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A Space Lower Bound for Acceptance by One-Way Π2-Alternating Machines

Published online by Cambridge University Press:  15 April 2002

Viliam Geffert  and
Norbert Popély
Viliam Geffert
Affiliation:
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04154 Košice, Slovakia; (geffert@kosice.upjs.sk)
Norbert Popély
Affiliation:
Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04154 Košice, Slovakia; (popely@kosice.upjs.sk)
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Abstract

We show that one-way Π2-alternating Turing machines cannotaccept unary nonregular languages in o(log n) space. This holdsfor an accept mode of space complexity measure, defined asthe worst cost of any accepting computation. This lower boundshould be compared with the corresponding bound for one-wayΣ2-alternating machines, that are able to accept unarynonregular languages in space O(log log n). Thus, Σ2-alternation is more powerful than Π2-alternationfor space bounded one-way machines with unary inputs.

Keywords

Alternationlower boundsnonregular languagesspace complexityTuring machine.

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 5 , September 2000 , pp. 357 - 372
Copyright
© EDP Sciences, 2000

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References

M. Alberts, Space complexity of alternating Turing machines, in Proc. Fund. Comput. Theory. Springer-Verlag, Lecture Notes in Comput. Sci. 199 (1985) 1-7.
Alt, H. and Mehlhorn, K., A language over a one symbol alphabet requiring only O(log log n) space. SIGACT News 7 (1975) 31-33. CrossRef
A. Bertoni, C. Mereghetti and G. Pighizzini, Strong optimal lower bounds for Turing machines that accept nonregular languages, in Proc. Math. Found. Comput. Sci. Springer-Verlag, Lecture Notes in Comput. Sci. 969 (1995) 309-18.
A. Bertoni, C. Mereghetti and G. Pighizzini, Space and reversal complexity of nonregular languages. Technical Report, University of Milano (1998).
Chandra, A.K., Kozen, D.C. and Stockmeyer, L.J., Alternation. J. Assoc. Comput. Math. 28 (1981) 114-33. CrossRef
P. van Emde Boas, Machine models and simulations, edited by J. van Leeuwen, Handbook of Theoretical Computer Science. Elsevier Science (1989).
R. Freivalds, On the work time of deterministic and nondeterministic Turing machines. Latv. Mat. Ezhegodnik 23 (1979) 158-65 (in Russian).
Geffert, V., Nondeterministic computations in sublogarithmic space and space constructibility. SIAM J. Comput. 20 (1991) 484-98. CrossRef
Geffert, V., A hierarchy that does not collapse: Alternations in low level space. RAIRO: Theoret. Informatics Appl. 28 (1994) 465-512.
Geffert, V., Mereghetti, C. and Pighizzini, G., Sublogarithmic bounds on space and reversals. SIAM J. Comput. 28 (1999) 325-40. CrossRef
J. Hartmanis, P.M. Lewis II and R.E. Stearns, Hierarchies of memory limited computations, in IEEE Conf. Record on Switching Circuit Theory and Logical Design (1965) 179-90.
J. Hartmanis, P.M. Lewis II and R.E. Stearns, Memory bounds for recognition of context-free and context-sensitive languages, in IEEE Conf. Record on Switching Circuit Theory and Logical Design (1965) 191-202.
Hopcroft, J.E. and Ullman, J.D., Some results on tape-bounded Turing machines. J. Assoc. Comput. Mach. 16 (1969) 168-77. CrossRef
Hromkovic, J., Rovan, B. and Slobodová, A., Deterministic versus nondeterministic space in terms of synchronized alternating machines. Theoret. Comput. Sci. 132 (1994) 319-36. CrossRef
Iwama, K., ASPACE o(log log n) is regular. SIAM J. Comput. 22 (1993) 136-46. CrossRef
Ladner, B.E., Lipton, R.J. and Stockmeyer, L.R., Alternation bounded auxiliary pushdown automata. Inform. and Control 62 (1984) 93-108. CrossRef
Mereghetti, C. and Pighizzini, G., A remark on middle space bounded alternating Turing machines. Inform. Process. Lett. 56 (1995) 229-32. CrossRef
C. Mereghetti and G. Pighizzini, Optimal simulations between unary automata, in Proc. Symp. Theoret. Aspects Comput. Sci. Springer-Verlag, Lecture Notes in Comput. Sci. 1373 (1998) 139-149 (to appear in SIAM J. Comput.).
Savitch, W.J., Relationships between nondeterministic and deterministic tape complexities. J. Comput. System Sci. 4 (1970) 177-92. CrossRef
I.H. Sudborough, Efficient algorithms for path system problems and applications to alternating and time-space complexity classes, in Proc. IEEE Symp. Found. of Comput. Sci. (1980) 62-73.
Szepietowski, A., Remarks on languages acceptable in log log n space. Inform. Process Lett. 27 (1988) 201-3. CrossRef