Autebert, J.M., Berstel, J., Boasson, L.: Context-free languages and pushdown automata. In Salomaa, A., Rozenberg, G., eds.: Handbook of Formal Languages. Volume 1, Word Language Grammar. Springer-Verlag, Berlin (1997) 111--174  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is witnessed, for example, by the languages used in the proofs of Propositions 10 and 11, i.e. the language of all words that contains as many 0 s as 1 and the language of even length palindromes. For background on formal language theory we refer to the survey by Autebert, Berstel, and Boasson [5]. However, determining exactly the class of languages preserving normality remains an open problem. The outline of the paper is as follows. In Section 2 we review the basic definitions related to normality and recap Champernowne s constructions of normal sequences. Section 3 discusses the two ....

J.-M. Autebert, J. Berstel, and L. Boasson, Context-Free Languages and Pushdown Automata. In G. Rozenberg and A. Salomaa (eds.), Handbook of formal languages. Springer, 1997.

....the number of bits needed to encode a grammar [14] We will consider here the size of G denoted (T,u)#P ( u 1) Another way of defining context free languages is through pushdown automata (pda) We will not formally define these here. A specific study on these machines can be found in [15]. Informally a pda is a one way finite state machine with a stack. Criteria for recognition can be by empty stack or by accepting states, but in both cases the class of languages is that of the context free ones. If the machine is deterministic (in a given configuration of the stack, with a ....

....computation of a pda, a turn in the computations is a move that decreases the height of the stack and is preceded by a move that did not decrease it. A pda is said to be one turn if in any computation there is at most one turn. A language is linear if and only if it is recognized by a one turn pda [15]. 2.2 Deterministic Linear Grammars A variety of definitions have been given capturing the ideas of determinism and linearity. We first give our own formalism: Definition 1 (Deterministic linear grammars) A deterministic linear (DL) grammar G = #, V, P, S is a linear grammar where all rules ....

[Article contains additional citation context not shown here]

Autebert, J., Berstel, J., Boasson, L.: Context-free languages and pushdown automata. In Salomaa, A., Rozenberg, G., eds.: Handbook of Formal Languages. Volume 1, Word Language Grammar. Springer-Verlag, Berlin (1997) 111--174

....of the relation G is denoted by and it is called the derivation relation. The language generated by the grammar G is L(G) u ] u . A language is called context free, or algebraic, if it is generated by a context free grammar. For details on rational and context free languages, we refer to [2], 24] 51] 69] 70] and [75] A set L C N k, k 1, is called linearif there are some u0, u, ui N k L = u0 mu . miui [ m, mi N . Equivalently, L is linear if L u0 t F , where F C N k is a finite set and the iteration F is done with respect to addition, i.e. in the ....

J.M. Autebert, J. Berstel, L. Boasson, Context-Free Languages and Pushdown Automata. In G. Rozenberg, A. Salomaa (eds.), Handbook of Formal Languages, vol. 1: 329-438, Springer-Verlag, 1997.

....equivalent by Theorem 1. Second, iii) clearly implies any of (i) and (ii) Third, i) implies (iii) follows from Remark 5 and the distributivity of the catenation and with respect to union. Characterization of k poly slenderness By the well known Chomsky Schutzenberger theorem (see, e.g. [2]) any context free language is characterized as a homomorphic image of the intersection between the Dyck language and a regular one. We show below that the structure of the Dyck language is also the base for the structure of the poly slender context free languages. In the above notations, the ....

....if needed, and therefore concludes the proof. We next give some examples of the construction in the proof of Theorem 8. Consider the 5 Dyck loop L 1 = f(ab) 2n 1 a(ba) 3n 2 aab n 2 b 2n 3 b n 4 aba n 4 a 3n 3 a n 5 a 2n 1 j n i 0g; the underlying Dyck word of which is z = 1 [ 2 ] 2 [ 3 [ 4 ] 4 ] 3 [ 5 ] 5 ] 1 (we assume h( 5 ) There are links and we have the classe of chain ] f1; 2g, f3; 4; 5g, f6; 7; 8; 10g and only one class of syst ] f1; 2; 8; 10g. We write L 1 as L 1 = fa(ba) 2n 1 3n 2 aab n 2 2n 3 n 4 aba 2n 1 3n 3 n 4 n 5 j n i ....

Autebert, J.-M., J. Bestel, and L. Boasson, Context-free languages and push-down automata, in G. Rozenberg, A. Salomaa, eds., Handbook of Formal Languages (Springer-Verlag, Berlin, Heidelberg, 1997) 111 -- 174.

....7 b 2n 7 b n 2 j n i 0g: 2) About the underlying morphism we mention only that the images of any of ] 4 and ] 6 are empty. Example 3. The underlying Dyck word for the Dyck loop L 2 = f(ab) 2n1 a(ba) 3n2 aab n2 b 2n3 b n4 aba n4 a 3n3 a n5 a 2n1 j n i 0g; 3) is z = 1 [ 2 ] 2 [ 3 [ 4 ] 4 ] 3 [ 5 ] 5 ] 1 and we assume h( 5 ) Bounded languages The following result of Ginsburg and Spanier [6] will be essential for our purpose. Theorem 4 ( 6] The family of bounded context free languages is the smallest family which contains all finite languages and is closed ....

Autebert, J.-M., J. Bestel, and L. Boasson, Context-free languages and push-down automata, in G. Rozenberg, A. Salomaa, eds., Handbook of Formal Languages (Springer-Verlag, Berlin, Heidelberg, 1997) 111 -- 174. 8

....rules of the forms (A ; 0) or (A a ; r) k rk 1 1, are produced. 2 Remark 5. 18 With some additional e ort, other normal forms, e.g. a quadratic double Greibach normal form, could be shown for L(Val; CF; Z k ) The interested reader should study the corresponding construction in [1]. 6 An Iteration Lemma We are going to prove iteration lemmas similar to the pumping lemmas for context free and regular languages. We use the idea of minimal cycles, already present in Vicolov s proof of the strictness of the inclusions L(Val; CF; Z k ) Sequential Grammars and Automata with ....

J.-M. Autebert, J. Berstel and L. Boasson. Context-free languages and pushdown automata. In: G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, Vol. 1, pages 111-174. Berlin: Springer, 1997.

....rewrite systems A Context Free Grammar (CFG) is a tuple G = hNG ; TG ; RG i where NG (the non terminal symbols) and TG (the terminal symbols) are disjoint alphabets and where, writing Sigma G for NG [ TG , RG NG Theta Sigma G is a finite set of production rules of the form X w. See [ABB97] for details. Here is an example where we group right hand sides related to a common left hand side symbol. G : S XY j aSS X bY j ffl Y XX The rules in RG induce a notion of rewrite step: if X w is in RG then uXv G uwv for any u; v. Usually, we are interested in derivation sequences ....

J.-M. Autebert, J. Berstel, and L. Boasson. Context-free languages and pushdown automata. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume 1, chapter 3, pages 111--174. Springer-Verlag, 1997.

.... as FO to which the single unary groupoidal quantifier Q un G is applied, FO to which a single non unary groupoidal quantifier is applied, written Q Grp FO, captures LOGCFL; our proof implies, remarkably, that adding a padding symbol to Greibach s hardest context free language [7] see also [1], yields a language which is LOGCFL complete under BIT free quantifier free interpretations. When the BIT predicate is present, first order with non unary groupoidal quantifiers of course still describes LOGCFL. In the setting of monoidal quantifiers [3] FO with BIT is known to capture uniform ....

J.-M. Autebert, J. Berstel, and L. Boasson. Context-free languages and pushdown automata. In R. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume I, chapter 3. Springer Verlag, Berlin Heidelberg, 1997.

..... As usual, a sequence of compatible transitions is called a computation. The language accepted by a PDA P is denoted by L(P) 28 It is known that the family of languages accepted by pushdown automata and the family of contextfree languages, denoted by L CF , coincide. For a proof of this, see [1, 9, 22]. A onecounter automaton is a pushdown automaton, where the stack alphabet consists of only one symbol other than the initial stack symbol, say Gamma = f1; z 0 g. The stack of a onecounter automata can be thought of as a counter, where the value of the counter is the number of 1 s in the stack. ....

J. Autebert, J. Berstel, and L. Boasson, Context-Free languages and Pushdown Automata, Handbook of Formal Languages (G. Rozenberg and A. Salomaa, eds.), vol. 1, Springer-Verlag, 1997.

....distinguish the least solution (w.r.t. inclusion) It is well known that a balanced linear system of n equations has a least solution w.r.t. any of its variables. One may compute such a solution using the Gauss elimination method. For more details related to this topic the reader may consult e.g. [3]. Suffixes, prefixes, quotients and remainders Given u; v; w 2 Sigma such that w = uv, u is called a prefix and v a suffix of w. When v 6= resp. u 6= u (resp. v) is a proper prefix (resp. suffix ) of w. We note pref (u) resp. suff (u) the set of all the prefixes (resp. suffixes) of ....

J.-M. Autebert, J. Berstel, and L. Boasson. Context--free languages and push--down automata. In G. Rozenberg and A. Salomaa, editors, Word, Language, Grammar, volume 1 of Handbook of Formal Languages, pages 111--174. Springer--Verlag, 1997.

....:2 to X aY . A weighted CFG G = V; P ) over the alphabet Sigma, with weights in a semiring (K ; Phi; Omega ; 0; 1) consists of a finite alphabet V of variables or nonterminals disjoint from Sigma, and a finite set P V Theta K Theta (V [ Sigma) of productions or derivation rules [Autebert, Berstel and Boasson 1997]. Given strings u; v 2 (V [ Sigma) and weights c and c 0 , we write (u; c) v; c 0 ) when there is a derivation from u with weight c to v with weight c 0 . We denote by LG (X) the weighted language generated by a nonterminal X: LG (X) f(w; c) 2 Sigma Theta K : X; 0) w; c)g ....

Autebert, J.-M., Berstel, J. and Boasson, L.: 1997, Context-free languages and pushdown automata, in G. Rozenberg and A. Salomaa (eds), Handbook of Formal Languages, Vol. 1, Springer, pp. 111--172.

No context found.

Autebert, J.M., Berstel, J., Boasson, L.: Context-free languages and pushdown automata. In Salomaa, A., Rozenberg, G., eds.: Handbook of Formal Languages. Volume 1, Word Language Grammar. Springer-Verlag, Berlin (1997) 111--174

No context found.

Jean-Michel Autebert, Jean Berstel, and Luc Boasson. Context-free languages and pushdown automata. In A. Salomaa and G. Rozenberg, editors, Handbook of Formal Languages, volume 1, Word Language Grammar, pages 111--174. Springer-Verlag, Berlin, 1997.

No context found.

J.-M. Autebert, J. Berstel, and L. Boasson. Context-free languages and pushdown automata. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume 1 { Word, Language, Grammar, chapter 3, pages 111-174. Springer-Verlag, 1997.

No context found.

AUTEBERT, J.-M., BERSTEL, J., AND BOASSON, L. Context-free languages and pushdown automata. In Handbook of Formal Languages, Vol. I, G. Rozenberg and A. Salomaa, Eds. Springer-Verlag, 1997, pp. 111--174.

No context found.

Autebert, J.-M., Berstel, J., and Boasson, L. Context-free languages and pushdown automata. In [12].

No context found.

J. Autebert, J. Berstel, L. Boasson. Context-free languages and pushdown automata. In Handbook of Formal Languages,Vol. 1, pages 111-174, Springer, 1997.

No context found.

J. Autebert, J. Berstel and L. Boasson, "Context-free languages and pushdown automata ", Handbook of Formal Languages, Vol. 1, 111--174, Springer-Verlag, Berlin, 1997.

No context found.

J.-M. Autebert, J. Berstel, and L. Boasson. Context-free languages and pushdown automata. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume 1, pages 111174. Springer, Berlin, 1997.

No context found.

Autebert, J.-M., Berstel, J., and Boasson, L. Context-free languages and pushdown automata. In Handbook of formal languages, G. Rozenberg and A. Salomaa, Eds. Springer, 1997.

No context found.

Autebert,J.-M., Berstel,J., Boasson,L.: Context-Free Languages and Pushdown Automata. In: Rozenberg, G., Salomaa, A. (eds.), Handbook of Formal Languages, vol. 1. Berlin Heidelberg New York: Springer, 1997, pp. 111-174

No context found.

Autebert,J.-M., Berstel,J., Boasson,L.: Context-Free Languages and Pushdown Automata. In: Rozenberg, G., Salomaa, A. (eds.), Handbook of Formal Languages, vol. 1. Berlin Heidelberg New York: Springer, 1997, pp. 111-174

No context found.

J.-M. Autebert, J. Berstel and L. Boasson, Context-Free Languages and Pushdown Automata, in: Handbook of Formal Languages, G. Rozenberg and A. Salomaa (Eds.), Vol. 1, Springer-Verlag, Berlin 1997, 111--174.

No context found.

J.-M. Autebert, J. Berstel, and L. Boasson. Context-free languages and pushdown automata. In R. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume I, chapter 3, pages 111-174. Springer Verlag, Berlin Heidelberg, 1997.

No context found.

J. Autebert, J. Berstel and L. Boasson, "Context-Free Languages and Pushdown Automata", Handbook of Formal Languages, Vol. 1, 111--174, Springer-Verlag, Berlin, 1997.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC