| A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer, Berlin, 1978. |
....which conditions there exists a sequential function mapping a given rational language onto another have been devised, cf. 7] and [9] In [6] the same problem is considered where bijective rational transductions are used in place of sequential functions. 2 Preliminaries We refer to [4] 2] and [8] for a more detailed exposition of the main notions briefly recalled here. 2.1 Free monoids Given a set A (an alphabet) consisting of letters, A denotes the free monoid it generates. The elements of A are words or strings. The length of a word w is denoted by jwj. The empty word, denoted ....
A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer, 1978.
....the language variables (nonterminals) as numerical variables, interpret the terminals by the given valuation, and finally interpret the catenation as multiplication and the union as addition. In the following, we assume that the reader is familiar with some basics of formal power series, see e.g. [29, 23]. One of the connections of valuations and formal power series is the next. Lemma 4. Any valuation fi : Sigma n (0; 1) induces a semiring morphism fi : 0; 1] Sigma n AE [0; 1] by s; w w 7 s; w fi(w) To the set of productions P of a contextfree grammar G = X; Sigma n ; ....
A. K. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. New York: Springer, 1978.
....we list some classes of generating functions: 2) 2) 2) 2) 3) 3) 2) 2) 2) 2) 3) 3) 3) 3) a) b) 2) 4) Figure 1: The rst levels of two equivalent generating trees. R is the set of rational generating functions of integer sequences (Z rational functions, using the notation in [SS]) R is the set of rational generating functions of positive integer sequences; REG is the set of generating functions of regular languages; S is the set of rational generating functions of succession rules; F is the set of generating functions of nite succession rules. Summarizing ....
....the set of rational generating functions of positive integer sequences; REG is the set of generating functions of regular languages; S is the set of rational generating functions of succession rules; F is the set of generating functions of nite succession rules. Summarizing the results in [SS], FPPR] we obtain the following scheme: REG F S The classes R, REG, and F are decidable, while R is not decidable. In [FPPR] is conjectured that F = S, i.e. every rational rule is equivalent to a nite one. This note proposes a simple tool to pass from a rational generating ....
A. Salomaa and M. Soittola, Automata-Theoretic Aspects of Formal Power Series, Springer-Verlag, 1978.
....recognition applications are typically acyclic weighted automata, however our algorithm is general and applies to all weighted automata. A weighted automaton is a directed weighted graph in which each edge or transition has a label a phoneme or a word in the case of phone or word lattices [9, 10, 11, 12]. The weights are often interpreted as negative log of probabilities, but in general they may correspond to some other measured quantity. They are added along each path and the weight of a string x is the weight of the minimum weight of a path labeled with x. In what follows, we will thus assume ....
Arto Salomaa and Matti Soittola, Automata-Theoretic Aspects of Formal Power Series, Springer-Verlag: New York, 1978.
....generated by the hybrid systems. The synthesis problem, then involves determining a controller such that the series representation of the continuous state trajectory satisfies specified safety conditions. The resulting series representations of the controlled systems, by way of the Schutzenberger [50] representation theorems, could then be used to extract finite automata generating the desired switching logic for the hybrid system. This continualized approach was first discussed in [48] 80] and that work combines concepts from logic, automata theory, and differential geometry to attempt to ....
A. Salomaa, M. Soittola, Automata Theoretic Aspects of formal power series, Springer-Verlag, Berlin, 1973.
....algorithm when used with an acyclic graph weighted with real valued numbers. The Generic Topological Single SourceShortest Distance algorithm is useful among other things for computing the coefficients of a rational power series represented by a weighted automaton or a weighted transducer [5, 6, 10, 36, 23]. An e#cient implementation of the Generic Single Source Shortest Distance algorithm with various queue disciplines including the generic topological order can be found in the latest version of the FSM library [30] The complexity of the Generic Topological Single Source Shortest Distance ....
A. Salomaa, M. Soittola, Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag, New York, 1978.
....sup ( G) A symbol X 2 V is Pb if fXg is Pb. The Parikh supremum is the maximum number of symbols which can occur in a word of L. We write sup (L) a) for sup (L) fag) sup (L) a) can be considered as the supremum of the corresponding component over all Parikh vectors for L. See [9] for the de nition of Parikh vectors. De nition 3.3. Let and be nite alphabets. A substitution : 2 is Parikh bounded for a language L if for each a 2 which is not Parikh bounded (a) fag holds. The projection (L) is a Parikh bounded projection if n contains Parikh ....
A. Salomaa and M. Soittola. Automata theoretic aspects of formal power series. Springer, 1978.
....of a language X A # , denoted X,is the power series associating 1 with the words belonging to X and 0 with the words not belonging to X. In the following we will often identify X with its characteristic series without stating it explicitly. Some classical references to formal power series are [4, 9, 20]. Definition 2.1 A language X A # factorizes T A # if there exists Y that X Y = T.IfX factorizes A # ,thenX A # is called factorizing. In other words, X factorizes A # if there exists a language Y A # such that any word w A # has a unique factorization w = xy,withx X and ....
A. Salomaa and M. Soittola, Automata-theoretic aspects of formal power series, Springer, Berlin Heidelberg New York (1978).
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer, Berlin, 1978.
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Salomaa, Arto and Matti Soittola. 1978. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag, Texts and Monographs in Computer Science.
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Texts and Monographs in Computer Science, Springer-Verlag, 1978.
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag, 1978.
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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Salomaa, A., and Soittola, M. Automata-Theoretic Aspects of Formal Power Series. Springer, 1978. Texts and monographs in computer science.
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Arto Salomaa and Matti Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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Arto Salomaa and Matti Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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Arto Salomaa and Matti Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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Arto Salomaa and Matti Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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A. Salomaa and M. Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag: New York, 1978.
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A. Salomaa and M. Soittola. Automata-theoretic aspects of formal power series, Texts and Monographs in Computer Science, Springer-Verlag, New York, 1978.
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Arto Salomaa and Matti Soittola, Automata-Theoretic Aspects of Formal Power Series, Springer-Verlag: New York, 1978.
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