Abstract
We show that fixed membership testing for many interesting subclasses of multi-pushdown machines is no harder than for pushdowns with single stack. The models we consider are MVPA, OVPA and MPDA, which have all been defined and studied in the past.
Multi-stack pushdown automata, MPDA, have ordered stacks with pop access restricted to the stack-top of the first non-empty stack. The membership for MPDAs is known to be in NSPACE(n) and in P. We show that the P-time algorithm can be implemented in the complexity class LogCFL; thus membership for MPDAs is LogCFL-complete.
It follows that membership testing for ordered visibly pushdown automata OVPA is also in LogCFL.
The membership problem for multi-stack visibly pushdown automata, MVPA, is known to be NP-complete. However, many applications focus on MVPA with O(1) phases. We show that for MVPA with O(1) phases, membership reduces to that in MPDAs, and so is in LogCFL.
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References
Hopcroft, A., Motwani, R., Ullman, J.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (2001)
Sudborough, I.H.: On the tape complexity of deterministic context-free language. Journal of Association of Computing Machinery 25(3), 405–414 (1978)
Sudborough, I.H.: A note on tape-bounded complexity classes and linear context-free languages. Journal of Association of Computing Machinery 22, 499–500 (1975)
Holzer, M., Lange, K.J.: On the complexities of linear LL(1) and LR(1) grammars. In: 9th International Symposium on Fundamentals of Computation Theory FCT, London, UK, pp. 299–308. Springer, Heidelberg (1993)
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: 36th ACM Symposium on Theory of Computing (STOC 2004), pp. 202–211 (2004)
Mehlhorn, K.: Pebbling mountain ranges and its application to DCFL recognition. In: 7th International Colloquium on Automata, Languages and Programming, pp. 422–432 (1980)
Dymond, P.W.: Input-driven languages are in logn depth. Information Processing Letters 26, 247–250 (1988)
Carotenuto, D., Murano, A., Peron, A.: 2-visibly pushdown automata. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 132–144. Springer, Heidelberg (2007)
La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: 22nd Symposium on Logic in Computer Science, pp. 161–170 (2007)
Cherubini, A., Breveglieri, L., Citrini, C., Crespi Reghizzi, S.: Multipushdown languages and grammars. International Journal of Foundations of Computer Science 7(3), 253–292 (1996)
Cherubini, A., Pietro, P.S.: A polynomial-time parsing algorithm for a class of non-deterministic two-stack automata. In: 4th Italian Conference on Theoretical Computer Science, pp. 150–164 (1992)
Cherubini, A., Pietro, P.S.: A polynomial-time parsing algorithm for k-depth languages. Journal of Computer and System Sciences 52(1), 61–79 (1996)
Allender, E., Jiao, J., Mahajan, M., Vinay, V.: Non-commutative arithmetic circuits: depth reduction and size lower bounds. Theoretical Computer Science 209, 47–86 (1998)
Ruzzo, W.: Tree-size bounded alternation. Journal of Computer and System Sciences 21, 218–235 (1980)
Vollmer, H.: Introduction to Circuit Complexity: A Uniform Approach. Springer, New York (1999)
Barrington, D.: Bounded-width polynomial size branching programs recognize exactly those languages in NC1. Journal of Computer and System Sciences 38, 150–164 (1989)
Pietro, P.S.: Two-stack automata. Rapporto Interno n. 92-073, Dipartimento Di Elettronica e Informazione, Politecnico di Milano, Milano (October 1992), http://home.dei.polimi.it/sanpietr/pubs/twostack92.ZIP
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Limaye, N., Mahajan, M. (2009). Membership Testing: Removing Extra Stacks from Multi-stack Pushdown Automata. In: Dediu, A.H., Ionescu, A.M., MartÃn-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2009. Lecture Notes in Computer Science, vol 5457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00982-2_42
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DOI: https://doi.org/10.1007/978-3-642-00982-2_42
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