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Deletion along Trajectories - Domaratzki (2003) (Correct)
....3.4 does not apply to the CSLs. We now construct an example demonstrating non closure of the CSLs under deletion of a regular language along a regular set of trajectories. This construction is similar to one used by Daley and Kari [2, Prop. 2. 4] We will require the following theorem (see Salomaa [22]) 6 Theorem 3.9 Let be a language and a; b = 2 . For all recursively enumerable languages L , there exists a CSL L 1 a bL such that for all x 2 L, there exists some a bx 2 L 1 . Theorem 3.10 There exist a CSL L, a regular set of trajectories T fi; dg and a regular language R ....
SALOMAA, A. Formal Languages. Academic Press, 1973.
Definable Relations and First-Order Query Languages.. - Benedikt, Libkin.. (Correct)
....given queries Q and Q returning sets of strings, one can substitute Q and Q within regular expressions to form new LIKE queries. However, as noticed in [40] for Sigma = f0; 1; g, RC concat expresses all computable queries on databases containing strings from f0; 1g (see [61] for a proof) In fact, it is easy to show a somewhat stronger result which only requires two letters in Sigma. Proposition 4.1 Let Sigma contain at least two letters. Then RC concat expresses all computable queries on databases over Sigma . Proof. We first show that all computable ....
....result which only requires two letters in Sigma. Proposition 4.1 Let Sigma contain at least two letters. Then RC concat expresses all computable queries on databases over Sigma . Proof. We first show that all computable predicates on f0; 1g are expressible. We follow the lines of [61], Chapter III, Theorem 12.4, which uses an extra symbol ] to encode a Turing machine computation in RC concat . Let M be a Turing machine. Let Q = fq 2 ; Delta Delta Delta ; q m g be the set of states of M , q 2 being the initial state. At step i of the execution of M over an input x, the ....
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A. Salomaa. Formal Languages. Academic Press, 1973.
Regulation by Valences - Fernau, Stiebe (1997) (Correct)
.... as introduced in [3] Taking abelian monoids as valence regulators, we found algebraic characterizations of the corresponding language families in the spirit of [1, 2] 2 Preliminaries Throughout the paper we assume the reader to be familiar with the theory of context free languages, see e.g. [19]. Let V = fa 1 ; ang, n 1, be an alphabet. The set of all words over V is denoted by V , the empty word by , and V = V n fg. For w 2 V , the length of w is denoted by jwj, the number of appearances of the letter a 2 V in w is denoted by jwj a . The Parikh mapping associated ....
A. K. Salomaa. Formal Languages. Academic Press, 1973.
Team Automata for Security Analysis of.. - Beek, Lenzini, Petrocchi (Correct)
....a list of mathematical notations that are used throughout this paper and which may be skipped on rst reading. Consequently, we formally de ne the framework of TA with multicast broadcast communication. 2. 1 Some Notation We assume some familiarity with basic notions of formal language theory [21]. Set inclusion is denoted by . Set di erence of sets V and W is denoted by V W . The powerset of set V , formed by its nite parts only, is denoted by 2 V . N denotes the set of positive integers. Let I N be a set of indices given by I = fi 1 ; i 2 ; g with i j i if 1 j . For ....
A. Salomaa. Formal Languages. Academic Press, 1973.
Context-Free Languages and Pushdown Automata - Autebert, Berstel, Boasson (1997) (29 citations) (Correct)
....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 ....
....it is of infinite index. It can be proved Proposition 6.6. A language is quasi rational iff it is generated by a grammar of finite index. This result can be made even more precise: the family Qrt(k) is exactly the family of languages generated by grammars of index k. We refer the reader to [22, 27, 47, 4] for a proof of this proposition. 6.3 Strong quasi rational languages We present now a less usual family of languages. It is derived from the bracket operation defined above. Recall that Lin is the smallest family closed under bracket containing the finite sets. Recall also that Rat Lin denotes ....
A. Salomaa. Formal Languages. Academic Press, 1973.
Definable Relations and First-Order Query Languages.. - Benedikt, Libkin.. (Correct)
....of compositionality: given queries Q and Q returning sets of strings, one can substitute Q and Q within regular expressions to form new LIKE queries. However, as noticed in [40] for = f0; 1; g, RC concat expresses all computable queries on databases containing strings from f0; 1g (see [61] for a proof) In fact, it is easy to show a somewhat stronger result which only requires two letters in . 4.1 Proposition Let contain at least two letters. Then RC concat expresses all computable queries on databases over . Proof. We rst show that all computable predicates on f0; 1g ....
....a somewhat stronger result which only requires two letters in . 4.1 Proposition Let contain at least two letters. Then RC concat expresses all computable queries on databases over . Proof. We rst show that all computable predicates on f0; 1g are expressible. We follow the lines of [61], Chapter III, Theorem 12.4, which uses an extra symbol ] to encode a Turing machine computation in RC concat . Let M be a Turing machine. Let Q = fq 2 ; q m g be the set of states of M , q 2 being the initial state. At step i of the execution of M over an input x, the con guration of M ....
[Article contains additional citation context not shown here]
A. Salomaa. Formal Languages. Academic Press, 1973.
Unification Phonology: Another look at "synthesis-by-rule" - Coleman (Correct)
....Epenthesis e.g, mince [mints] pence [pents] Rule: ns nts Deletion: Elision e.g. sandwich [sanWit f] Rule: nd n Permutation: Metathesis e.g. burnt [brunt] Rule: ur , ru The probhms inherent in this approach are many: 1. Deletion rules cau make Context Sensitive grammars undecidable. (Salomaa 1973:83, Levelt 1976:243, Lgpointe 1977:228, Berwick and Weinberg 1984:127) 2. Non monotonicity mM[es for computational complexity. 3. There is no principled way of limiting the do main of rule application to specific linguistic domains, such as syllables. 4. Using sequences as data structures is ....
....the transformational component as the epiphenomenal result of several interacting general constraints . Numerous such constraints and principles have been proposed, such as the Well Formedness Con dition (Goldsmith 1976 and several subsequent fornmlations) the Obligatory Contour Principle (Leben 1973), Cyclicity (Kaisse and Shaw 1985, Kiparsky 1985) Structure Preservation (Kiparsky 1985) the Elsewhere Condition (Kiparsky 1973) etc. While this line of research is in some respects conceptually cleaner than primitive transformational grammars, there has been no demonstration that a principle ....
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Salomaa, A. 1973. Formal Languages. New York: Academic Press.
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Salomaa, A. 1973. Formal Languages. Academic Press, New York, NY.
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A. Salomaa. Formal Languages. Academic Press, New York, 1973.
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