Abstract
As its name suggests, a stateless pushdown automaton has no states. As a result, each of its computational steps depends only on the currently scanned symbol and the current pushdown-store top. In this paper, we consider stateless pushdown automata whose size of their pushdown alphabet is limited by a positive integer. More specifically, we establish an infinite hierarchy of language families resulting from stateless pushdown automata with limited pushdown alphabets. In addition, we prove analogous results for stateless deterministic pushdown automata and stateless real-time pushdown automata. A formulation of an open problem closes the paper.
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References
Eğecioğlu, Ö., Hegedüs, L., Nagy, B.: Hierarchies of stateless multicounter 5’ → 3’ Watson-Crick automata languages. Fundamenta Informaticae 110(1-4), 111–123 (2011)
Nagy, B., Hegedüs, L., Eğecioğlu, Ö.: Hierarchy Results on Stateless Multicounter 5′ → 3′ Watson-Crick Automata. In: Cabestany, J., Rojas, I., Joya, G. (eds.) IWANN 2011, Part I. LNCS, vol. 6691, pp. 465–472. Springer, Heidelberg (2011)
Eğecioğlu, Ö., Ibarra, O.H.: On Stateless Multicounter Machines. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds.) CiE 2009. LNCS, vol. 5635, pp. 178–187. Springer, Heidelberg (2009)
Frisco, P., Ibarra, O.H.: On Stateless Multihead Finite Automata and Multihead Pushdown Automata. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 240–251. Springer, Heidelberg (2009)
Gallier, J.H.: DPDA’s in ’atomic normal form’ and applications to equivalence problems. Theoretical Computer Science 14(2), 155–186 (1981)
Harrison, M.: Introduction to Formal Language Theory. Addison-Wesley, Boston (1978)
Ibarra, O.H., Karhumäki, J., Okhotin, A.: On Stateless Multihead Automata: Hierarchies and the Emptiness Problem. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 94–105. Springer, Heidelberg (2008)
Kutrib, M., Messerschmidt, H., Otto, F.: On stateless deterministic restarting automata. Acta Informatica 47(7), 391–412 (2010)
Kutrib, M., Messerschmidt, H., Otto, F.: On stateless two-pushdown automata and restarting automata. International Journal of Foundations of Computer Science 21(5), 781–798 (2010)
Meduna, A.: Elements of Compiler Design. Auerbach Publications, Boston (2007)
Oyamaguchi, M., Honda, N.: The decidability of equivalence for deterministic stateless pushdown automata. Information and Control 38(3), 367–376 (1978)
Valiant, L.G.: Decision procedures for families of deterministic pushdown automata. Research Report CS-RR-001, Department of Computer Science, University of Warwick, Coventry, UK (1973)
Yang, L., Dang, Z., Ibarra, O.H.: On stateless automata and P systems. International Journal of Foundations of Computer Science, 1259–1276 (2008)
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Meduna, A., Vrábel, L., Zemek, P. (2012). An Infinite Hierarchy of Language Families Resulting from Stateless Pushdown Automata with Limited Pushdown Alphabets. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_18
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DOI: https://doi.org/10.1007/978-3-642-31623-4_18
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