A. Salomaa. Formal languages and power series. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, pages 103--132. Elsevier, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....from the fact that if the execution of a trace is possible, then the execution of any of its pre x is also possible. We call such maps probabilistic languages and use them for modeling the stochastic qualitative behavior of DESs. A probabilistic language can be viewed as a formal power series [24], but satisfying the constraints mentioned above. As discussed in [7] this probabilistic language model di ers in various ways from other existing models of stochastic behavior of DESs such as Markov chains [1] stochastic Petri nets [18] Rabin s probabilistic automata [21, 20, 4] and their ....

A. Salomaa. Formal languages and power series. In J. v. Leeuwen, editor, Handbook of theoretical computer science. MIT Press, Cambridge, MA, 1994.

....of Naval Research under the Grant ONR N00014 96 1 5026, a General Motors Fellowship, a Texas Higher Education Coordinating Board Grant ARP 320, and an IBM grant. use them for modeling the stochastic qualitative behavior of DESs. A probabilistic language can be viewed as a formal power series [21], but satisfying the constraints mentioned above. As discussed in [7] this probabilistic language model differs in various ways from other existing models of stochastic behavior of DESs such as Markov chains [1] stochastic Petri nets [15] Rabin s probabilistic automata [18, 17, 4] and their ....

A. Salomaa. Formal languages and power series. In J. v. Leeuwen, editor, Handbook of theoretical computer science. MIT Press, Cambridge, MA, 1994.

....probability of all its extensions. By relaxing this constraint we are able to model the possibility of termination, which also allows us to define concatenation or sequential operation of two or more stochastic discrete event systems. A probabilistic language can be viewed a formal power series [20] a map over the set of traces, but with the additional two constraints described above. There are many important differences in our work from the classical work on formal series. Our definition of concatenation (product) and therefore of concatenation closure is quite different from that of ....

.... as: f ffi g(s) X t f(t)g(t Gamma1 s) Then the concatenation operation can be simply defined as: L 1 : e L 2 = L 1 Gamma e Delta(L 1 ) e Delta(L 1 ) ffi L 2 : The convolution operator defined above is termed as product (or Cauchy product) in the theory of formal power series [20]. We use convolution to avoid any confusion with concatenation product. The following lemma describes certain properties of the convolution operator. Lemma 1 Let f; g; h : Sigma R be real valued functions, and e; e 0 2 R. 1. 1] I is the identity for convolution, i.e. f ffi I = I ffi f ....

A. Salomaa. Formal languages and power series. In J. v. Leeuwen, editor, Handbook of theoretical computer science. MIT Press, Cambridge, MA, 1994.

.... context free languages) which is an important subclass of P and has been studied intensively (both from the perspective of parallel computation and circuit complexity) Coo85, Lan93, Ven91, BLM93] Viewing languages as formal power series is an important unifying paradigm in formal language theory [SS78, Gin75, KS85, Sal90]. It has led to an arithmetization of the theory and to the unification of disparate looking proofs in the area. Furthermore, the general approach has also yielded several new results. With this success in mind, it is natural to try and apply formal power series techniques in the study of ....

A. Salomaa. Formal languages and power series. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, pages 103--132. Elsevier, 1990.

....rules which describe how different characters are to be rewritten. In other applications, production rules are applied in a sequential way, whereas in an L System, all characters in a string are rewritten in parallel to form a new string. We refer the reader to the chapter written by A. Salomaa [18] for more information about other generalizations and applications of L Systems. By attaching a specific meaning based on the LOGO style turtle to some of the characters in the string, we will be able to code a path on the plane and, in particular, a space filling curve. 4. MNPeano In 1959, ....

A. Salomaa. Chapter 3. Formal languages and power series. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics. Elsevier Science Publishers, Amsterdam, 1990.

....a rewriting system, and S 2 N . We call N the nonterminal alphabet or the set of nonterminals. The set of tokens T is called the terminal alphabet or the set of terminals. The symbol S is the start symbol of G. Grammars are classified according to the Chomsky hierarchy into four groups [Cho59, Sal90] It can be shown that the hierarchy is a strictly decreasing hierarchy of language families. In the first group, we set no restrictions on the productions. In the second group, the productions are of type ffAfi ffffifi, where ff and fi are arbitrary strings over V , ffi is a nonempty string ....

Arto Salomaa. Formal languages and power series. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, pages 103 -- 132. Elsevier, 1990.

....for expressing the addition operation. In order to optimize the alternations of quantifiers the iterative processes of addition and multiplication has to be performed in one list apparatus, thus yielding a more complex reduction proof. For a similar reason Post s Canonical Production Systems (see Salomaa (1990)) do not qualify for natural candidates . Here the constructibility of a given word is undecidable. As in the cases considered above, we are able to express the notion of a construction sequence easily once we can simulate the elementary construction steps. But in the case of Post s Canonical ....

Salomaa, A. (1990). Formal languages and power series. In van Leeuwen, J., editor, Handbook of Theoretical Computer Science, volume B, pages 103--132. Elsevier.

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A. Salomaa. Formal languages and power series. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, pages 103--132. Elsevier, 1990.

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