Abstract
A text is a word together with an additional linear order on it. We study quantitative models for texts, i. e. text series which assign to texts elements of a semiring. We consider an algebraic notion of recognizability following Reutenauer and Bozapalidis and show that recognizable text series coincide with text series definable in weighted logics as introduced by Droste and Gastin. In order to do so, we study certain definable transductions and show that they are compatible with weighted logics. Moreover, we show that the behavior of weighted parenthesizing automata coincides with certain definable series.
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References
Bozapalidis, S.: Equational elements in additive algebras. Theory of Computing Systems 32(1), 1–33 (1999)
Bozapalidis, S., Alexandrakis, A.: Représentations matricielles des séries d’arbre reconnaissables. Theoretical Informatics and Applications 23(4), 449–459 (1989)
Courcelle, B.: Monadic second-order definable graph transductions: a survey. Theoretical Computer Science 126, 53–75 (1994)
Doner, J.: Tree acceptors and some of their applications. Journal of Computer and System Sciences 4, 406–451 (1970)
Droste, M., Gastin, P.: Weighted automata and weighted logics. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 513–525. Springer, Heidelberg (2005)
Droste, M., Rahonis, G.: Weighted automata and weighted logics on infinite words. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 49–58. Springer, Heidelberg (2006)
Droste, M., Vogler, H.: Weighted tree automata and weighted logics. Theoretical Computer Science 366, 228–247 (2006)
Ehrenfeucht, A., Harju, T., Rozenberg, G.: The Theory of 2-structures: A Framework for Decomposition and Transformation of Graphs. World Scientific, Singapore (1999)
Ehrenfeucht, A., Rozenberg, G.: Theory of 2-structures. I and II. Theoretical Computer Science 70, 277–342 (1990)
Ehrenfeucht, A., Rozenberg, G.: T-structures, T-functions, and texts. Theoretical Computer Science 116, 227–290 (1993)
Ehrenfeucht, A., ten Pas, P., Rozenberg, G.: Context-free text grammars. Acta Informatica 31(2), 161–206 (1994)
Ésik, Z., Németh, Z.L.: Higher dimensional automata. Journal of Automata, Languages and Combinatorics 9(1), 3–29 (2004)
Hashiguchi, K., Ichihara, S., Jimbo, S.: Formal languages over free bionoids. Journal of Automata, Languages and Combinatorics 5(3), 219–234 (2000)
Hoogeboom, H.J., ten Pas, P.: Text languages in an algebraic framework. Fundamenta Informaticae 25(3), 353–380 (1996)
Hoogeboom, H.J., ten Pas, P.: Monadic second-order definable text languages. Theory of Computing Systems 30, 335–354 (1997)
Mäurer, I.: Weighted picture automata and weighted logics. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 313–324. Springer, Heidelberg (2006)
Meinecke, I.: Weighted logics for traces. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, Springer, Heidelberg (2006)
Mezei, J., Wright, J.B.: Algebraic automata and context-free sets. Information and Control 11(1/2), 3–29 (1967)
Reutenauer, Ch.: Séries formelles et algèbres syntactiques. J. Algebra 66, 448–483 (1980)
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Mathissen, C. (2007). Definable Transductions and Weighted Logics for Texts. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_31
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DOI: https://doi.org/10.1007/978-3-540-73208-2_31
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