Abstract
Hertrampf's locally definable acceptance types showed that many complexity classes can be defined in terms of polynomially time bounded NTM's with simple local conditions on the nodes of its computation tree, rather than global concepts like number of accepting paths etc. We introduce extended locally definable acceptance types as an extension of Hertrampf's work with respect to the number of characterizable complexity classes. Among the new characterizable classes are UP and MODZkP. It is shown how different types of oracle access, e.g. guarded access, can be characterized by this model. This sheds new light on the discussion on how to access unambiguous computation. We present simple functions that describe precisely objects of current research as the unambiguous oracle, alternation, and promise hierarchies. We exhibit the new class UAP which seems to be an unambiguous analogue of Wagner's ∇P.
Research supported by DFG-SFB 0342 TP A4 “KLARA”
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R. Beigel, J. Gill, and U. Hertrampf. Counting classes: Threshold, parity, mods, and fewness. In Proc. of 7th STACS, number 415 in LNCS, pages 49–57. Springer, 1990.
G. Buntrock, L. A. Hemachandra, and D. Siefkes. Using inductive counting to simulate nondeterministic computation. In Proc. of 15th MFCS, number 452 in LNCS, pages 187–194. Springer, 1990. (to appear in Information and Computation).
J.-Y. Cai, L. Hemachandra, and J. Vyskoč. Promise problems and access to unambiguous computation. In Proc. of 17th MFCS, number 629 in LNCS, pages 162–171. Springer, 1992.
S. Even, A. Selman, and Y. Yacobi. The complexity of promise problems with applications to public-key cryptography. Inform. and Control, 61(2):159–173, 1984.
S. A. Fenner, L. J. Fortnow, and S. A. Kurtz. Gap-definable counting classes. In Proc. of 6th Conference on Structure in Complexity Theory, pages 30–42, 1991.
L. Goldschlager and I. Parberry. On the construction of parallel computers from various bases of boolean functions. Theoretical Comput. Sci., 43:43–58, 1986.
J. Grollmann and A. Selman. Complexity measures for public-key cryptosystems. SIAM J. Comput., 17:309–335, 1988.
U. Hertrampf. Locally definable acceptance types—the three valued case. In Proc. of LATIN'92, number 583 in LNCS, pages 262–271. Springer, 1992.
U. Hertrampf. Locally definable acceptance types for polynomial time machines. In Proc. of 9th STACS, number 577 in LNCS, pages 199–207. Springer, 1992.
K.-J. Lange. Unambiguity of circuits. In Proc. of 5th Conference on Structure in Complexity Theory, pages 130–137, 1990. (to appear in TCS).
K.-J. Lange and P. Rossmanith. Characterizing unambiguous augmented pushdown automata by circuits. In Proc. of 15th MFCS, number 452 in LNCS, pages 399–406. Springer, 1990.
R. Niedermeier and P. Rossmanith. Unambiguous simulations of auxiliary pushdown automata and circuits. In Proc. of LATIN'92, number 583 in LNCS, pages 387–400. Springer, 1992.
A. L. Selman. A survey of one-way functions in complexity theory. Mathematical Systems Theory, 25(3):203–221, 1992.
L. Valiant. The relative complexity of checking and evaluating. Inform. Proc. Letters, 5:20–23, 1976.
K. W. Wagner. Alternating machines using partially defined “AND” and “OR”. Technical Report 39, Institut für Informatik, Universität Würzburg, Jan. 1992.
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© 1993 Springer-Verlag Berlin Heidelberg
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Niedermeier, R., Rossmanith, P. (1993). Extended locally definable acceptance types. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_47
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DOI: https://doi.org/10.1007/3-540-56503-5_47
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