Michael A. Harrison. Introduction to Formal Language Theory, chapter 4. Addison-Wesley, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....automaton A. All these variables only need logarithmic space. We use the following routines: brother(h) returns the position of the right brother of h, or unde ned if h does not have a right brother. This value can be calculated in log space by counting, using the characterization of L from [17], see the proof of Lemma 2. f; q; i) where f 2 F , q 2 Q, and i 2 f1; arity(f)g, returns the state q such that if q(f(x 1 ; xn ) f(q 1 (x 1 ) q n (x n ) 2 R then q = q i . For instance for the term t above we have brother(2) 5. Finally we present the ....

M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, 1978.

....9 1 ; k 2 G , such that # = 1 k . Let k = k 1 and k : then the unique prime factorization of is 1 k . From Theorem 3.5 and 3.9 we immediately obtain the following theorem. Theorem 3.10. G is a free monoid over G . Thus we can apply [2] (Corollary of Theorem 1.3.3 and Theorem 1.3.4) and obtain: Theorem 3.11. Let # 1 ; # 2 2 G . Then (i) # 1 # 2 = # 2 # 1 y # 1 = # G and some k; l 2 N. ii) # 1 # 2 6= # 2 # 1 y f# 1 ; # 2 g is a free submonoid of G . 6 3.2 Pumping up ambiguity The de nition of pumping trees ....

....Let : fa; b; c; d; #g Let x 1 ; xn ; y 1 ; yn 2 fa; bg . And let P 1 : fS A; S Bg [ fA x j Adc j 1 j ng [ fB y j Adc P 2 : fA x j dc j 1 j ng [ fB y j dc P 2 : fA x j Cdc j 1 j ng [ fB y j Cdc j 1 j ng [ fC g: In [2] (Theorem 8.4.5) it is shown that the grammar G 1 : fS; A; B; g; P 1 [ P 2 ; S) is ambiguous if and only if the instance ( x 1 ; xn ) y 1 ; yn ) of Post Correspondence Problem has a solution. The same argument applies to G 2 : fS; A; B; Cg; P 1 [ P 2 ; S) We only ....

M.A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, 1978 12

....cyclic permutation. We prove here that the language L of Lyndon words over a two alphabet fa; bg is not context free. This is an easy consequence of Ogden s iteration lemma, and may constitute a good exercise in a course on Formal Languages. 2 Proof Recall that Ogden s iteration lemma (see e.g. [3]) states that, for every context free language L there exists an integer N such that, for any word w 2 L and for any choice of at least N distiguished positions in w, there exists a factorization w = x u y v z such that (1) either x; u; y each contain at least one distiguished position, or y; ....

M. Harrison. Introduction to Formal Language Theory. Addison-Wesley, 1978.

....will elaborate on this and show that, if the homomorphism is simple in the sense of [21] one can conclude that relative liveness properties that hold on the abstract system also hold on the concrete system. 3 Preliminaries For de ning our concepts, we need several notions from language theory [5, 7, 11, 24]. Let L be a language and let L be an language. De nition 3.1 The left quotient of L by a word w 2 is de ned by cont(w; L) fv 2 j wv 2 Lg. The left quotient of L by w 2 is similarly de ned by cont(w; L ) fx 2 j wx 2 L g. The left quotient describes ....

Harrison, M. A. Introduction to Formal Language Theory, rst ed. Addison-Wesley, Reading, Mass., 1978.

....analyze the more subtle point how many di#erent nested arc structures there are which can be associated with each such string. It is crucial here to observe that there is a one to one correspondence between nested arc structures and Dyck languages well known from formal language theory (e.g. cf. [15]) More precisely, each arc structure corresponds to a Dyck word over a two letter alphabet, namely opening and closing brackets. The number of ways to parenthesize is exactly given by the Catalan numbers (cf. e.g. 12] Thus, D(i) for even i) denoting the number of di#erent Dyck words of ....

M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesely Publishing Company. 1978.

....the form X am b, with m 2 (V [ C) Moreover, there is a bijection between the set A of colors and the set of productions. Thus, in a bracketed grammar, every derivation step is marked. Chomsky Sch utzenberger grammars are used in the proof of the ChomskySch utzenberger theorem (see e.g. [5]) even if they were never studied for their own. Here the terminal alphabet is of the form T = A[ A[B, and the productions are of the form X am a. Again, there is only one production for each color a 2 A. So it is a special kind of balanced grammar with nite number of productions. ....

Michael A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, Mass., 1978.

....i a for some n i 2 N. We de ne n = maxfn i j i 2 f1; kgg 1. Let R : a . Then L R = i=1 U i ) i=1 L i ) R = i=1 U i ) R) i=1 L i ) R) i=1 U i ) R = i=1 (U i R) Since unambiguous languages are closed under intersection with regular sets [5], this implies L R 2 UCFL[ Moreover, unambiguous languages are closed under cancellation of singletons [5] By cancellation of a # from the left hand side and #a from the right hand side, we obtain L p L p 2 UCFL[ But this is false since in [3] it is proved that L p L p has in nite ....

.... = i=1 U i ) i=1 L i ) R = i=1 U i ) R) i=1 L i ) R) i=1 U i ) R = i=1 (U i R) Since unambiguous languages are closed under intersection with regular sets [5] this implies L R 2 UCFL[ Moreover, unambiguous languages are closed under cancellation of singletons [5]. By cancellation of a # from the left hand side and #a from the right hand side, we obtain L p L p 2 UCFL[ But this is false since in [3] it is proved that L p L p has in nite ambiguity. Therefore L = 2 UCFL[ ut As an immediate consequence of Lemmas 3.4, 7.4 and 7.5 we obtain: ....

M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, 1978.

....not consider complexity results at all, neither of recognition by various classes of sequential or parallel Turing machines nor of succinctness (see e.g. 52] that is a measure of the size of the description of a language. We have chosen to present material which is not available in textbooks [17, 29, 1, 47, 28, 4, 30, 32, 2] (more precisely not available in more than one textbook) because it is on the borderline between classical stuff and advanced topics. However, we feel that a succinct exposition of these results may give some insight in the theory of context free languages for advanced beginners, and also provide ....

....) over the terminal alphabet A is in weak Chomsky normal form if each nonterminal rule has a right member in V each terminal rule has a right member in A [ f g. It is in Chomsky normal form if it is in Chomsky normal form and each right member of a nonterminal rule has length 2. Theorem 3.1. [28, 9] Given a context free grammar, an equivalent contextfree grammar in Chomsky normal form can effectively be constructed. Proof. The construction is divided into three steps. In the first step, the original grammar is transformed into a new equivalent grammar in weak Chomsky normal form. In the ....

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M.A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, 1978.

....algorithm [6] For a certain instance of a rule, the initial position of the dot is given by the position of the diamond in the corresponding filter item. There are several ways to. construct U. For presentational reasons our algorithm will be relatively simple, in the style of the CYK algorithm [8]: 1. Initially U is empty. 2. We perform one of the following until no more new elements can be added to U: a) We choose a transition (q,A o,q ) A and add an item [q,A r c ,q ] to U. b) We choose a transition (q, A r c o B, q ) A and an item [q , B r 7, q ] U and add an item [q, A ....

M.A. Harrison. 1978. Introduction to Formal Language Theory. Addison-Wesley.

....the CFG case and then move on to file case of definite grammar schemes. CFGs, Algebraic Systems, and the GGNK The most powerful transformation methods existing for contextfree grammars are algebraic ( matrix based [8] ones relying on the concepts of formal power series and algebraic systems (see [5, 9]) Using such concepts, u context free grammar such as: a 1 ala l a I [1 is refonuulated into the algebraic system: al ala2 a2 l a = V] which represents a fixpoint equation in the variables (or nonterminals ) a,a on a certain algebraic structure (u non commntative semiring) of formal power ....

Harrison, M.A. 1978. Introduction to Formal Lan- guage Theory. Reading, MA: Addison-Wesley.

....4.3.3. A regular language L satis es all of the following: a) Strong Pumping lemma) 16]There exists an n 0 such that every word z 2 L such that jzj n has a decomposition z = vpxy such that (i) p 6= ii) jvpxj n, and (iii) vp xy 2 L for all k 0. 49 (b) Weak Pumping Lemma)[15] There exists an n 0 such that for every word z 2 L k 0. c) Weaker Pumping Lemma) There exists an n 0 such that for every word z 2 L k 1. d) 90 Pound Weakling Pumping Lemma) There exists a word z 2 L and a decomposition z = xpy such that xp y 2 L for all k 0. These ....

Michael A. Harrison, An Introduction to Formal Language Theory, Addison-Wesley, 1987.

....G over the set of atoms of plus 0 and the new start symbol R, which generates the same fully labelled trees ignoring the deviant start symbol. It is known that there is an effective procedure to eliminate from a cfg labels that never occur in a finite tree generated by the grammar (see e.g. [Harrison, 1978]) This procedure can easily be adapted to boolean grammars. A boolean grammar without such superfluous symbols is called normal. 3.2 Domain Specification Each boolean label a defines the relation of a command on a fully labelled tree via the set of nodes of category a. This is the classical ....

....for special choices of X that we need these composite elements, so there is nothing recursive or infinite in this procedure. For the sake of simplicity we assume the grammar to be in Chomsky Normal Form; that is, we only have rules ot type X YZ, X Y, X 0 for X, Y and Z atoms or = R (see [Harrison, 1978]) For any rule p = A BC and any X we distribute the new labels GX and tX as follows. If B ( X but C X then we replace p by AnGX B n However, if C X but B X then we use this rule AFIX B n t 1 x It is clear what we do if both B, C X. If neither is the case, however, we have this rule ....

Michael A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading (Mass.), 1978.

....the following forms: z 1 ; p ] p ; z 2 ; q] 5) p z 1 z 2 2 ffi (pz; x) z ; q] 6) 2 ffi (pz; x) p; z; q] a) 7) where p; q; 2 Q; a 2 X [ ffflg; q 2 ffi (pz; a) GM is a strict deterministic grammar. A general theory of this class of grammars is exposed in [Har78] and used in [HHY79] We call mode every element of QZ [ ffflg. For every q 2 Q; z 2 Z, qz is said ffl bound (respectively ffl free) iff condition (1) resp. condition (2) in the above definition of deterministic automata is realized. The mode ffl is said ffl free. We define a mapping : V ....

....3.2) Let us consider a pair (W; where W is an alphabet and is an equivalence relation over W . We call (W; a structured alphabet. The two examples we have in mind are: the case where W = V , the variable alphabet associated to M and [p; A; q] p ] iff p = p and A = A (see [Har78]) the case where W = X, the terminal alphabet of M and x y holds for every x; y 2 X (see [Har78] Definitions Definition 3.1 Let S 2 B W . S is said left deterministic iff either (1) S = or (2) S = ffl or Sw = Sw 0 = 1 ) 9A; A 1 2 W ; A A ; w = A Deltaw 1 and w ....

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M.A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, Mass., 1978.

.... system is not a consequence of its embedding mechanism as suggested by Main and 3 Rozenberg (see discussion in [25] In order to prove that a graph rewriting model has the power of recursive enumerability, the following method is generally used : i) prove that any phrase structure string grammar [16] can be simulated by a graph rewriting system, ii) find a linear encoding of graphs as strings such that the decoding process can be handled by a graph rewriting system, iii) merge the two above defined systems in order to generate any family of graphs whose corresponding set of encodings is ....

....graph, around a given vertex, which always leads to a complete graph) Hence, the set L irr (R 10 ; Z A ) is exactly the set of all connected graphs having one distinguished (that is C labeled) vertex. 21 3 e GRS s and Phrase Structure String Grammars A phrase structure string grammar [16] is given as a 4 tuple G = T; NT;P;Z where T is a finite set of terminal letters, NT a finite set of non terminal symbols such that NT T = Z 2 NT the axiom symbol and P a finite set of string productions p : ff Gamma fi with ff 2 (T [ NT ) n T and fi 2 (T [ NT ) Let u and v ....

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M. Harrison, Introduction to formal language theory, Addison-Wesley (1978).

....of M. Let us consider a pair (W; where W is an alphabet and is an equivalence relation over W . We call (W; a structured alphabet. The two examples we have in mind are: the case where W = V , the variable alphabet associated to M and [p; A; q] p ] iff p = p and A = A (see [Har78]) the case where W = X, the terminal alphabet of M and x y holds for every x; y 2 X (see [Har78] Let us also consider a group K. Definitions Definition 4.1 Let S; T 2 Bhh K W ii. S; T are said proportional and we note S T , if and only if, there exists k 2 K such that S = k Delta T ....

....We call (W; a structured alphabet. The two examples we have in mind are: the case where W = V , the variable alphabet associated to M and [p; A; q] p ] iff p = p and A = A (see [Har78] the case where W = X, the terminal alphabet of M and x y holds for every x; y 2 X (see [Har78]) Let us also consider a group K. Definitions Definition 4.1 Let S; T 2 Bhh K W ii. S; T are said proportional and we note S T , if and only if, there exists k 2 K such that S = k Delta T . The right action ffl : Bhh K W ii Theta K W Bhh K W ii is compatible with the ....

M.A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, Mass., 1978.

.... following forms: z 1 ; p ] p ; z 2 ; q] 7) p z 1 z 2 2 (pz; x) q] 8) z 2 (pz; x) p; z; q] a) 9) where p; q; 2 Q; a 2 X [ f g; q 2 (pz; a) GM is a strict deterministic grammar (see de nition 313 below) A general theory of this class of grammars is exposed in [Har78] and used in [HHY79] 2.3 Free monoids acting on semi rings Semi ring Bhh W ii Let (B; 0; 1) where B = f0; 1g denote the semi ring of booleans . Let W be some alphabet. By (Bhh W ii; we denote the semi ring of boolean series over W : the set Bhh W ii is de ned as B ; the sum ....

....a pair (W; where W is an alphabet (i.e. a set ) and is an equivalence relation over W . We call (W; a structured alphabet. The most classical examples are: the case where W = VM , the variable alphabet associated to M and [p; z; q] p ; q ] i p = p and z = z (see [Har78]) the case where W = X , the terminal alphabet of M and x y holds for every x; y 2 X (see [Har78] De nitions De nition 31 Let S 2 Bhh W ii. S is said left deterministic i either (1) S = or (2) S = or (3) 9i 0 2 [1; m] S i 0 6= and 8w; w Sw = Sw 0 = 1 ) 9A; A 1 2 W ; w ....

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M.A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, Mass., 1978.

....Change and Bounded Incremental Parsing Mats Wirdn Fchrichtung 8. 7, Computerlinguis[ik Univcrsititt des Starlandcs Posthch 1150 D 66041 Saarbrficken, Germany wircn coli.uni sb.dc Abstract Ideally, the time titat an incremental algorithm uses to process a change should be a timetlon o the size of the change rather than, say, the size of the entire currc,tt input. Based on a formalization of the set of things changed by an ....

....Change and Bounded Incremental Parsing Mats Wirdn Fchrichtung 8. 7, Computerlinguis[ik Univcrsititt des Starlandcs Posthch 1150 D 66041 Saarbrficken, Germany wircn coli.uni sb.dc Abstract Ideally, the time titat an incremental algorithm uses to process a change should be a timetlon o the size of the change rather than, say, the size of the entire currc,tt input. Based on a formalization of the set of things changed by an ....

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Michael A. Ilarrison. introduction to Formal Language Theory. Addison-Wesley, Reading, Mssa- clmsc.ts, flSA, 1978.

....An important step in the decidability proof is a syntactic representation of DPDA configurations that dispenses with # transitions. The key is nondeterministic pushdown automata with a single state and without # transitions, introduced by Harrison and Havel [3] as grammars, and further studied in [2, 4]. Because the state is redundant, a configuration of a pushdown automaton with a single state is a sequence of stack symbols. Ingredients of such an automaton without # transitions, an SDA, are finite sets of stack symbols S, terminals A and basic transitions T of the form S # where a A, ....

Harrison, M. (1978). Introduction to Formal Language Theory, Addison-Wesley.

....We would have liked to be able to state here that the inclusion and equivalence problems for K are decidable and thus that PDL cannot be proved undecidable by Proposition 2.1. However, an attempt to prove this has revealed some subtle problems with applying the appropriate results from, e.g. [5, 7, 8, 15] to K. All we can state here at this point is the following informal observation which can be proved by showing that all languages involved are simple deterministic stack uniform, and then apply the results from [8] PROPOSITION 2.3. For all subsets K of K used in the undecidability proofs in ....

M. HARRISON, "Introduction to Formal Language Theory," Addison-Wesley, Reading, Mass., 1978. 243

....the maximum number of generations. GP has been used successfully in generating computer programs for solving a number of problems in a wide range of areas [3] 2. 2 Context free Grammars A context free grammar G can be defined as a stringrewiring system comprising of four components as follows [4]: G= N, T, P, S) Where N is a finite set of non terminal symbols; T is a finite set of terminal symbols; and TN= SN is a distinguished symbol called the start symbol. P is the set of production rules. Each rule in P is of the form: Ab where AN and b(TN) If Ab is a production, then aAg # abg, ....

....depicted in Figure 1: EXP EXP OP EXP PREOP ( EXP ) PREOP ( EXP ) sin VAR cos PREOP ( EXP ) x cos VAR Figure 1. Derivation tree for the expression sin(x) cos(cos (x ) A grammar G is called (structurally) ambiguous if for some string xT there is more than one derivation tree that yields x [4]. We define a grammar G as having semantic redundancies if for some string xL(G) there are some derivation trees that yield x and have the same meaning. For instance, in the above example, grammar G is (structurally) ambiguous since the string x x cos(x) L(G) can be parsed in at least two ways. ....

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M.A. Harrison, Introduction to Formal Language Theory, Addison-Wesley, USA, 1978.

....questions regarding the notions of motif and primitive root: is it decidable if a language is primitive, is it decidable if a language is a root premotif of another one We prove first that any rational language has a rational root. For this, we use the notion of syntactical monoid, see [25], and the techniques of [12] Note that a similar result is proved in [28] using elementary techniques of finite automata. 101 We prove in fact that any root of a rational language can be enlarged to a rational root of that language. This is usually referred to as the saturation method. A general ....

M. A. Harrison, Introduction to formal language theory, Addison- Wesley Publishing Co., Reading, Mass., 1978.

....but we are not aware of any automata theoretic results similar to ours. In [Gua92] the construction of a class of automata accepting coupled context free languages was stated as an open question. The tree generating automata, de ned in this paper, are basically pushdown automata ( Cho62] see e.g. [Har78]) with some additional details. Similarly to coupled context free grammars, which place restrictions on context free derivations, tree generating automata place restrictions on the computations of underlying pushdown automaton. We show that these restrictions are equivalent , i.e. the generating ....

....hold. Example 4. The coupled context free grammar ( fs; A; a; b; c; dg; g] fa; b; c; dg; fs A 1 A 2 ; A 1 ; A 2 ) aA 1 b; cA 2 d) A 1 ; A 2 ) g; s) where g(A) 2, generates the language fa j n 2 N 0 g. The non contextfreeness of this language is a well known fact (e.g. [Har78]) 3 De nition of tree generating automata De nition 6. Let [K; g] be bracket al..phabet. Bracketed tree over [K; g] is a tree whose vertices are labeled with the elements of [K; g] together with a partitioning on the set of its vertices, de ned inductively as follows: 1. One vertex, labeled with ....

M. Harrison. Introduction to Formal Language Theory. AddisonWesley, 1978.

....datalog program that is contained in P and uses only the given views as EDB predicates# it remains undecidable even in the case where both program P and the views are given bychain programs. The reduction, in the following theorem is done from the containmentproblem of context free grammars [17,11] Theorem 6. Given a datalog chain program P and views v 1 #v 2 #: #v m which are also given by chain programs over the EDB predicates of P, it is undecidable whether there is a non empty retrievable datalogprogram P v containedinP. In some cases, though, we can have a negativeanswer in the ....

M. A. Harrison. Introduction to formal language theory. Addison-Wesley, 1978.

....In addition, simpler and clearer automaton based proofs for several known results on this family of languages are given. 1 Introduction The main properties of linear context free grammars and the languages they generate have been uncovered already in the early days of formal language theory [1]. One of their most attractive properties is low computational complexity: the general membership problem is known to be NLOGSPACE complete [5] while every particular language can be recognized in square time and linear space using a well known algorithm that inductively computes for each ....

M. A. Harrison, Introduction to formal language theory, AddisonWesley, Reading, Mass., 1978.

....equations is to show that some relations are not expressible. A similar situation a need to show that certain languages are not generated by a certain type of devices was encountered at the early stages of the formal language theory. By now there are a lot of tools for the latter problem cf. [9], while there seems to be none for the former. As the main contribution of this paper we introduce such tools for word equations. More precisely, we prove theorems resembling pumping lemmas of formal languages, which allow to prove the nonexpressibility. Very intuitively, we show that if a given ....

....any solution s which would satisfy s s in the natural componentwise ordering. Further we call the numbers o(S) t, s(S) q and d(S) maxfjb j j; ja j jg the order, the size and the depth of S, respectively. Finally, we recall a formulation of the fundamental Konig Infinity Lemma, cf. [9]: Theorem 20 [The Konig Infinity Lemma] Each set of pairwise incomparable elements of N is finite. With the above terminology we now prove our crucial lemma. In the formulation of the lemma we interpret a set of integers as a vector in an appropriate way. Lemma 21 Let L be expressible by an ....

Harrison, M.A., Introduction to Formal Language Theory, AddisonWesley Publishing Company, 1978.

....and view concatenation as the product operator then x 2 D k if and only if x equals the identity in the free group generated by A. For example, a 1 a 2 a 2 a 1 2 D 2 because a 1 a 2 a 2 a 1 evaluates to unity. The Dyck languages are covered in detail in Harrison s classical treatment [6]. 1.2. The Dynamic Membership problem. In this paper we consider the problem of maintaining membership in D k or D k of a string from (A [ A) dynamically. More precisely, we want to implement a data type that contains a string x 2 (A [ A) of even length, initially a 1 , with the ....

....number of occurrences of a in u. All logarithms are base two. We call a string reduced if it contains no neighbouring pair of matching parentheses. So, for the one sided case, is not reduced but [ is. In the two sided case, the latter is not reduced. To formalise this (following Harrison [6]) we introduce two mappings 1 ; 2 : A [ A) A [ A) We want 1 (u) and 2 (u) to be the reduced form of u using one and two sided cancellation, respectively. To this end we define for each 1 i k and j = 1; 2: 1 (ffl) 2 (ffl) ffl; 1 (ua i ) 1 (u)a i ; 2 (ua i ) 2 ....

Michael A. Harrison, Introduction to formal language theory, Addison-Wesley, 1978.

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Michael A. Harrison. Introduction to Formal Language Theory, chapter 4. Addison-Wesley, 1978.

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M.A. Harrison. Introduction to formal language theory. Addison Wesley, 1978.

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M.A. Harrison. Introduction to formal language theory. Addison Wesley, 1978.

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M. A. Harrison, Introduction to Formal Language Theory. Addison-Wesley, Reading, 1st edition, 1978.

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M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, 1st edition, 1978.

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M. A. Harrison. Introduction to Formal Language theory. Addison-Wesley, 1978.

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M. Harrison. Introduction to Formal Language Theory. Addison-Wesley, 1978.

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M. H. Harrison, Introduction to Formal Language Theory. Reading, MA: Addison-Wesley Publishing Company, Inc., 1978.

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M. A. Harrison, Introduction to Formal Language Theory, AddisonWesley (1978). 9

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Harrison, M. A. (1978) Introduction to Formal Language Theory. Addison-Wesley, Reading, MA.

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M. A. Harrison, Introduction to formal language theory, Addison-Wesley, Reading, Mass., 1978.

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M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, MA, 1978.

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Harrison, M. A., \Introduction to Formal Language Theory," AddisonWesley, Reading, 1978, 1 edition.

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M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesely Publishing Company. 1978.

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Harrison, M. (1978). Introduction to Formal Language Theory, AddisonWesley.

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M. A. Harrison, Introduction to Formal Language Theory, AddisonWesley (1978).

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Harrison, M. A., "Introduction to Formal Language Theory," Addison-Wesley, Reading, 1978, 1 edition.

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M. A. Harrison, Introduction to formal language theory (Addison Wesley, 1978).

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M.A. Harrison, Introduction to Formal Languages Theory, (Addison-Wesley, Reading, 1978).

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Michael A. Harrison. Introduction to Formal Language Theory. AddisonWesley, Reading, Mass., 1978.

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Michael A. Harrison. Introduction to Formal Language Theory. Addison Wesley, Reading, Massachusetts, 1978.

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Michael A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, Massachusetts, USA, 1978.

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M.A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, Mass., 1978.

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Harrison, M.A., Introduction to Formal Language Theory, AddisonWesley Publishing Company, 1978.

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