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On truth-table reducibility to SAT and the difference hierarchy over NP

S.R. Buss, L. Hay
1988 [1988] Proceedings. Structure in Complexity Theory Third Annual Conference  
Finally, we show that the infinite difference hierarchy over NP is equal to ∆ p 2 and give an oracle oracle separating ∆ p 2 from the class of predicates polynomial time truth-table reducible to SAT.  ...  We show that polynomial time truth-table reducibility via Boolean circuits to SAT is the same as log space truth-table reducibility via Boolean formulas to SAT and the same as log space Turing reducibility  ...  In this section we consider the infinite difference hierarchy over NP and investigate the connection with truth-table reducibility and Turing reducibility to SAT.  ... 
doi:10.1109/sct.1988.5282 dblp:conf/coco/BussH88 fatcat:tvrzntst7zggbb44g743uguysa

On truth-table reducibility to SAT

Samuel R. Buss, Louise Hay
1991 Information and Computation  
We show that polynomial time truth-table reducibility via Boolean circuits to SAT is the same as logspace truth-table reducibility via Boolean formulas to SAT and the same as logspace Turing reducibility  ...  We give an oracle relative to which ∆ p 2 is not equal to the class of predicates polynomial time truth-table reducible to SAT.  ...  Cai and Hemachandra [7] defined a hierarchy Σ L k , Π L k above the finite levels of the difference hierarchy over NP; we show this hierarchy collapses with Σ L 2 = Π L 2 = ≤ p tt (NP).  ... 
doi:10.1016/0890-5401(91)90075-d fatcat:rgymrlwjirbwrhdhdiclwayrga

The difference and truth-table hierarchies for NP

Johannes Köbler, Uwe Schöning, Klaus W. Wagner
1987 RAIRO - Theoretical Informatics and Applications  
Using Corollary 3.12 it follows that the différence hierarchy, and consequently also the truth-table hierarchy, is finite. • Thus the union of the différence hierarchy and the union of the truth-table  ...  On the other hand, it turns out that SAT*"*^SAP 0 " 6 ', i. e. that the oo-jump of the différence hierarchy has the same complexity as one of the oe-jumps of the truth-table hierarchy, THEOREM 5.1  ... 
doi:10.1051/ita/1987210404191 fatcat:u6ragzrbbndktbjjnoveibir74

Probabilistic Autoreductions [chapter]

Liyu Zhang, Chen Yuan, Haibin Kan
2016 Lecture Notes in Computer Science  
autoreducible with respect to the BPP truth-table reductions.  ...  We also prove that complete sets of classes in the truth-table Polynomial Hierarchy, which is the polynomial hierarchy defined using the truth-table reduction instead of the general Turing reduction, are  ...  Now let L a be a BPP truth-table-complete set for Σ P,tt k for k ≥ 1. Then L a reduces to SAT (k),tt via a many-one reduction f that does not use any oracle.  ... 
doi:10.1007/978-3-662-49192-8_34 fatcat:mtudxhfu35hnlmuya5g2o562mm

Bounded queries to SAT and the Boolean hierarchy

Richard Beigel
1991 Theoretical Computer Science  
., Bounded queries to SAT and the Boolean hierarchy, Theoretical Computer Science 84(1991)199-223.  ...  difference hierarchy over NP.  ...  Suppose that L sk_tt B, for some BE NP. We could simulate the truth -table reduction as follows: We determine the truth table and its entries q, , . . . , qk.  ... 
doi:10.1016/0304-3975(91)90160-4 fatcat:q5kfoes22jb3lk3hzwpntdywxa

Semi-membership algorithms

Derek Denny-Brown, Yenjo Han, Lane A. Hemaspaandra, Leen Torenvliet
1994 ACM SIGACT News  
Acknowledgment s We are grateful to M . Cierniak and A . Selman for enjoyable discussions . All errors and opinions of course are the responsibility of the authors .  ...  So if it were the case that every set that bounded-truth-table reduced to a P-selective se t necessarily many-one reduced to some (perhaps different) P-selective set, then the recent boundedtruth-table  ...  For example, the theorem below states that one-truth-tabl e reduction to P-selective sets yields the same class as one-truth-table equivalence to P-selective sets .  ... 
doi:10.1145/193820.193828 fatcat:hgefsctwpvgdjop25d6pkyp7zu

Learning Reductions to Sparse Sets [chapter]

Harry Buhrman, Lance Fortnow, John M. Hitchcock, Bruno Loff
2013 Lecture Notes in Computer Science  
We furthermore show that if Sat disjunctive truth-table (or majority truth-table) reduces to a sparse set then Sat ≤ p m LT1 and hence a collapse of PH to P NP also follows.  ...  We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being many-one reducible to functions computable by non-uniform circuits consisting of a single weighted threshold gate.  ...  Karp and Lipton showed that if NP is Turing reducible to a sparse set then the polynomial time hierarchy collapses to its second level.  ... 
doi:10.1007/978-3-642-40313-2_23 fatcat:ocm23fh4lzfyppn3w2qp5q4nyq

Page 564 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
We show that ModP is polynomial time truth-table equiv- alent in power to #P and that Mod P is contained in the class AmpMP.  ...  Specifically, SAT v SAT is reducible to SATA SAT with proba- bility }+2-" , but if there were such a reduction with probability 5 + 1/polynomial, then the polynomial hierarchy would collapse (to £$).  ... 

On computing Boolean connectives of characteristic functions

R. Chang, J. Kadin
1995 Mathematical Systems Theory  
Finally, most of the structural properties of the Boolean hierarchy and query hierarchies are shown to depend only on the existence of AND and OR functions for the NP complete sets.  ...  The results in this paper characterize the complete sets for the classes D P and P SAT[O(log n)] in terms of AND and OR, and relate these functions to the structure of the Boolean hierarchy and the query  ...  The ≤ P m -complete languages for the different levels of query hierarchy and the parallel query hierarchy (over SAT) also do not have AND 2 or OR 2 unless the PH collapses.  ... 
doi:10.1007/bf01303054 fatcat:vqvwvg4t5bccnhhs4gwn7pfn2i

Open questions in the theory of semifeasible computation

Piotr Faliszewski, Lane Hemaspaandra
2006 ACM SIGACT News  
The intuition here is that it is saying: "Regarding membership in L, if you put a gun to my head and forced me to bet on one of x or y as belonging to L, my money would be on f (x, y)."  ...  polynomial-time function f such that when at least one of x and y belongs to L, then f (x, y) ∈ L ∩ {x, y}.  ...  Selman for helpful comments on the background of function refinement.  ... 
doi:10.1145/1122480.1122495 fatcat:ppgk4ixf2jf65fajtkkw5wfp5u

Worst-Case Vs. Algorithmic Average-Case Complexity in the Polynomial-Time Hierarchy [chapter]

Dan Gutfreund
2006 Lecture Notes in Computer Science  
(n) (where the probability is over the choice of instances and the randomness of the algorithm).  ...  for every probabilistic polynomial-time algorithm that attempts to decide it, there is a samplable distribution over the instances of L, on which the algorithm errs with probability at least 1/2 − 1/poly  ...  Similar to their proof, we will encode the truth-tables of a langauge (SAT in our case) at different lengths, to obtain truth-tables of a new language.  ... 
doi:10.1007/11830924_36 fatcat:zdsx4z5asvbs3ka2crwaymplqy

Open Questions in the Theory of Semifeasible Computation [article]

Piotr Faliszewski, Lane A. Hemaspaandra
2005 arXiv   pre-print
The intuition here is that it is saying: "Regarding membership in L, if you put a gun to my head and forced me to bet on one of x or y as belonging to L, my money would be on f(x,y)."  ...  polynomial-time function f such that when at least one of x and y belongs to L, then f(x,y) ∈ L ∩{x,y}.  ...  Selman for helpful comments on the background of function refinement.  ... 
arXiv:cs/0506082v1 fatcat:npyrblatqffhzinwhfscp6bkqy

Analogues of semirecursive sets and effective reducibilities to the study of NP complexity

Alan L. Selman
1982 Information and Control  
Rather than restrict our attention to many-one and Turing reducibilities (see Selman (1979) ), it will be more interesting to study positive vs. truth-table reducibilities.  ...  It would be a stronger result to cause ~<~tt and ~<tPt to differ on NP, so that both of the sets B and C belong to NP. The following corollary is due to a lovely observation made by C. B.  ... 
doi:10.1016/s0019-9958(82)80084-3 fatcat:m5mvoqsy7vc37einfmirb4rfdq

Page 9241 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
Thus, posi- tive Turing and Turing reducibility to NP differ sharply unless the polynomial hierarchy collapses.  ...  positive bias reduction, a truth-table reduction that encodes a positive, ef- ficient, approximate simulation of one bias sequence by another; and (iii) the use of such a reduction to dilate an efficient  ... 

The Minimum Oracle Circuit Size Problem

Eric Allender, Dhiraj Holden, Valentine Kabanets
2016 Computational Complexity  
When the oracle is QBF, the resulting problem MCSP QBF is known to be complete for PSPACE under ZPP reductions.  ...  We consider variants of the Minimum Circuit Size Problem MCSP, where the goal is to minimize the size of oracle circuits computing a given function.  ...  Some of this work was carried out at the 2014 Dagstuhl Workshop on Algebra in Computational Complexity (Dagstuhl Seminar 14391).  ... 
doi:10.1007/s00037-016-0124-0 fatcat:jbrp3snmjreknjbl24w2maqqbi
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