Giovanni Pighizzini
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Abstract
We present two restricted versions of one-tape Turing machines. Both characterize the class of context-free languages. In the first version, proposed by Hibbard in 1967 and called limited automata, each tape cell can be rewritten only in the first d visits, for a fixed constant d ≥ 2. Furthermore, for d = 2 deterministic limited automata are equivalent to deterministic pushdown automata, namely they characterize deterministic context-free languages. Further restricting the possible operations, we consider strongly limited automata. These models still characterize context-free languages. However, the deterministic version is less powerful than the deterministic version of limited automata. In fact, there exist deterministic context-free languages that are not accepted by any deterministic strongly limited automaton.
- Alberts, M.: Space complexity of alternating Turing machines. In: Budach, L. (ed.) FCT. Lecture Notes in Computer Science, vol. 199, pp. 1--7. Springer (1985) Google Scholar
Digital Library
- Chomsky, N., Schützenberger, M.: The algebraic theory of context-free languages. In: Braffort, P., Hirschberg, D. (eds.) Computer Programming and Formal Systems, Studies in Logic and the Foundations of Mathematics, vol. 35, pp. 118--161. Elsevier (1963)Google ScholarCross Ref
- Geffert, V.: Bridging across the log(n) space frontier. Inf. Comput. 142(2), 127--158 (1998), http://dx.doi.org/10.1006/inco.1997.2682 Google ScholarDigital Library
- Ginsburg, S., Rice, H.G.: Two families of languages related to ALGOL. J. ACM 9(3), 350--371 (1962), http://doi.acm.org/10.1145/321127.321132 Google ScholarDigital Library
- Hartmanis, J.: Computational complexity of one-tape Turing machine computations. J. ACM 15(2), 325--339 (1968) Google ScholarDigital Library
- Hemaspaandra, L.A., Mukherji, P., Tantau, T.: Context-free languages can be accepted with absolutely no space overhead. Inf. Comput. 203(2), 163--180 (2005) Google ScholarDigital Library
- Hennie, F.C.: One-tape, off-line Turing machine computations. Information and Control 8(6), 553--578 (1965)Google ScholarCross Ref
- Hibbard, T.N.: A generalization of context-free determinism. Information and Control 11(1/2), 196--238 (1967)Google ScholarCross Ref
- Hopcroft, J.E., Ullman, J.D.: Some results on tape-bounded Turing machines. J. ACM 16(1), 168--177 (1969) Google ScholarDigital Library
- Jancar, P., Mráz, F., Plátek, M.: Forgetting automata and context-free languages. Acta Inf. 33(5), 409--420 (1996) Google ScholarDigital Library
- Kuroda, S.: Classes of languages and linear-bounded automata. Information and Control 7(2), 207--223 (1964), http://dx.doi.org/10.1016/S0019-9958(64)90120-2Google ScholarCross Ref
- Kutrib, M., Wendlandt, M.: On simulation cost of unary limited automata. In: Shallit, J., Okhotin, A. (eds.) Descriptional Complexity of Formal Systems - 17th International Workshop, DCFS 2015, Waterloo, ON, Canada, June 25-27, 2015. Proceedings. Lecture Notes in Computer Science, vol. 9118, pp. 153--164. Springer (2015), http://dx.doi.org/10.1007/978-3-319-19225-3_13Google Scholar
- Lewis II, P.M., Stearns, R.E., Hartmanis, J.: Memory bounds for recognition of context-free and context-sensitive languages. In: FOCS. pp. 191--202. IEEE (1965) Google ScholarDigital Library
- McNaughton, R., Papert, S.A.: Counter-Free Automata (M.I.T. Research Monograph No. 65). The MIT Press (1971) Google ScholarDigital Library
- Mereghetti, C.: Testing the descriptional power of small Turing machines on nonregular language acceptance. Int. J. Found. Comput. Sci. 19(4), 827--843 (2008)Google ScholarCross Ref
- Michel, P.: An NP-complete language accepted in linear time by a one-tape Turing machine. Theor. Comput. Sci. 85(1), 205--212 (1991) Google ScholarDigital Library
- Michel, P.: A survey of space complexity. Theor. Comput. Sci. 101(1), 99--132 (1992) Google ScholarDigital Library
- Okhotin, A.: Non-erasing variants of the Chomsky-Schützenberger theorem. In: Yen, H., Ibarra, O.H. (eds.) Developments in Language Theory - 16th International Conference, DLT 2012, Taipei, Taiwan, August 14-17, 2012. Proceedings, Lecture Notes in Computer Science, vol. 7410, pp. 121--129. Springer (2012), http://dx.doi.org/10.1007/978-3-642-31653-1_12 Google ScholarDigital Library
- Peckel, J.: On a deterministic subclass of context-free languages. In: Gruska, J. (ed.) Mathematical Foundations of Computer Science 1977, 6th Symposium, Tatranska Lomnica, Czechoslovakia, September 5-9, 1977, Proceedings. Lecture Notes in Computer Science, vol. 53, pp. 430--434. Springer (1977), http://dx.doi.org/10.1007/3-540-08353-7_164Google Scholar
- Pighizzini, G.: Nondeterministic one-tape off-line Turing machines. Journal of Automata, Languages and Combinatorics 14(1), 107--124 (2009) Google ScholarDigital Library
- Pighizzini, G.: Strongly limited automata. Fundam. Inform. (to appear), a preliminary version appeared in: Bensch, S., Freund, R., Otto, F. (eds.) Sixth Workshop on Non-Classical Models for Automata and Applications - NCMA 2014, Kassel, Germany, July 28-29, 2014. Proceedings. [email protected], vol. 304, pp. 191--206. Osterreichische Computer Gesellschaft (2014)Google Scholar
- Pighizzini, G., Pisoni, A.: Limited automata and regular languages. Int. J. Found. Comput. Sci. 25(7), 897--916 (2014), http://dx.doi.org/10.1142/S0129054114400140Google ScholarCross Ref
- Pighizzini, G., Pisoni, A.: Limited automata and context-free languages. Fundam. Inform. 136(1-2), 157--176 (2015), http://dx.doi.org/10.3233/FI-2015-1148 Google ScholarDigital Library
- Shepherdson, J.C.: The reduction of two-way automata to one-way automata. IBM J. Res. Dev. 3(2), 198 --200 (1959) Google ScholarDigital Library
- Anat Ganor, Gillat Kol, and Ran Raz. Exponential separation of information and communication. Electronic Colloquium on Computational Complexity (ECCC), 21:49, 2014Stearns, R.E., Hartmanis, J., Lewis II, P.M.: Hierarchies of memory limited computations. In: FOCS. pp. 179--190. IEEE (1965). Google ScholarDigital Library
- Szepietowski, A.: Turing Machines with Sublogarithmic Space, Lecture Notes in Computer Science, vol. 843. Springer (1994), http://dx.doi.org/10.1007/3-540-58355-6 Google ScholarDigital Library
- Tadaki, K., Yamakami, T., Lin, J.C.H.: Theory of one-tape linear-time Turing machines. Theor. Comput. Sci. 411(1), 22--43 (2010), http://dx.doi.org/10.1016/j.tcs.2009.08.031 Google ScholarDigital Library
- Trakhtenbrot, B.A.: Turing machine computations with logarithmic delay, (in russian). Algebra I Logica 3, 33--48 (1964)Google Scholar
- Wagner, K.W., Wechsung, G.: Computational Complexity. D. Reidel Publishing Company, Dordrecht (1986)Google Scholar
- Wechsung, G.: Characterization of some classes of context-free languages in terms of complexity classes. In: Becvár, J. (ed.) Mathematical Foundations of Computer Science 1975, 4th Symposium, Mariánské Lázne, Czechoslovakia, September 1-5, 1975, Proceedings. Lecture Notes in Computer Science, vol. 32, pp. 457--461. Springer (1975), http://dx.doi.org/10.1007/3-540-07389-2_233Google Scholar
- Wechsung, G., Brandstädt, A.: A relation between space, return and dual return complexities. Theor. Comput. Sci. 9, 127--140 (1979), http://dx.doi.org/10.1016/0304-3975(79) 90010-0Google ScholarCross Ref
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- Guest Column: One-Tape Turing Machine Variants and Language Recognition
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