Krentel, M. The Complexity of Optimization Problems. J. Computer and Systems Sciences, 1988, 36:490-509. Home/Search Document Not in Database Summary Related Articles Check |
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Links Between Complexity Theory and Constrained Block Coding - Stockmeyer, Modha (2002) (Correct)
....that is typically used in hardness and completeness results is polynomial time Turing reduction, denoted . If and are functions, then if can be computed in polynomial time using an oracle for ; that is, in the notation of Section II D3, We use a stronger reduction, introduced by Krentel [49], called metric reduction. Let : Then is metric reducible to , which we write , if there is a pair of polynomial time computable functions such that, for all , Using metric reduction in place of in a hardness proof gives a stronger result, because implies , but the converse implication is not ....
M. W. Krentel, "The complexity of optimization problems," J. Comput. Syst. Sci., vol. 36, pp. 490--509, 1988.
Propositional Circumscription and Extended Closed World.. - Eiter, Gottlob (1993) (70 citations) (Correct)
.... how much k completeness is in a 13 CWR rule lower bound upper bound CWA(T ) j= F NP hard GCWA(T ) j= F EGCWA(T ) j= F CCWA(T ; P ; Q;Z) j= F ECWA(T ; P ; Q;Z) j= F CIRC(T ; Q;P ; Z) j= F Table 1: Complexity Results for Propositional Closed World Deduction problem, cf. [19, 34]. This may be measured by the number of necessary calls to a k oracle [19, 17, 33] Closure computation with O(n) oracle calls is straightforward for CWA, GCWA, and CCWA. For CWA, it is not dicult to show that closure computation is (under suitable polynomial transformability) equivalent to the ....
.... ) j= F NP hard GCWA(T ) j= F EGCWA(T ) j= F CCWA(T ; P ; Q;Z) j= F ECWA(T ; P ; Q;Z) j= F CIRC(T ; Q;P ; Z) j= F Table 1: Complexity Results for Propositional Closed World Deduction problem, cf. 19, 34] This may be measured by the number of necessary calls to a k oracle [19, 17, 33]. Closure computation with O(n) oracle calls is straightforward for CWA, GCWA, and CCWA. For CWA, it is not dicult to show that closure computation is (under suitable polynomial transformability) equivalent to the following problem QUERY [11] Given Boolean expressions E 1 ; Em , compute b ....
M. Krentel. The Complexity of Optimization Problems. Journal of Computer and System Sciences, 36:490-509, 1988.
Proving SAT does not have Small Circuits with an.. - Fortnow, Pavan, Sengupta (2002) (Correct)
....Department of Computer Science, Iowa State University, Ames, IA 50011. Work done while the author was a postdoc at NEC Research Institute. Email: pavan cs.iastate.edu Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY 14260. Email: samik cse.buffalo.edu Krentel [Kre88] showed that if any function that can be computed by two queries to SAT can be computed by one query, then P = NP, i.e, if PF = PF P = NP. It is natural to ask whether we can obtain such collapse if we focus on languages instead of functions. Kadin [Kad88] showed that if P the ....
M. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36(1988), pp. 490--509.
Reductions between Disjoint NP-Pairs - Glaßer, Selman, Sengupta (Correct)
....a refinement g of f , and we define F # if for every f , f G. Let sat be the multivalued function defined by sat(x) y if and only if x encodes a propositional formula and y encodes a satisfying assignment of x. Let f and g be partial, multivalued functions. Then g# m f [FGH 96, Kre88] if there exist polynomial time computable total functions h and h # such that the partial, multivalued function defined by g 1 (x) h # (x, f(h(x) is a refinement of g. A function f m complete for the class if for every g , g# m f . 3 Existence of Complete Disjoint NP Pairs The ....
M. W. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36:490--509, 1988.
The Complexity of Temporal Logic Model Checking - Schnoebelen (2002) (2 citations) (Correct)
....4.12 [LMS01] The model checking problem for CTL BT # is # 2 complete. In fact the hardness proofs in [LMS01] even apply to B(L (F) and B(L F) Theorem 4. 12 is mainly interesting for complexity theorists: there exist very few problems known to be complete for # 2 (see [Wag87, Kre88] in particular none from temporal logic model checking , and any addition from a new eld helps understand the class. The techniques from [LMS01] also have more general relevance: they have been used to show # 2 completeness of model checking for some temporal logics featuring ....
M. W. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36(3):490509, 1988.
On the Complexity of Data Disjunctions - Eiter, Veith (1999) (1 citation) (Correct)
.... [46,22] In particular, the following classes coincide with 2 : k[k] polynomial time computation with k rounds of parallel queries to an NP oracle [28,9] log : polynomial time computation where the number of queries to an NP oracle is at most logarithmic in the input size [26]. L log : logarithmic space computation where the number of queries to an NP oracle is at most logarithmic in the input size [27] For an overview of di erent characterizations and their history, consult [46,22] It is shown in [22,4,38,41] that this picture changes when we turn to function ....
.... i.e. promise SAT, is in P [4,41] FewP=P; NP=R [38] coNP = US; SAT 2 NP(n= log n) and, furthermore, NP DTIME(2 O(1= log log n) 22] To compare the complexity of functions, and to obtain a notion of completeness in function classes, we use Krentel s notion of metric reducibility [26]: De nition 2.6 A function f is metric reducible ( reducible) to a function g (in symbols, f g) if there is a pair (h 1 ; h 2 ) of polynomial time computable functions h 1 and h 2 such that for every x, f(x) h 2 (x; g(h 1 (x) Proviso 1. Let C be a complexity class. Unless stated ....
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M. Krentel. The Complexity of Optimization Problems. Journal of Computer and System Sciences, 36:490-509, 1988. 32
On the Complexity of Data Disjunctions - Eiter, Veith (1999) (1 citation) (Correct)
.... characterizations [45, 21] In particular, the following classes coincide with 2 : k[k] polynomial time computation with k rounds of parallel queries to an NP oracle [27] polynomial time computation where the number of queries to an NP oracle is at most logarithmic in the input size [25]. ffl L : logarithmic space computation where the number of queries to an NP oracle is at most logarithmic in the input size [26] Observe that the space for the oracle tape is not bounded. Unbounded oracle space is also assumed for all other classes using an oracle in this paper. 5 ....
.... then (1SAT,SAT) i.e. promise SAT, is in P [4, 40] FewP=P, NP=R [37] coNP = US, SAT 2 NP(n= log n) and NP DTIME(2 O(1= log log n) 21] To compare the complexity of functions, and to obtain a notion of completeness in function classes, we use Krentel s notion of metric reducibility [25]: Definition 2.2 A function f is metric reducible ( reducible) to a function g (in symbols, f if there is a pair of polynomial time computable functions h 1 and h 2 such that for every x, f(x) h 2 (x; g(h 1 ; x) Proviso 1. Let C be a complexity class. Unless stated otherwise, we use ....
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M. Krentel. The complexity of optimization problems. J. Computer and System Sciences, 36:490--509, 1988.
One Bit of Advice - Buhrman, Chang, Fortnow (2002) (Correct)
....hand side of (3) with its SAT oracle. Thus, and we have established (1) 3 To prove that (2) also holds, we show that coNP NP=1 implies that LexMaxSat, de ned below, is in D . LexMaxSat = f j the lexically largest satisfying assignment of ends with 1 g: Since LexMaxSat is [Kre88], we have P . Note that 2 = PH P . Thus by (1) we have PH D . Using the assumption that coNP NP=1, we can construct an NP=1 machine NLMS that given outputs max , the lexically largest satisfying assignment for . When NLMS is given the correct advice bit, all of its ....
M. W. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36(3):490-509, 1988.
The Communication Complexity of Enumeration.. - Ambainis.. (Correct)
....k(D(f) c) DSC is interesting for two reasons. 1) It is quite natural to compare solving k problems seperately to solving them together. The complexity of doing k instances of a problem has been looked at in a variety of fields including decision trees [9, 40] computability [7, 22] complexity [2, 10, 11, 31], straightline programs [15, 14, 21, 52] and circuits [43] 2) This conjecture arose in the study of circuits since a variant of it implies NC (see [29, 28] for connections to circuits, and see [34, Pages 42 48] for a more recent discussion) The reasons for the form ) k(D(f) O(1) ....
M. Krentel. The complexity of optimization problems. Journal of Computer and Systems Sciences, 36(3):490--509, 1988.
Default Reasoning from Conditional Knowledge Bases.. - Eiter, Lukasiewicz (2000) (2 citations) (Correct)
....ranking R can be constructed bottom up, starting with defaults having lowest rank, and then computing the rank of the next default by doing a binary search on the range of its possible values. This resembles the FP complete problem of computing the lexicographic maximum model of a formula [58] and suggests that computing R has the same complexity. This intuition turns out to be correct in all cases except one. In case of z entailment, it is possible to compute with parallel queries to an NP oracle in polynomial time a certificate, given by the sum of all ranks of all defaults, which ....
....i = 2 , where c i 0 is a nonnegative integer, and some r 2 f1; mg, decide whether I j= r ) r for every maximum weight world I under C , that is, world I such that w i is maximum over all worlds in I At . hardness of this problem follows by a minor adaptation of the proof in [58] that computing the maximum weight assignment under a set C of weighted arbitrary clauses is FP complete; the proof in [58] implies that deciding whether I j= r ) r holds for a particular clause r ) r in every maximum weight assignment I under C is P complete. We now construct a ....
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M. W. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36(3):490-- 509, 1988.
Probabilistic Polynomial Time is Closed Under Parity.. - Beigel, Hemachandra.. (1991) (13 citations) (Correct)
....by polynomial time Turing machines allowed O(log n) calls to an NP oracle, and was first studied by Papadimitriou and Zachos in [14] Recently, the class has taken on new importance. The class P defines the Theta 2 level of Wagner s refined polynomial hierarchy, has natural complete sets [8, 10, 11, 21], and is equal to the class of sets polynomial time truth table reducible to an NP set. 3, 7, 10, 21] Buss and Hay [3] and Kobler, Schoning, and Wagner [10, 21] have shown that P is equal to the closure of NP under polynomial time parityreductions. Since NP PP [5] it follows that is ....
M. W. Krentel. The complexity of optimization problems. JCSS, 36(3):490--509, 1988.
Complexity and Approximation of Fixing - Numerical Attributes In (Correct)
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Krentel, M. The Complexity of Optimization Problems. J. Computer and Systems Sciences, 1988, 36:490-509.
Complexity and Approximation of Fixing - Numerical Attributes In (Correct)
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Krentel, M. The Complexity of Optimization Problems. J. Computer and Systems Sciences, 1988, 36:490-509.
Complexity and Approximation of Fixing - Numerical Attributes In (Correct)
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Krentel, M. The Complexity of Optimization Problems. J. Computer and Systems Sciences, 1988, 36:490-509.
Multivalued Functions: Turing Characterizations and.. - Domenico Sacca And (Correct)
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M. Krentel. The complexity of Optimization Problems. Journal of Computer and System Sciences, 36:490--509, 1988.
On Truth-Table Reducibility to SAT - Buss, Hay (2002) (32 citations) (Correct)
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M. W. Krentel, The complexity of optimization problems, Journal of Computer and System Sciences, 36 (1988), pp. 490--509.
Provably Total Functions in - Bounded Arithmetic Theories (Correct)
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M. W. Krentel, The complexity of optimization problems, Journal of Computer and System Sciences, 36 (1988), pp. 490--509.
The Complexity of Temporal Logic Model Checking - Schnoebelen (2003) (2 citations) (Correct)
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M. W. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36(3):490-509, 1988.
On Truth-Table Reducibility to SAT and the Difference Hierarchy.. - Buss, Hay (1987) (5 citations) (Correct)
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M. W. Krentel, The complexity of optimization problems, Journal of Computer and System Sciences, 36 (1988), pp. 490--509.
A Knowledge-Based Approach for Selecting Information Sources - Eiter, al. (2003) (Correct)
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M. Krentel. The Complexity of Optimization Problems. J. Comput. Syst. Sci., 36:490--509, 1988.
One Bit of Advice - Buhrman, Chang, Fortnow (Correct)
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M. W. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36(3):490-509, 1988.
Semiring-based CSPs and Valued CSPs: Frameworks.. - Bistarelli.. (1999) (Correct)
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M. Krentel (1988). The complexity of optimization problems. Journal of Computer and System Sciences 36: 490--509.
Resource-Bounded Kolmogorov Complexity Revisited - Buhrman, Fortnow, Laplante (2001) (9 citations) (Correct)
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M. Krentel. The complexity of optimization problem. J. Computer and System Sciences, 36:490-509, 1988.
On Approximation Preserving Reductions: Complete Problems.. - Orponen, Mannila (1990) (14 citations) (Correct)
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M. Krentel, The complexity of optimization problems, J. Comput. System Sciences 36 (1988) 490509.
Algorithms and Experiments on Finding Minimal - Models Paolo Liberatore (Correct)
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M. V. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36:490--509, 1988.
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