Abstract
In this paper, we introduce a notion of a right-sequential function on infinite words. The main result is that any rational function is the composition of a right-sequential function and a left-sequential function. This extends a classical result of Elgot and Mezei on finite words to infinite words. We also show that our class of right-sequential functions includes the normalization of real numbers in some base and the truth value of linear temporal logic. Finally, we apply the decomposition theorem to show that automatic sequences are preserved by rational letter-to-letter functions.
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References
Allouche, J.-P., Shallit, J.: Automatic Sequences. Cambridge University Press, Cambridge (2003)
Béal, M.-P., Carton, O.: Determinization of transducers over infinite words: the general case. TOCS 37(4), 483–502 (2004)
Berstel, J.: Transductions and Context-Free Languages. B.G. Teubner (1979)
Carton, O., Michel, M.: Unambiguous Büchi automata. Theo. Comput. Sci. 297, 37–81 (2003)
Choffrut, C.: Une caractérisation des fonctions séquentielles et des fonctions sous-séquentielles en tant que relations rationnelles. Theo. Comput. Sci. 5, 325–337 (1977)
Cohen, A., Collard, J.-F.: Instance-wise reaching definition analysis for recursive programs using context-free transductions. In: Parallel Architectures and Compilation Techniques, pp. 332–340. IEEE Computer Society Press, Los Alamitos (1998)
Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM J. of Res. and Dev. 9, 47–68 (1965)
Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995)
Lothaire, M.: Algebraic Combinatorics on Words, ch. 7, pp. 230–268. Cambridge University Press, Cambridge (2002)
Mohri, M.: On some applications of finite-state automata theory to natural languages processing. Journal of Natural Language Engineering 2, 1–20 (1996)
Perrin, D., Pin, J.-É.: Infinite Words. Elsevier, Amsterdam (2004)
Roche, E., Schabes, Y.: Finite-State Language Processing, ch. 7. MIT Press, Cambridge (1997)
Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, Cambridge (2009)
Schützenberger, M.-P.: Sur les relations rationnelles entre monoïdes libres. Theo. Comput. Sci. 4, 47–57 (1976)
Weber, A., Klemm, R.: Economy of description for single-valued transducers. Inform. and Comput. 118, 327–340 (1995)
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Carton, O. (2010). Right-Sequential Functions on Infinite Words. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_9
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DOI: https://doi.org/10.1007/978-3-642-13182-0_9
Publisher Name: Springer, Berlin, Heidelberg
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