T. Thierauf, S. Toda, and O. Watanabe. On sets bounded truth-table reducible to p-selective sets. In Proc. 11th Annual Symposium on Theoretical Aspects of Computer Science, volume 775 of Lecture Notes in Computer Science, pages 427--438. SpringerVerlag, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... if NP has a tt hard p selective set, then NP = RP (this result also follows from the work of Beigel [Bei88] Ogihara [Ogi94] Beigel, Kummer, and Stephan [BKS94] and Agrawal and Arvind [AA94] showed that if NP has a bounded truth table hard p selective set, then NP = P (see also [HHO 93, TTW94] Thus the reducibility of NP sets to p selective sets offers precise characterizations of the questions NP = P and NP P poly , and a sufficient condition for NP = RP. Besides these, p selective sets have found other (surprising) applications in complexity theory. For example, Buhrman and ....

T. Thierauf, S. Toda, and O. Watanabe. On sets bounded truth-table reducible to p-selective sets. In Proc. 11th Annual Symposium on Theoretical Aspects of Computer Science, volume 775 of Lecture Notes in Computer Science, pages 427--438. SpringerVerlag, 1994.

....A is P selective if there exists a polynomial time computable function that selects one of two given input strings such that if any one of the two strings is in A, then also the selected one. Let SELECT denote the class of P selective sets. Then we know the following facts: 1. Selman and Ko (see [14]) P T (SPARSE) P T (SELECT) 2. Watanabe [17] PT (SELECT) 6 P tt (SELECT) Regarding our above question, the following results are known: 1. Selman [13] If P 6= NP, then NP 6 Pm (SELECT) 2. Agrawal and Arvind [1] Beigel, Kummer and Stephan [3] Ogihara [11] If P 6= NP, then NP 6 Pn ....

T. Thierauf, S. Toda, and O. Watanabe. On sets bounded truth-table reducible to P-selective sets. In Proc. 11th STACS, Lecture Notes in Comput. Sci., 775, pages 427--438. Springer Verlag, 1994.

....if there exists a p selective set that is NP hard under positive truth table reductions, then P = NP. Buhrman, Torenvliet and van Emde Boas [BTvEB94] generalized this to show that if there exists a pselective that is NP hard under positive Turing reductions, then P =NP. Thierauf, Toda and Watanabe [TTW94] showed that if every set in NP is bounded truth table reducible to a p selective set, then NP DTIME[2 n O(1= p logn) Agrawal and Arvind [AA94] Beigel, Kummer and Stephan [BKS94] and Ogihara [Ogi94] independently have proved that the existence of a btt hard p selective set for NP ....

T. Thierauf, S. Toda, and O. Watanabe. On sets bounded truth-table reducible to p-selective sets. In Proceedings of 11th Annual Symposium on Theoretical Aspects of Computer Science, pages 427--438, 1994.

.... If there is an approximable set that is p k tt hard for the Boolean hierarchy then P = NP [2, Corollary 39] 3) If SAT is p 1 tt reducible to a p selective set then P = NP [13, Corollary 15] 4) If SAT is p btt reducible to a p selective set then NP DTIME(2 n O(1= p log n) [32]. In the following we generalize those three results for the case of sets that are NPhard under n o(1) tt reductions. In particular, we show that every btt hard set for NP is p superterse unless P = NP. Since p selective sets are approximable, this implies that SAT is not btt reducible to a ....

T. Thierauf, S. Toda, O. Watanabe. On sets bounded truth-table reducible to p-selective sets. In STACS 94, pp. 427--438, Lecture Notes in Computer Science, Vol. 775, 1994.

....a p selective that is NP hard under positive Turing reductions, then P = NP. Toda [Tod91] proved that if there is a p selective set that is truth table hard for NP, then P = FewP and R = NP. He asked if this assumption would imply the stronger collapse of P = NP. Thierauf, Toda and Watanabe [TTW93] showed that if every set in NP is bounded truth table reducible to a p selective set, then NP DT IME[2 n O(1= p log n) Agrawal and Arvind [AA93] Beigel, Kummer and Stephan [BKS93] and Ogiwara [Ogi93] independently have proved that the existence of a btt hard p selective set for NP ....

T. Thierauf, S. Toda, and O. Watanabe. On sets bounded truth-table reducible to p-selective sets. Technical Report 93-03, Universitat Ulm, Germany, Juni 93. To be presented at STACS 94.

....there exists a p selective set that is NP hard under positive truthtable reductions, then P = NP. Buhrman, Torenvliet and van Emde Boas [BTvEB94] generalized this to show that if there exists a p selective that is NP hard under positive Turing reductions, then P = NP. Thierauf, Toda and Watanabe [TTW94] showed that if every set in NP is bounded truth table reducible to a p selective set, then NP DT IME[2 n O(1= p log n) Agrawal and Arvind [AA94] Beigel, Kummer and Stephan [BKS94] and Ogihara [Ogi94] independently have proved that the existence of a btt hard p selective set for NP ....

T. Thierauf, S. Toda, and O. Watanabe. On sets bounded truth-table reducible to p-selective sets. In Proceedings of 11th Annual Symposium on Theoretical Aspects of Computer Science, pages 427438, 1994.

....output. If such a polynomial time algorithm exists, then A is said to be P selective. 34 P selective sets were defined by Selman 34 as a complexity theoretic analog of semi recursive sets in recursion theory. 20 Subsequently, this property has been studied by many researchers (e.g. see Ref. [39,19,18,11,40,10,32,7,1]) This research has revealed that P selective sets are an important tool in studying several important structural concepts such as function complexity classes, 19;32;7;1;12 reducing search to decision and self reducibility, 18;41;11 and promise problems. 36;29 A survey of the current state ....

T. Thierauf, S. Toda, and O. Watanabe. On sets bounded truth-table reducible to p-selective sets. In Proceedings of 11th Annual Symposium on Theoretical Aspects of Computer Science, pages 427--438, 1994.

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