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The operators minCh and maxCh on the polynomial hierarchy

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Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

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Abstract

In this paper we introduce a new acceptance concept for nondeterministic Turing machines with output device which allows a characterization of the complexity class Θ p2 = PNP[log] as a polynomial time bounded class. Thereby the internal structure of the output is essential: it looks at output with maximal number of mind changes instead of output with maximal value which was realized for the first time by Krentel [Kre88].

Motivated by this characterization we define in a general way two operators, the so called maxCh- and minCh- operator, respectively which are special types of optimization operators.

Following a paper by Hempel/Wechsung [HW96] we investigate the behaviour of these operators on the polynomial hierarchy. We prove a collection of relations regarding the interaction of operators maxCh, minCh, $, Θ, Θ, Θ, Sig, C and U. So we get a tool to show that the maxCh- and minCh- classes are distinct under reasonable structural assumptions. Finally, our proof techniques allow to solve one of the open questions of Hempel/Wechsung.

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References

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© 1999 Springer-Verlag Berlin Heidelberg

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Spakowski, H., Vogel, J. (1999). The operators minCh and maxCh on the polynomial hierarchy. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_44

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  • DOI: https://doi.org/10.1007/3-540-48321-7_44

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

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