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HFST : The library functions as an interchanging interface to multiple backends, such as OpenFST, foma and SFST. The utilities comprise various compilers, such as hfst-twolc (a compiler for morphological two-level rules), hfst-lexc (a compiler for lexicon definitions) and hfst-regexp2fst (a regular expression compiler)... |
HFST : HFST has been used for writing various linguistic tools, such as spell-checkers, hyphenators, and morphologies. Morphological dictionaries written in other formalisms have also been converted to HFST's formats. |
HFST : Foma (software) |
HFST : Official website https://github.com/hfst/hfst/wiki - A documentation wiki |
HFST : Lindén, Krister; Axelson, Erik; Drobac, Senka; Hardwick, Sam; Kuokkala, Juha; Niemi, Jyrki; Pirinen, Tommi; Silfverberg, Miikka (2013). "HFST - A System for Creating NLP Tools". In Mahlow, Cerstin; Piotrowski, Michael (eds.). Systems and Frameworks for Computational Morphology. Systems and Frameworks for Computa... |
Kleene's algorithm : In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular lan... |
Kleene's algorithm : According to Gross and Yellen (2004), the algorithm can be traced back to Kleene (1956). A presentation of the algorithm in the case of deterministic finite automata (DFAs) is given in Hopcroft and Ullman (1979). The presentation of the algorithm for NFAs below follows Gross and Yellen (2004). Give... |
Kleene's algorithm : The automaton shown in the picture can be described as M = (Q, Σ, δ, q0, F) with the set of states Q = , the input alphabet Σ = , the transition function δ with δ(q0,a)=q0, δ(q0,b)=q1, δ(q1,a)=q2, δ(q1,b)=q1, δ(q2,a)=q1, and δ(q2,b)=q1, the start state q0, and set of accept states F = . Kleene's al... |
Kleene's algorithm : Floyd–Warshall algorithm — an algorithm on weighted graphs that can be implemented by Kleene's algorithm using a particular Kleene algebra Star height problem — what is the minimum stars' nesting depth of all regular expressions corresponding to a given DFA? Generalized star height problem — if a c... |
Krohn–Rhodes theory : In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and finite simple gro... |
Krohn–Rhodes theory : Let T be a semigroup. A semigroup S that is a homomorphic image of a subsemigroup of T is said to be a divisor of T. The Krohn–Rhodes theorem for finite semigroups states that every finite semigroup S is a divisor of a finite alternating wreath product of finite simple groups, each a divisor of S,... |
Krohn–Rhodes theory : The Krohn–Rhodes complexity (also called group complexity or just complexity) of a finite semigroup S is the least number of groups in a wreath product of finite groups and finite aperiodic semigroups of which S is a divisor. All finite aperiodic semigroups have complexity 0, while non-trivial fin... |
Krohn–Rhodes theory : At a conference in 1962, Kenneth Krohn and John Rhodes announced a method for decomposing a (deterministic) finite automaton into "simple" components that are themselves finite automata. This joint work, which has implications for philosophy, comprised both Krohn's doctoral thesis at Harvard Unive... |
Krohn–Rhodes theory : Semigroup action Transformation semigroup Green's relations |
Krohn–Rhodes theory : Rhodes, John L. (2010). Chrystopher L. Nehaniv (ed.). Applications of automata theory and algebra: via the mathematical theory of complexity to biology, physics, psychology, philosophy, and games. World Scientific Pub Co Inc. ISBN 978-981-283-696-0. Rhodes, John; Steinberg, Benjamin (2008-12-17). ... |
Krohn–Rhodes theory : Prof. John L. Rhodes, University of California at Berkeley webpage SgpDec: Hierarchical Composition and Decomposition of Permutation Groups and Transformation Semigroups, developed by A. Egri-Nagy and C. L. Nehaniv. Open-source software package for the GAP computer algebra system. John L. Rhodes (... |
Laws of Form : Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems: The primary arithmetic (described in Chapter 4 of LoF), whose models include Boolean arithmetic; The primary algeb... |
Laws of Form : The preface states that the work was first explored in 1959, and Spencer Brown cites Bertrand Russell as being supportive of his endeavour. He also thanks J. C. P. Miller of University College London for helping with the proofreading and offering other guidance. In 1963 Spencer Brown was invited by Harry... |
Laws of Form : Ostensibly a work of formal mathematics and philosophy, LoF became something of a cult classic: it was praised by Heinz von Foerster when he reviewed it for the Whole Earth Catalog. Those who agree point to LoF as embodying an enigmatic "mathematics of consciousness", its algebraic symbolism capturing an... |
Laws of Form : The symbol: Also called the "mark" or "cross", is the essential feature of the Laws of Form. In Spencer-Brown's inimitable and enigmatic fashion, the Mark symbolizes the root of cognition, i.e., the dualistic Mark indicates the capability of differentiating a "this" from "everything else but this". In Lo... |
Laws of Form : The syntax of the primary arithmetic goes as follows. There are just two atomic expressions: The empty Cross ; All or part of the blank page (the "void"). There are two inductive rules: A Cross may be written over any expression; Any two expressions may be concatenated. The semantics of the primary arith... |
Laws of Form : Chapter 11 of LoF introduces equations of the second degree, composed of recursive formulae that can be seen as having "infinite" depth. Some recursive formulae simplify to the marked or unmarked state. Others "oscillate" indefinitely between the two states depending on whether a given depth is even or o... |
Laws of Form : Gottfried Leibniz, in memoranda not published before the late 19th and early 20th centuries, invented Boolean logic. His notation was isomorphic to that of LoF: concatenation read as conjunction, and "non-(X)" read as the complement of X. Recognition of Leibniz's pioneering role in algebraic logic was fo... |
Laws of Form : 1969. London: Allen & Unwin, hardcover. ISBN 0-04-510028-4 1972. Crown Publishers, hardcover: ISBN 0-517-52776-6 1973. Bantam Books, paperback. ISBN 0-553-07782-1 1979. E. P. Dutton, paperback. ISBN 0-525-47544-3 1994. Portland, Oregon: Cognizer Company, paperback. ISBN 0-9639899-0-1 1997 German translat... |
Laws of Form : Boolean algebra – Algebraic manipulation of "true" and "false" Boolean algebras canonically defined – Technical treatment of Boolean algebras Entitative graph – Type of diagrammatic notation for propositional logicPages displaying short descriptions of redirect targets Existential graph – Type of diagram... |
Laws of Form : Laws of Form, archive of website by Richard Shoup. Spencer-Brown's talks at Esalen, 1973. Self-referential forms are introduced in the section entitled "Degree of Equations and the Theory of Types". Audio recording of the opening session, 1973 AUM Conference at Esalen. Louis H. Kauffman, "Box Algebra, Bo... |
Levenshtein automaton : In computer science, a Levenshtein automaton for a string w and a number n is a finite-state automaton that can recognize the set of all strings whose Levenshtein distance from w is at most n. That is, a string x is in the formal language recognized by the Levenshtein automaton if and only if x ... |
Levenshtein automaton : Levenshtein automata may be used for spelling correction, by finding words in a given dictionary that are close to a misspelled word. In this application, once a word is identified as being misspelled, its Levenshtein automaton may be constructed, and then applied to all of the words in the dict... |
Levenshtein automaton : For any fixed constant n, the Levenshtein automaton for w and n may be constructed in time O(|w|). Mitankin studies a variant of this construction called the universal Levenshtein automaton, determined only by a numeric parameter n, that can recognize pairs of words (encoded in a certain way by ... |
Levenshtein automaton : agrep, tool (implemented several times) for approximate regular expression matching TRE, library for regular expression matching that is tolerant to Levenshtein-style edits == References == |
Lex (software) : Lex is a computer program that generates lexical analyzers ("scanners" or "lexers"). It is commonly used with the yacc parser generator and is the standard lexical analyzer generator on many Unix and Unix-like systems. An equivalent tool is specified as part of the POSIX standard. Lex reads an input st... |
Lex (software) : Lex was originally written by Mike Lesk and Eric Schmidt and described in 1975. In the following years, Lex became standard lexical analyzer generator on many Unix and Unix-like systems. In 1983, Lex was one of several UNIX tools available for Charles River Data Systems' UNOS operating system under Bel... |
Lex (software) : The structure of a Lex file is intentionally similar to that of a yacc file: files are divided into three sections, separated by lines that contain only two percent signs, as follows: The definitions section defines macros and imports header files written in C. It is also possible to write any C code h... |
Lex (software) : The following is an example Lex file for the flex version of Lex. It recognizes strings of numbers (positive integers) in the input, and simply prints them out. If this input is given to flex, it will be converted into a C file, lex.yy.c. This can be compiled into an executable which matches and output... |
Lex (software) : Flex lexical analyser Yacc Ragel PLY (Python Lex-Yacc) Comparison of parser generators |
Lex (software) : Using Flex and Bison at Macworld.com lex(1) – Solaris 11.4 User Commands Reference Manual lex(1) – Plan 9 Programmer's Manual, Volume 1 |
Mealy machine : In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs. This is in contrast to a Moore machine, whose output values are determined solely by its current state. A Mealy machine is a deterministic finite-s... |
Mealy machine : The Mealy machine is named after George H. Mealy, who presented the concept in a 1955 paper, "A Method for Synthesizing Sequential Circuits". |
Mealy machine : A Mealy machine is a 6-tuple ( S , S 0 , Σ , Λ , T , G ) ,\Sigma ,\Lambda ,T,G) consisting of the following: a finite set of states S a start state (also called initial state) S 0 which is an element of S a finite set called the input alphabet Σ a finite set called the output alphabet Λ a transitio... |
Mealy machine : Mealy machines tend to have fewer states: Different outputs on arcs (n2) rather than states (n). When implemented as electronic circuits (rather than as mathematical abstractions or code): Moore machines are safer to use than Mealy machines: Outputs change at the clock edge (always one cycle later). In ... |
Mealy machine : The state diagram for a Mealy machine associates an output value with each transition edge, in contrast to the state diagram for a Moore machine, which associates an output value with each state. When the input and output alphabet are both Σ, one can also associate to a Mealy automata a Helix directed g... |
Mealy machine : Mealy machines provide a rudimentary mathematical model for cipher machines. Considering the input and output alphabet the Latin alphabet, for example, then a Mealy machine can be designed that given a string of letters (a sequence of inputs) can process it into a ciphered string (a sequence of outputs)... |
Mealy machine : Synchronous circuit Moore machine Algorithmic state machine Richards controller |
Mealy machine : Mealy, George H. (1955). A Method for Synthesizing Sequential Circuits. Bell System Technical Journal. pp. 1045–1079. Holcombe, W.M.L. (1982). Algebraic automata theory. Cambridge Studies in Advanced Mathematics. Vol. 1. Cambridge University Press. ISBN 0-521-60492-3. Zbl 0489.68046. Roth, Charles H. Jr... |
Mealy machine : Media related to Mealy machine at Wikimedia Commons |
Moore machine : In the theory of computation, a Moore machine is a finite-state machine whose current output values are determined only by its current state. This is in contrast to a Mealy machine, whose output values are determined both by its current state and by the values of its inputs. Like other finite state mach... |
Moore machine : A Moore machine can be defined as a 6-tuple ( S , s 0 , Σ , O , δ , G ) ,\Sigma ,O,\delta ,G) consisting of the following: A finite set of states S A start state (also called initial state) s 0 which is an element of S A finite set called the input alphabet Σ A finite set called the output alphabet ... |
Moore machine : As Moore and Mealy machines are both types of finite-state machines, they are equally expressive: either type can be used to parse a regular language. The difference between Moore machines and Mealy machines is that in the latter, the output of a transition is determined by the combination of current st... |
Moore machine : Types according to number of inputs/outputs. |
Moore machine : In Moore's 1956 paper "Gedanken-experiments on Sequential Machines", the ( n ; m ; p ) automata (or machines) S are defined as having n states, m input symbols and p output symbols. Nine theorems are proved about the structure of S , and experiments with S . Later, " S machines" became known as ... |
Moore machine : Synchronous circuit Mealy machine Algorithmic state machine Autonomous system (mathematics) |
Moore machine : Conway, J.H. (1971). Regular algebra and finite machines. London: Chapman and Hall. ISBN 0-412-10620-5. Zbl 0231.94041. Moore E. F. Gedanken-experiments on Sequential Machines. Automata Studies, Annals of Mathematical Studies, 34, 129–153. Princeton University Press, Princeton, N.J.(1956). Karatsuba A. ... |
Moore machine : Media related to Moore machine at Wikimedia Commons |
Muller automaton : In automata theory, a Muller automaton is a type of an ω-automaton. The acceptance condition separates a Muller automaton from other ω-automata. The Muller automaton is defined using a Muller acceptance condition, i.e. the set of all states visited infinitely often must be an element of the acceptanc... |
Muller automaton : Formally, a deterministic Muller-automaton is a tuple A = (Q,Σ,δ,q0,F) that consists of the following information: Q is a finite set. The elements of Q are called the states of A. Σ is a finite set called the alphabet of A. δ: Q × Σ → Q is a function, called the transition function of A. q0 is an ele... |
Muller automaton : The Muller automata are equally expressive as parity automata, Rabin automata, Streett automata, and non-deterministic Büchi automata, to mention some, and strictly more expressive than the deterministic Büchi automata. The equivalence of the above automata and non-deterministic Muller automata can b... |
Muller automaton : Following is a list of automata constructions that each transforms a type of ω-automata to a non-deterministic Muller automaton. From Büchi automata If B is the set of final states in a Büchi automaton with the set of states Q , we can construct a Muller automaton with same set of states, transitio... |
Muller automaton : From Büchi automaton McNaughton's theorem provides a procedure to transform any non-deterministic Büchi automaton into a deterministic Muller automaton. |
Muller automaton : Automata on Infinite Words Slides for a tutorial by Paritosh K. Pandya. Yde Venema (2008) Lectures on the Modal μ-calculus; the 2006 version was presented at The 18th European Summer School in Logic, Language and Information |
Myhill–Nerode theorem : In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957 (Nerode & Sauer 1957, p. ii). |
Myhill–Nerode theorem : Given a language L , and a pair of strings x and y , define a distinguishing extension to be a string z such that exactly one of the two strings x z and y z belongs to L . Define a relation ∼ L on strings as x ∼ L y \ y if there is no distinguishing extension for x and y . It is easy t... |
Myhill–Nerode theorem : The Myhill–Nerode theorem may be used to show that a language L is regular by proving that the number of equivalence classes of ∼ L is finite. This may be done by an exhaustive case analysis in which, beginning from the empty string, distinguishing extensions are used to find additional equiva... |
Myhill–Nerode theorem : The Myhill–Nerode theorem can be generalized to tree automata. |
Myhill–Nerode theorem : Pumping lemma for regular languages, an alternative method for proving that a language is not regular. The pumping lemma may not always be able to prove that a language is not regular. Syntactic monoid |
Myhill–Nerode theorem : Hopcroft, John E.; Ullman, Jeffrey D. (1979), "Chapter 3.4", Introduction to Automata Theory, Languages, and Computation, Reading, Massachusetts: Addison-Wesley Publishing, ISBN 0-201-02988-X. Nerode, Anil (1958), "Linear Automaton Transformations", Proceedings of the American Mathematical Socie... |
Myhill–Nerode theorem : Bakhadyr Khoussainov; Anil Nerode (6 December 2012). Automata Theory and its Applications. Springer Science & Business Media. ISBN 978-1-4612-0171-7. |
NFA minimization : In automata theory (a branch of theoretical computer science), NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states, transitions, or both. While efficient algorithms exist for DFA minimization, NFA mini... |
NFA minimization : Unlike deterministic finite automata, minimal NFAs may not be unique. There may be multiple NFAs of the same size which accept the same regular language, but for which there is no equivalent NFA or DFA with fewer states. |
NFA minimization : A modified C# implementation of Kameda-Weiner (1970) [1] |
Nondeterministic finite automaton : In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its source state and input symbol, and reading an input symbol is required for each state transition. A nondeterministic finite automaton ... |
Nondeterministic finite automaton : There are at least two equivalent ways to describe the behavior of an NFA. The first way makes use of the nondeterminism in the name of an NFA. For each input symbol, the NFA transitions to a new state until all input symbols have been consumed. In each step, the automaton nondetermi... |
Nondeterministic finite automaton : For a more elementary introduction of the formal definition, see automata theory. |
Nondeterministic finite automaton : The following automaton M, with a binary alphabet, determines if the input ends with a 1. Let M = ( , , δ , p , ) ,\,\delta ,p,\) where the transition function δ can be defined by this state transition table (cf. upper left picture): State Input 0 1 p q ∅ ∅ _\quad ^&0&1\\\hline... |
Nondeterministic finite automaton : A deterministic finite automaton (DFA) can be seen as a special kind of NFA, in which for each state and symbol, the transition function has exactly one state. Thus, it is clear that every formal language that can be recognized by a DFA can be recognized by an NFA. Conversely, for ea... |
Nondeterministic finite automaton : Nondeterministic finite automaton with ε-moves (NFA-ε) is a further generalization to NFA. In this kind of automaton, the transition function is additionally defined on the empty string ε. A transition without consuming an input symbol is called an ε-transition and is represented in ... |
Nondeterministic finite automaton : The set of languages recognized by NFAs is closed under the following operations. These closure operations are used in Thompson's construction algorithm, which constructs an NFA from any regular expression. They can also be used to prove that NFAs recognize exactly the regular langua... |
Nondeterministic finite automaton : The machine starts in the specified initial state and reads in a string of symbols from its alphabet. The automaton uses the state transition function Δ to determine the next state using the current state, and the symbol just read or the empty string. However, "the next state of an N... |
Nondeterministic finite automaton : There are many ways to implement a NFA: Convert to the equivalent DFA. In some cases this may cause exponential blowup in the number of states. Keep a set data structure of all states which the NFA might currently be in. On the consumption of an input symbol, unite the results of the... |
Nondeterministic finite automaton : One can solve in linear time the emptiness problem for NFA, i.e., check whether the language of a given NFA is empty. To do this, we can simply perform a depth-first search from the initial state and check if some final state can be reached. It is PSPACE-complete to test, given an NF... |
Nondeterministic finite automaton : NFAs and DFAs are equivalent in that if a language is recognized by an NFA, it is also recognized by a DFA and vice versa. The establishment of such equivalence is important and useful. It is useful because constructing an NFA to recognize a given language is sometimes much easier th... |
Nondeterministic finite automaton : Deterministic finite automaton Two-way nondeterministic finite automaton Pushdown automaton Nondeterministic Turing machine |
Nondeterministic finite automaton : Rabin, M. O.; Scott, D. (April 1959). "Finite Automata and Their Decision Problems". IBM Journal of Research and Development. 3 (2): 114–125. doi:10.1147/rd.32.0114. Sipser, Michael (1997). Introduction to the Theory of Computation (1st ed.). PWS Publishing. ISBN 978-0-534-94728-6. (... |
Ω-automaton : In automata theory, a branch of theoretical computer science, an ω-automaton (or stream automaton) is a variation of a finite automaton that runs on infinite, rather than finite, strings as input. Since ω-automata do not stop, they have a variety of acceptance conditions rather than simply a set of accept... |
Ω-automaton : Formally, a deterministic ω-automaton is a tuple A = (Q,Σ,δ,Q0,Acc) that consists of the following components: Q is a finite set. The elements of Q are called the states of A. Σ is a finite set called the alphabet of A. δ: Q × Σ → Q is a function, called the transition function of A. Q0 is an element of Q... |
Ω-automaton : Formally, a nondeterministic ω-automaton is a tuple A = (Q,Σ,Δ,Q0,Acc) that consists of the following components: Q is a finite set. The elements of Q are called the states of A. Σ is a finite set called the alphabet of A. Δ is a subset of Q × Σ × Q and is called the transition relation of A. Q0 is a subs... |
Ω-automaton : Acceptance conditions may be infinite sets of ω-words. However, people mostly study acceptance conditions that are finitely representable. The following lists a variety of popular acceptance conditions. Before discussing the list, let's make the following observation. In the case of infinitely running sys... |
Ω-automaton : The following ω-language L over the alphabet Σ = , which can be recognized by a nondeterministic Büchi automaton: L consists of all ω-words in Σω in which 1 occurs only finitely many times. A non-deterministic Büchi automaton recognizing L needs only two states q0 (the initial state) and q1. Δ consists of... |
Ω-automaton : An ω-language over a finite alphabet Σ is a set of ω-words over Σ, i.e. it is a subset of Σω. An ω-language over Σ is said to be recognized by an ω-automaton A (with the same alphabet) if it is the set of all ω-words accepted by A. The expressive power of a class of ω-automata is measured by the class of ... |
Ω-automaton : Because nondeterministic Muller, Rabin, Streett, parity, and Büchi automata are equally expressive, they can be translated to each other. Let us use the following abbreviation × \times \ : for example, NB stands for nondeterministic Büchi ω-automaton, while DP stands for deterministic parity ω-automaton... |
Ω-automaton : ω-automata can be used to prove decidability of S1S, the monadic second-order (MSO) theory of natural numbers under successor. Infinite-tree automata extend ω-automata to infinite trees and can be used to prove decidability of S2S, the MSO theory with two successors, and this can be extended to the MSO th... |
Ω-automaton : Farwer, Berndt (2002), "ω-Automata", in Grädel, Erich; Thomas, Wolfgang; Wilke, Thomas (eds.), Automata, Logics, and Infinite Games, Lecture Notes in Computer Science, Springer, pp. 3–21, ISBN 978-3-540-00388-5. Perrin, Dominique; Pin, Jean-Éric (2004), Infinite Words: Automata, Semigroups, Logic and Game... |
Permutation automaton : In automata theory, a permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states. Formally, a deterministic finite automaton A may be defined by the tuple (Q, Σ, δ, q0, F), where Q is the set of states of the automat... |
Permutation automaton : The pure-group languages were the first interesting family of regular languages for which the star height problem was proved to be computable. Another mathematical problem on regular languages is the separating words problem, which asks for the size of a smallest deterministic finite automaton t... |
Powerset construction : In the theory of computation and automata theory, the powerset construction or subset construction is a standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) which recognizes the same formal language. It is important in theory becaus... |
Powerset construction : To simulate the operation of a DFA on a given input string, one needs to keep track of a single state at any time: the state that the automaton will reach after seeing a prefix of the input. In contrast, to simulate an NFA, one needs to keep track of a set of states: all of the states that the a... |
Powerset construction : The powerset construction applies most directly to an NFA that does not allow state transformations without consuming input symbols (aka: "ε-moves"). Such an automaton may be defined as a 5-tuple (Q, Σ, T, q0, F), in which Q is the set of states, Σ is the set of input symbols, T is the transitio... |
Powerset construction : The NFA below has four states; state 1 is initial, and states 3 and 4 are accepting. Its alphabet consists of the two symbols 0 and 1, and it has ε-moves. The initial state of the DFA constructed from this NFA is the set of all NFA states that are reachable from state 1 by ε-moves; that is, it i... |
Powerset construction : Because the DFA states consist of sets of NFA states, an n-state NFA may be converted to a DFA with at most 2n states. For every n, there exist n-state NFAs such that every subset of states is reachable from the initial subset, so that the converted DFA has exactly 2n states, giving Θ(2n) worst-... |
Powerset construction : Brzozowski's algorithm for DFA minimization uses the powerset construction, twice. It converts the input DFA into an NFA for the reverse language, by reversing all its arrows and exchanging the roles of initial and accepting states, converts the NFA back into a DFA using the powerset constructio... |
Powerset construction : Anderson, James Andrew (2006). Automata theory with modern applications. Cambridge University Press. pp. 43–49. ISBN 978-0-521-84887-9. |
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