J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The Boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95-111, February 1989. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Oracles That Compute Values - Fenner, Homer, Ogihara, Selman (1997) (6 citations) (Correct)
....N with h 2 NPMV as the oracle. Then we can easily construct a machine that computes f by making k queries to h and m queries to g. Therefore, f 2 PF NPMV[k m] tt . This proves the lemma. The Boolean hierarchy over NP is defined by Wagner and Wechsung [19] and has been studied extensively [6, 7, 8, 12]. We denote the k th level of the Boolean hierarchy as NP(k) By definition, 1. NP(1) NP, and 2. for every k 2, NP(k) NP Gamma NP(k Gamma 1) The Boolean hierarchy over NP, denoted by BH is the union of all NP(k) k 1. Kadin [12] proved that the Boolean hierarchy collapses only if the ....
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM J. Comput., 18(1):95--111, 1989.
Computational Politics: Electoral Systems - Hemaspaandra, Hemaspaandra (2000) (3 citations) (Correct)
...., i.e. whether parallel and sequential access to NP coincide. Buss and Hay [10] have shown that P NP jj exactly captures the class of sets acceptable 4 via multiple rounds of parallel queries to NP and also exactly captures the disjunctive closure of the second level of the Boolean Hierarchy [11, 12]. Notwithstanding all the above appearances of P NP jj in complexity theory, P NP jj was strangely devoid of natural complete problems. The class was known somewhat indirectly to have a variety of complete problems, but they were not overwhelmingly natural. In particular, a seminal paper by ....
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95-111, 1989.
Relating Equivalence And Reducibility To Sparse Sets - Allender, Hemaspaandra, al. (1992) (20 citations) (Correct)
.... small information content can be crisply formalized: R p T (SPARSE) is precisely the class more commonly referred to as P poly of sets having polynomial sized (nonuniform) circuits (Meyer, see [7] R p T (SPARSE) has been intensely studied, both in terms of the question NP R p T (SPARSE) [19,16, 10,18], and in terms of the robustness of R p T (SPARSE) R p T (SPARSE) is indeed quite robust; in addition to its characterization in terms of small circuits, R p T (SPARSE) is easily noted equivalent to R p T (TALLY) R p tt (TALLY) and R p tt (SPARSE) see [6] Nonetheless, Book and Ko ....
.... Additionally, equivalence has been used by Balc azar and Book to characterize completely a natural subset of R p T (SPARSE) namely the sets with self producible circuits [4] The study of equivalence to sparse sets and the study of reducibility to sparse sets have each yielded a urry of results [9,31,10,16,18,20,3,1,21]. Nonetheless, many of the most basic questions have remained unanswered and, in some cases, unasked. In particular, the relationships between equivalence and reducibility to sparse sets have remained wholly 1 Though formal de nitions will be given in Section 2, it is useful to introduce some ....
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, The boolean hierarchy II: Applications, SIAM Journal on Computing, 18 (1989), pp. 95-111.
How Reductions to Sparse Sets Collapse the Polynomial-time.. - Young (1993) (22 citations) (Correct)
....one truth table reduction. SAT P m S iff SAT P 10tt S via a fixed negative one truth table reduction. 14 Bounded truth table reductions are the basic reductions used to define Boolean hierarchies, which have recently been investigated by surprisingly large groups of authors, CGHHSWW 88] [CGHHSWW 89], BBJSY 89] 15 Conjunctive truth tables, P conj ) are truth tables which are given by a simple conjunction of the variables (with no negations) Similarly, disjunctive truth tables use only disjuncts of the variables. Conjunctive and disjunctive truth tables are each special cases of ....
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, "The Boolean hierarchy II: applications," SIAM J Comput, 7 (1989), 95-111.
Downward Collapse from a Weaker Hypothesis - Hemaspaandra, Hemaspaandra.. (1998) (Correct)
....in light of the strongest known BH PH collapse connection, see [8,7] Definition 1.1 1. For any classes C and D, C DeltaD = fL fi fi (9C 2 C) 9D 2 D) L = C DeltaD]g; where C DeltaD = C Gamma D) D Gamma C) 2. For any sets C and D, C DeltaD = fhx; yi fi fi x 2 C , y 62 Dg: 3. [13,14], see also [15,16] Let C be any complexity class. We now define the levels of the boolean hierarchy. a) DIFF 1 (C) C. b) For any k 1, DIFF k 1 (C) fL fi fi (9L 1 2 C) 9L 2 2 DIFF k (C) L = L 1 Gamma L 2 ]g. c) For any k 1, coDIFF k (C) fL fi fi L 2 DIFF k (C)g. d) BH(C) ....
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
The Boolean Hierarchy of NP-Partitions - Kosub, Wagner (2000) (3 citations) Self-citation (Wagner) (Correct)
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J.-Y. Cai, T. Gundermann, J. Hartmanis, L. A. Hemachandra, V. Sewelson, K. W. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18:95-111, 1989.
Simultaneous Strong Separations of Probabilistic.. - Eppstein.. (1992) Self-citation (Hemachandra) (Correct)
....set y P (x, y) # y # x k . Though UP machines can never have more than one accepting path, US machines can this simply causes them to reject. Immediate relationships are: US is coNP hard and UP#US#NP [7] A further generalization of US that has been studied is the Counting Hierarchy [10, 18]. The usual definition of the counting hierarchy is as follows: Definition 4 Given a nondeterministic polynomial time machine M and a set of integers S, let L(M,S) be the strings that, when input to machine M , cause the number of accepting paths of M to be a member of S. Then CH is the class of ....
....C [28] We say a class C 1 is C 2 immune if C 1 contains a C 2 immune set. There is a large literature on relativization. Among the results that inspired this paper are the following. Relativized relations between US and NP were found by Blass and Gurevich [7] and have been generalized [10]. With respect to a random oracle, it has long been known that US #=P=R=BPP [6] and Kurtz, Mahaney, and Royer have recently shown that P#=UP with probability one relative to a random oracle ( 24] see also [29] 1 Racko# initially relativized unambiguous and probabilistic classes to separate ....
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM J. on Comput., 18(1):95--111, February 1989. 16
The Structural Complexity Column - By Juris Hartmanis Self-citation (Hartmanis) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The Boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, February 1989.
A Complexity Theory for Feasible Closure Properties - Ogiwara, Hemachandra (1991) (28 citations) Self-citation (Hemachandra) (Correct)
....3. Let DF be a class of functions. We say that DF has closure property f (of arity i) if: g 1 ; g i 2 DF = h 2 DF ; where h(x) f(g 1 (x) g i (x) 4. Let DF and CF be classes of functions. We say that DF is CF closed if DF has every CF closure property. 1 For example, in [38,9,5]; note also the striking recent closure results for the language classes PP [7,6,16] and C=P [21,33,49] 1 5. Let DF and CF be classes of functions. Let f be a CF closure property. We say that f is hard for the CF closure properties of DF (for short, a DF hard CF closure property, or, in the ....
....two functions f; g 2 F there is a function h 2 F such that for every x 2 , it holds that h(x) maxff(x) g(x)g. 3 A Complexity Theory for Closure Properties of #P It is well known that #P is closed under addition and multiplication [38] and indeed, #P has many other closure properties [9,5]. Proposition 3.1 1. 38] #P is closed under multiplication; that is, for every pair of nondeterministic polynomial time Turing machines, M 1 and M 2 , there exists a nondeterministic polynomial time Turing machine N such that for every x 2 , #accN (x) #accM1 (x) #accM2 (x) 2. 38] #P ....
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95-111, 1989.
On High and Low Sets for the Boolean Hierarchy - Steffen Reith, Klaus W. Wagner (1998) (2 citations) Self-citation (Wagner) (Correct)
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J.-Y. CAI, T. GUNDERMANN, J. HARTMANIS, L. A. HEMACHANDRA, V. SEWELSON, K. WAGNER, AND G. WECHSUNG. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95 -- 111, February 1989.
Robust Reductions - Cai, Hemaspaandra, Wechsung (1997) (3 citations) Self-citation (Cai Wechsung) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Reductions to Sets of Low Information Content - Arvind, Han, Hemachandra.. (1993) (21 citations) Self-citation (Hemachandra) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Query Order and Self-Specifying Machines - Hemaspaandra, Hempel, Wechsung (1995) (1 citation) Self-citation (Wechsung) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Relating Equivalence And Reducibility To Sparse Sets - Allender, Hemachandra.. (1992) (20 citations) Self-citation (Hemachandra) (Correct)
.... information content can be crisply formalized: R p T (SPARSE) is precisely the class more commonly referred to as P poly of sets having polynomial sized (nonuniform) circuits (Meyer, see [7] R p T (SPARSE) has been intensely studied, both in terms of the question NP R p T (SPARSE) [19,16,10,18], and in terms of the robustness of R p T (SPARSE) R p T (SPARSE) is indeed quite robust; in addition to its characterization in terms of small circuits, R p T (SPARSE) is easily noted equivalent to R p T (TALLY) R p tt (TALLY) and R p tt (SPARSE) see [6] Nonetheless, Book and Ko ....
....p r (SPARSE) as the class of sets L such that, for some sparse set S, L p r S, and (2) R p r (TALLY) as the class of sets L such that, for some tally set T , L p r T . The study of equivalence to sparse sets and the study of reducibility to sparse sets have each yielded a flurry of results [9,31,10,16,18,20,3,1,21]. Nonetheless, many of the most basic questions have remained unanswered and, in some cases, unasked. In particular, the relationships between equivalence and reducibility to sparse sets have remained wholly unknown. The first results along this line are those of the present paper and the ....
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, The boolean hierarchy II: Applications, SIAM Journal on Computing, 18 (1989), pp. 95--111.
One Bit of Advice - Buhrman, Chang, Fortnow (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The Boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95-111, February 1989.
Lower Bounds and the Hardness of Counting Properties - Hemaspaandra, Thakur (2002) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Rice-Style Theorems for Complexity Theory - Hemaspaandra, Thakur (2001) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Commutative Queries - Beigel, Chang (1999) (4 citations) (Correct)
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] J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The Boolean hierarchy II: Applications. SIAM Journal on Computing,
On Unique Satisfiability and Randomized Reductions - Chang, Rohatgi (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The Boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, February 1989.
A Note on Query Order: Solving the Missing Case - Hempel (1999) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Commutative Queries - Beigel, Chang (2000) (4 citations) (Correct)
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] J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The Boolean hierarchy II: Applications. SIAM Journal on Computing,
Reductions to Sets of Low Information Content.. - Arvind, Han.. (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
The Computational Complexity Column - Allender (1998) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
The Complexity of Matrix Rank and Feasible Systems of.. - Allender, Beals, Ogihara (1997) (14 citations) (Correct)
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J-Y Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, The Boolean Hierarchy II: Applications. SIAM Journal on Computing 18 (1989), 95--111.
The Complexity of Matrix Rank and Feasible Systems of Linear.. - Allender, al. (1996) (14 citations) (Correct)
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J-Y Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, The Boolean Hierarchy II: Applications, SIAM J. Comput. 18 (1989) 95-111.
The Satanic Notations: Counting Classes Beyond #P.. - Lane A.. (1994) (7 citations) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
What's Up with Downward Collapse: Using the.. - Hemaspaandra.. (1998) (2 citations) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Complexity-Theoretic Analogs of Rice's Theorem - Hemaspaandra, Rothe (1997) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
On Using Oracles That Compute Values - Fenner, Homer, Ogiwara, Selman (1993) (11 citations) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM J. Comput., 18(1):95--111, 1989.
Unambiguous Computation: Boolean Hierarchies and Sparse.. - Hemaspaandra, Rothe (1994) (3 citations) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Selectivity: Reductions, Nondeterminism, and Function.. - Hemaspaandra, Hoene.. (1993) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Translating Equality Downwards - Hemaspaandra, Hemaspaandra, Hempel (1997) (2 citations) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
Universally Serializable Computation - Lane A. Hemaspaandra, Mitsunori.. (1996) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
The Complexity of Matrix Rank and Feasible Systems of.. - Allender, Beals, Ogihara (1996) (14 citations) (Correct)
No context found.
J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
A Downward Translation in the Polynomial Hierarchy - Hemaspaandra, Hemaspaandra.. (1997) (5 citations) (Correct)
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J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95--111, 1989.
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