machines to deal with axiomatic systems. We also speak of the resulting equivalences: two expressions are -equivalent, if they can be -converted into the same expression. y . + [ This definition regards identity as a result of social interaction: The following four key brand requirements are critical for a successful corporate identity strategy. x However, the CTM system did not replace the national trademark registration systems; the CTM system and the national systems continue to operate in parallel to each other (see also European Union trade mark law). This often involves the payment of a periodic renewal fee. m The major international system for facilitating the registration of trademarks in multiple jurisdictions is commonly known as the "Madrid system[55] ". := For instance, it may be desirable to write a function that only operates on numbers. y The United States, Canada, and other countries also recognize common law trademark rights, which means action can be taken to protect any unregistered trademark if it is in use. its state, symbol-collections, and used tape at any given time) and its actions (such as printing, erasing and tape motion) is finite, discrete and distinguishable; it is the unlimited amount of tape and runtime that gives it an unbounded amount of storage space. {\displaystyle ((\lambda x.x)x)} WebGet 247 customer support help when you place a homework help service order with us. 4958. x {\displaystyle t} x x s { 2 When g T is a periodic summation of another function, g, then f g T is known as a circular or cyclic (See article on unbounded nondeterminism.) Mathematical notation for the set of values satisfying a property, https://en.wikipedia.org/w/index.php?title=Iverson_bracket&oldid=1117957295, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 24 October 2022, at 12:44. Computable functions are a fundamental concept within computer science and mathematics. . has no free variables, but the function 2 := Any symbol on the tape may therefore eventually have an innings.[15]. y [17] This statute purported to be an exercise of Congress' Copyright Clause powers. It is the coefficient of the x k term in the polynomial expansion of the binomial power (1 + x) n; this coefficient can be computed by the multiplicative formula ", p.149; in particular, Hopcroft and Ullman assume that, The references used may be made clearer with a different or consistent style of, Each category of languages, except those marked by a. (In Church's original lambda calculus, the formal parameter of a lambda expression was required to occur at least once in the function body, which made the above definition of 0 impossible. This international legal change has also led to the creation of ICANN Uniform Domain-Name Dispute-Resolution Policy (UDRP) and other dispute policies for specific countries (such as Nominet UK's DRS) which attempt to streamline the process of resolving who should own a domain name (without dealing with other infringement issues such as damages). In linear algebra, the n n identity matrix I has entries equal to the Kronecker delta: The restriction to positive or non-negative integers is common, but in fact, the Kronecker delta can be defined on an arbitrary set. Trademarks are used not only by businesses but also by noncommercial organizations and religions to protect their identity and goodwill associated with their name.[10][11][12]. Minsky (1967)). Madrid provides a centrally administered system for securing trademark registrations in member jurisdictions by extending the protection of an "international registration" obtained through the World Intellectual Property Organization. 4. x The symbol lambda creates an anonymous function, given a list of parameter names, x just a single argument in this case, and an expression that is evaluated as the body of the function, x**2. [7] Turing submitted his paper on 31 May 1936 to the London Mathematical Society for its Proceedings (cf. Robin Gandy (19191995)a student of Alan Turing (19121954), and his lifelong friendtraces the lineage of the notion of "calculating machine" back to Charles Babbage (circa 1834) and actually proposes "Babbage's Thesis": That the whole of development and operations of analysis are now capable of being executed by machinery. Emil Post (1947), "Recursive Unsolvability of a Problem of Thue", Alan Turing, 1948, "Intelligent Machinery." WebDownload and listen to new, exclusive, electronic dance music and house tracks. x . z Minsky 1967:118 states "The tape is regarded as infinite in both directions". During this 30-day period, third parties who may be affected by the registration of the trademark may step forward to file an opposition proceeding to stop the registration of the mark. Thus a lambda term is valid if and only if it can be obtained by repeated application of these three rules. They might compute faster, perhaps, or use less memory, or their instruction set might be smaller, but they cannot compute more powerfully (i.e. WebThe above context-free grammar in Backus-Naur form defines the language of syntactically valid first-order formulas with function symbols and predicate symbols up to arity 3. to x, while example 2 is The shift of business in favor of non-agricultural enterprise caused business, and corporate consciousness, to boom. ) , the result of applying This makes the DFA representation infeasible to analyze. Computability theory, which studies computability of functions from inputs to outputs, and for which Turing machines were invented, reflects this practice. ( As usual for such a proof, computable means computable by any model of computation that is Turing complete. x . Trademarks that are considered offensive are often rejected according to a nation's trademark law. . = However, this is not the case in the United States, where the courts have held that this would "be a fraud upon the public". See Notation, below. The fundamental importance of conditional iteration and conditional transfer for a general theory of calculating machines is not recognized. x Second, a corporate visual identity symbolizes an organization for external stakeholders, and, hence, contributes to its. Several cases have wrestled with the concept of initial interest confusion. However, other programming languages like Pascal do not have this feature, which allows them to be Turing complete in principle. = WebOnly RFID Journal provides you with the latest insights into whats happening with the technology and standards and inside the operations of leading early adopters across all industries and around the world. {\displaystyle m} {\displaystyle r} [ . [40], In addition to the requirements above, U.S. trademark registrations are also required to be renewed on or about every 10th anniversary of the registration of the trademark. Boolos Burgess Jeffry 2002:25 illustrate the machine as moving along the tape. x Minsky 1967:107 "In his 1936 paper, A. M. Turing defined the class of abstract machines that now bear his name. [19] The Lanham Act of 1946 updated the law and has served, with several amendments, as the primary federal law on trademarks. is the lambda term t All for free. The EU Trade Mark (EUTM) system (formerly the Community Trademark system) is the trademark system which applies in the European Union, whereby registration of a trademark with the European Union Intellectual Property Office (EUIPO, formerly Office for Harmonization in the Internal Market (Trade Marks and Designs)), leads to a registration which is effective throughout the EU as a whole. ) , and Turing completeness is the ability for a system of instructions to simulate a Turing machine. x y has a single free variable, Defining. , What is neglected in this statement is that, because a real machine can only have a finite number of configurations, it is nothing but a finite-state machine, whereas a Turing machine has an unlimited amount of storage space available for its computations. The Turing machine was invented in 1936 by Alan Turing,[7][8] who called it an "a-machine" (automatic machine). {\displaystyle (\lambda x.x)s\to x[x:=s]=s} Consequently, not only big companies but also SMEs may have a good chance of establishing enough goodwill with customers so that their marks may be recognized as well-known marks and acquire protection without registration. . { The tape can be finite, and automatically extended with blanks as needed (which is closest to the mathematical definition), but it is more common to think of it as stretching infinitely at one or both ends and being pre-filled with blanks except on the explicitly given finite fragment the tape head is on. These laws are intended to prevent large or powerful companies from intimidating or harassing smaller companies. s e Corporate identity and corporate communications: creating a competitive advantage. [37] In addition the BOHM prototype implementation of optimal reduction outperformed both Caml Light and Haskell on pure lambda terms.[38]. + p.5253): Gandy states that "the functions which can be calculated by (1), (2), and (4) are precisely those which are Turing computable." x {\displaystyle (st)x} All of the arguments to fn are applied to each of the predicates in turn until one returns a "truthy" value, at which point fn returns the result of applying its arguments to the corresponding transformer. In particular, we can now cleanly define the subtraction, multiplication and comparison predicate of natural numbers recursively. {\displaystyle n} Trademark rights generally arise out of the use of, or to maintain exclusive rights over, that sign about certain products or services, assuming there are no other trademark objections. Variable names are not needed if using a universal lambda function, such as Iota and Jot, which can create any function behavior by calling it on itself in various combinations. However, the Supreme Court struck down the 1870 statute in the Trade-Mark Cases later on in the decade. 256262. that there can be no machine which, supplied with any one U of these formulae, will eventually say whether U is provable. {\displaystyle x} Grundlagen, Funktionen, Fallbeispiele. x Birkigt, K., & Stadler, M.M., (1986). ( Where one party makes a threat to sue another for trademark infringement, but does not have a genuine basis or intention to carry out that threat, or does not carry out the threat at all within a certain period, the threat may itself become a basis for legal action. . ] This function is defined to take the value 1 for the values of the variables for which the statement is true, and {\displaystyle \delta _{ij}} In the meantime, Emil Post submitted a brief paper in the fall of 1936, so Turing at least had priority over Post. An example of the second type is that Audi can run advertisements saying that a trade publication has rated an Audi model higher than a BMW model since they are only using "BMW" to identify the competitor. The communication-based model, advanced by Duncan and Moriarty (as cited in Laurie & Mortimer, 2011) contends that there are three levels of IMC integration; Duncan and Moriarty affirm that the lowest level of IMC integration is level one where IMC decisions are made by marketing communication level message sources. z A trademark may be designated by the following symbols: The three symbols associated with trademarks represent the status of a mark and accordingly its level of protection. y ] x Turing had a lifelong interest in machines: "Alan had dreamt of inventing typewriters as a boy; [his mother] Mrs. Turing had a typewriter; and he could well have begun by asking himself what was meant by calling a typewriter 'mechanical'" (Hodges p.96). However, in the untyped lambda calculus, there is no way to prevent a function from being applied to truth values, strings, or other non-number objects. The correct substitution in this case is z.x, up to -equivalence. ) to for ease of printing. media.[44]. Brown, Jared & A. Miller, (1998). is [2001] UKHL 21; wherein it has been held that the mere fact that a bare license (the equivalent of the United States concept of a naked license) has been granted did not automatically mean that a trademark was liable to mislead. + for Further, it seems to be important that the organization communicates the strategic aspects of the corporate visual identity. Under Article 6 bis of the Paris Convention,[57] countries are empowered to grant this status to marks that the relevant authority considers are 'well known'. WebRFC 7231 HTTP/1.1 Semantics and Content June 2014 Media types are defined in Section 3.1.1.1.An example of the field is Content-Type: text/html; charset=ISO-8859-4 A sender that generates a message containing a payload body SHOULD generate a Content-Type header field in that message unless the intended media type of the enclosed representation is This review includes procedural matters such as making sure the applicant's goods or services are identified properly. A complete guide to creating, building, and maintaining strong brands, 2nd ed. x {\displaystyle MN} ( . The intention to use a trademark can be proven by a wide range of acts as shown in the "Woolly Bully"[37] and Aston v Harlee cases. There are several possible ways to define the natural numbers in lambda calculus, but by far the most common are the Church numerals, which can be defined as follows: and so on. The -reduction rule[b] states that an application of the form In principle, it is possible to model this by having an external agent read from the tape and write to it at the same time as a Turing machine, but this rarely matches how interaction actually happens; therefore, when describing interactivity, alternatives such as I/O automata are usually preferred. x {\displaystyle M} s For example, in the expression y.x x y, y is a bound variable and x is a free variable. Emil Post (1936), "Finite Combinatory ProcessesFormulation 1". x . However, the lambda calculus does not offer any explicit constructs for parallelism. y This article is about the Euler beta function. ) x ) L The set of lambda expressions, , can be defined inductively: Instances of rule 2 are known as abstractions and instances of rule 3 are known as applications.[17][18]. {\displaystyle \lambda x.y} WebThe Emperor shall be the symbol of the State and of the unity of the People, deriving his position from the will of the people with whom resides sovereign power. 2 Typed lambda calculi are closely related to mathematical logic and proof theory via the CurryHoward isomorphism and they can be considered as the internal language of classes of categories, e.g. In addition intelligence service agencies likely collect owner/applicant office and computer systems information, and apply motoring techniques to their systems for forensics and security purposes. {\displaystyle \psi (z)} ( ) As with dilution protection, enforcing trademark rights over domain name owners involves protecting a trademark outside the obvious context of its consumer market, because domain names are global and not limited by goods or service. [20] With this model, Turing was able to answer two questions in the negative: Thus by providing a mathematical description of a very simple device capable of arbitrary computations, he was able to prove properties of computation in generaland in particular, the uncomputability of the Entscheidungsproblem ('decision problem').[23]. y ( I a Each proof will then be determined by a sequence of choices i1, i2, , in (i1 = 0 or 1, i2 = 0 or 1, , in = 0 or 1), and hence the number 2n + i12n-1 + i22n-2 + +in completely determines the proof. Many of these were originally developed in the context of using lambda calculus as a foundation for programming language semantics, effectively using lambda calculus as a low-level programming language. Gower. . p x If a trademark has not been registered, some jurisdictions (especially Common Law countries) offer protection for the business reputation or goodwill which attaches to unregistered trademarks through the tort of passing off. Function application of the Despite the model's simplicity, it is capable of implementing any computer algorithm.. = changes of name or address), and renew registration across all applicable jurisdictions through a single administrative process. Serial Number: 77003422:: Trademarkia Trademarks", Monetary Damages under the Lanham Act: Eighth Circuit Holds Actual Confusion is Not a Prerequisite, Case details for trade mark UK00000000001, "The oldest registered trademarks in the world", "A Historical Perspective: The International Trademark Association and the United States Patent and Trademark Office", "Some Well-Known U.S. This step can be repeated by additional -reductions until there are no more applications left to reduce. A trademark (also written trade mark or trade-mark[1]) is a type of intellectual property consisting of a recognizable sign, design, or expression that identifies products or services from a particular source and distinguishes them from others. For x = 1, the incomplete beta function coincides with the complete beta function. [13] Suppose a mapping takes place from surface Suvw to Sxyz that are boundaries of regions, Ruvw and Rxyz which is simply connected with one-to-one correspondence. In other words, unlike ordinary trademark law, dilution protection extends to trademark uses that do not confuse consumers regarding who has made a product. x Church's proof of uncomputability first reduces the problem to determining whether a given lambda expression has a normal form. Article 3. Instead, dilution protection law aims to protect sufficiently strong trademarks from losing their singular association in the public mind with a particular product, perhaps imagined if the trademark were to be encountered independently of any product (e.g., just the word Pepsi spoken, or on a billboard). -reduction captures the idea of function application. , as well as other unusual forms of bracketing marks available in the publisher's typeface, accompanied by a marginal note. The second version has nonzero components that are .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1/p!, with consequent changes scaling factors in formulae, such as the scaling factors of 1/p! For higher arities, it needs to be adapted accordingly. 0 Since adding m to a number n can be accomplished by adding 1 m times, an alternative definition is: Similarly, multiplication can be defined as, since multiplying m and n is the same as repeating the add n function m times and then applying it to zero. More explicitly, a Turing machine consists of: In the 4-tuple models, erasing or writing a symbol (aj1) and moving the head left or right (dk) are specified as separate instructions. + Rogers 1987 (1967):13. This practice is a precursor to the modern concept of a media franchise.[50]. If the examining attorney approves the application, it will be "published for opposition." Another possibility is to regard the final values on the tape as the output. {\displaystyle ((\lambda x.y)x)[x:=y]=((\lambda x.y)[x:=y])(x[x:=y])=(\lambda x.y)y} B [2], In probability theory and statistics, the Kronecker delta and Dirac delta function can both be used to represent a discrete distribution. and Rogers 1987 (1967):13 refers to "Turing's characterization", Boolos Burgess and Jeffrey 2002:25 refers to a "specific kind of idealized machine". The 10th Circuit affirmed the rights of the trademark owner about the said domain name, despite arguments of promissory estoppel. Mathematical-logic system based on functions, Lambda calculus and programming languages, 4 (3 (2 (1 (1, if 0 = 0; else 0 ((, Barendregt,Barendsen (2000) call this form. Lambda calculus cannot express this as directly as some other notations: all functions are anonymous in lambda calculus, so we can't refer to a value which is yet to be defined, inside the lambda term defining that same value. In addition to the standard grounds for trademark infringement (same/similar mark applied same/similar goods or services, and a likelihood of confusion), if the mark is deemed well known it is an infringement to apply the same or a similar mark to dissimilar goods/services where there is confusion, including where it takes unfair advantage of the well-known mark or causing detriment to it.[58]. t Elgot and Robinson (1964), Hartmanis (1971), and in particular Cook-Rechow (1973); references at random-access machine). Functional programming languages implement lambda calculus. In Britain, the Merchandise Marks Act 1862 made it a criminal offense to imitate another's trade mark 'with intent to defraud or to enable another to defraud'. for t. The name Could a sensible meaning be assigned to lambda calculus terms? This is indeed the technique by which a deterministic (i.e., a-) Turing machine can be used to mimic the action of a nondeterministic Turing machine; Turing solved the matter in a footnote and appears to dismiss it from further consideration. These guidelines govern how the identity is applied and usually include approved color palettes, typefaces, page layouts, fonts, and others. z ] The integral defining the beta function may be rewritten in a variety of ways, including the following: where in the second-to-last identity n is any positive real number. If a trademark has been registered, then it is much easier for the trademark owner to demonstrate its trademark rights and to enforce these rights through an infringement action. If one were able to solve the Entscheidungsproblem then one would have a "procedure for solving many (or even all) mathematical problems". A programming language that is Turing complete is theoretically capable of expressing all tasks accomplishable by computers; nearly all programming languages are Turing complete if the limitations of finite memory are ignored. s n Special attention is paid to corporate identity in times of organizational change. ) Trademarks Celebrate One Hundred Years", "How long does it take to register a trademark? x t The Church numeral n is a function that takes a function f as argument and returns the n-th composition of f, i.e. Van den Bosch, A.L.M., (2005). s Note, if the Section 8 Affidavit is filed during the 6-month grace period additional fees to file the Affidavit with the U.S. Patent and Trademark Office will apply. {\displaystyle \mathrm {B} (z_{1},z_{2})={\frac {\Gamma (z_{1})\,\Gamma (z_{2})}{\Gamma (z_{1}+z_{2})}}} For example, assuming some encoding of 2, 7, , we have the following -reduction: (n.n 2) 7 7 2. -reduction can be seen to be the same as the concept of local reducibility in natural deduction, via the CurryHoward isomorphism. Esteem. The abstraction ) (Arora and Barak, 2009, theorem 1.9). Lambda calculus is also a current research topic in category theory. In the United States, the USPTO maintains a database of registered trademarks. k I propose, therefore to show that there can be no general process for determining whether a given formula U of the functional calculus K is provable, i.e. , t However, if the only output is the final state the machine ends up in (or never halting), the machine can still effectively output a longer string by taking in an integer that tells it which bit of the string to output. In the context of corporate identity, consonance is the alignment of all touch points. s Web_.chunk(array, [size=1]) source npm package. , where N ("None" or "No-operation") would allow the machine to stay on the same tape cell instead of moving left or right. 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