Computation with Absolutely No Space Overhead
We study Turing machines that are allowed absolutely no space overhead. The only work space the machines have, beyond the fixed amount of memory implicit in their finite-state control, is that which they can create by cannibalizing the input bits’ own space. This model more closely reflects the fixed-sized memory of real computers than does the standard complexity-theoretic model of linear space. Though some context-sensitive languages cannot be accepted by such machines, we show that subclasses of the context-free languages can even be accepted in polynomial time with absolutely no space overhead.
Keywordsspace overhead space reuse overhead-free computation context-sensitive languages context-free languages linear space deterministic linear languages metalinear languages
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- 2.N. Chomsky and M. Schützenberger. The algebraic theory of context-free languages. In P. Braffort and D. Hirschberg, editors, Computer Programming and Formal Systems, pages 118–161. North Holland, Amsterdam, 1963.Google Scholar
- 6.K. Fishkin. Performing in-place affine transformations in constant space. In Proceedings of Graphics Interface’ 92, pages 106–114, 1992.Google Scholar
- 8.J. Geske. Nondeterminism, bi-immunity and almost-everywhere complexity. IEICE Trans. on Communications, Electronics, Information, and Systems, E76, 1993.Google Scholar
- 10.L. Hemaspaandra, P. Mukherji, and T. Tantau. Computation with absolutely no space overhead. Technical Report TR-779, Department of Computer Science, University of Rochester, Rochester, NY, May 2002.Google Scholar
- 11.M. Holzer and K. Lange. On the complexities of linear LL(1) and LR(1) grammars. In Proc. of the 9th Conference on Fundamentals of Computation Theory, volume 710 of Lecture Notes in Computer Science, pages 299–308. Springer-Verlag, 2003.Google Scholar
- 12.J. Hopcroft and J. Ullman. Formal Languages and their Relation to Automata. Addison-Wesley, 1969.Google Scholar
- 13.J. Hopcroft and J. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.Google Scholar
- 16.T. Kasami. An efficient recognition and syntax algorithm for context-free languages. Scientific Report AFCRL-65-758, Air Force Cambridge Research Lab., Bedford, Mass., 1965.Google Scholar
- 20.A. Salomaa. Formal Languages. Academic Press, 1973.Google Scholar