On the equivalence of two-way pushdown automata and counter machines over bounded languages
It is known that two-way pushdown automata ate more powerful than two-way counter machines. The result is also true for the case when the pushdown store and counter are reversal-bounded. In contrast, we show that two-way reversal-bounded pushdown automata over bounded languages (i.e., subsets of w 1 * ... w k * for some nonnull words w1 ..., wk) are equivalent to two-way reversal-bounded counter machines. We also show that, unlike the unbounded input case, two-way reversal-bounded pushdown automata over bounded languages have decidable emptiness, equivalence and containment problems.
KeywordsTurn Point Counter Machine Pushdown Automaton Input Segment Finite Control
Unable to display preview. Download preview PDF.
- [Chr84]M. Chrobak. A note on bounded-reversal multipushdown machines. Info. Proc. Letters, 19:179–180, 1984.Google Scholar
- [DG82]P. Duris and Z. Galil. Fooling a two way automaton or one pushdown store is better than one counter for two way machines. Theoretical Computer Science, 21:39–53, 1982.Google Scholar
- [GI79]E. M. Gurari and O. H. Ibarra. Simple counter machines and number-theoretic problems. J. Comput. System Sci., 19:145–162, 1979.Google Scholar
- [GI82]E. M. Gurari and O. H. Ibarra. Two-way counter machines and diophantine equations. J. Assoc. Comput. Mach., 29:863–873, 1982.Google Scholar
- [Iba78]O. H. Ibarra. Reversal-bounded multicounter machines and their decision problems. J. Assoc. Comput. Mach., 25:116–133, 1978.Google Scholar
- [IJ91]O. Ibarra and T. Jiang. The power of alternating one-reversal counters and stacks. SIAM Journal on Computing, 20(2):278–290, 1991.Google Scholar
- [Min61]M. Minsky. Recursive unsolvability of Post's problem of tag and other topics in the theory of Turing machines. Ann. of Math., 74:437–455, 1961.Google Scholar
- [Mon84]B. Monien. Deterministic two-way one-head pushdown automata are very powerful. Info. Proc. Letters, 18:239–242, 1984.Google Scholar
- [Val74]L. Valiant. The equivalence problem for deterministic finite-turn pushdown automata. Inform. and Contr., 25:123–133, 1974.Google Scholar