Abstract
In input-driven pushdown automata (\(\text {IDPDA}\)) the input alphabet is divided into three distinct classes and the actions on the pushdown store (push, pop, nothing) are solely governed by the input symbols. Here, this model is extended in such a way that the input of an \(\text {IDPDA}\) is preprocessed by a deterministic sequential transducer. These automata are called tinput-driven pushdown automata (\(\text {TDPDA}\)) and it turns out that \(\text {TDPDA}\)s are more powerful than \(\text {IDPDA}\)s but still not as powerful as real-time deterministic pushdown automata. Nevertheless, even this stronger model has still good closure and decidability properties. In detail, it is shown that \(\text {TDPDA}\)s are closed under the Boolean operations union, intersection, and complementation. Furthermore, decidability procedures for the inclusion problem as well as for the questions of whether a given automaton is a \(\text {TDPDA}\) or an \(\text {IDPDA}\) are developed. Finally, representation theorems for the context-free languages using \(\text {IDPDA}\)s and \(\text {TDPDA}\)s are established.
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References
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Babai, L. (ed.) Symposium on Theory of Computing (STOC 2004), pp. 202–211. ACM (2004)
Alur, R., Madhusudan, P.: Adding nesting structure to words. J. ACM 56, 16 (2009)
Bensch, S., Holzer, M., Kutrib, M., Malcher, A.: Input-driven stack automata. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds.) TCS 2012. LNCS, vol. 7604, pp. 28–42. Springer, Heidelberg (2012)
Bordihn, H., Holzer, M., Kutrib, M.: Economy of description for basic constructions on rational transductions. J. Autom. Lang. Comb. 9, 175–188 (2004)
von Braunmühl, B., Verbeek, R.: Input-driven languages are recognized in \(\log n\) space. In: Karpinski, M., van Leeuwen, J. (eds.) Topics in the Theory of Computation, Mathematics Studies, vol. 102, pp. 1–19. North-Holland (1985)
Chervet, P., Walukiewicz, I.: Minimizing variants of visibly pushdown automata. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 135–146. Springer, Heidelberg (2007)
Crespi-Reghizzi, S., Mandrioli, D.: Operator precedence and the visibly pushdown property. J. Comput. Syst. Sci. 78, 1837–1867 (2012)
Dymond, P.W.: Input-driven languages are in \(\log n\) depth. Inform. Process. Lett. 26, 247–250 (1988)
Hartmanis, J.: Context-free languages and turing machine computations. Proc. Symposia in Applied Mathematics 19, 42–51 (1967)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)
Kutrib, M., Malcher, A., Mereghetti, C., Palano, B., Wendlandt, M.: Deterministic input-driven queue automata: finite turns, decidability, and closure properties. Theor. Comput. Sci. 578, 58–71 (2015)
La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: Logic in Computer Science (LICS 2007), pp. 161–170. IEEE Computer Society (2007)
Madhusudan, P., Parlato, G.: The tree width of auxiliary storage. In: Ball, T., Sagiv, M. (eds.) Principles of Programming Languages (POPL 2011), pp. 283–294. ACM (2011)
Mehlhorn, K.: Pebbling mountain ranges and its application to DCFL-recognition. In: de Bakker, J.W., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 422–435. Springer, Heidelberg (1980)
Myhill, J.: Finite automata and the representation of events. Technical Report TR 57–624, WADC (1957)
Okhotin, A., Salomaa, K.: Complexity of input-driven pushdown automata. SIGACT News 45, 47–67 (2014)
Schützenberger, M.P.: Sur les relations rationnelles. In: Brakhage, H. (ed.) Automata Theory and Formal Languages. LNCS, vol. 33, pp. 209–213. Springer, Heidelberg (1975)
Sheng, Y.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 41–110. Springer, Heidelberg (1997)
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Kutrib, M., Malcher, A., Wendlandt, M. (2015). Tinput-Driven Pushdown Automata. In: Durand-Lose, J., Nagy, B. (eds) Machines, Computations, and Universality. MCU 2015. Lecture Notes in Computer Science(), vol 9288. Springer, Cham. https://doi.org/10.1007/978-3-319-23111-2_7
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DOI: https://doi.org/10.1007/978-3-319-23111-2_7
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