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

1988
*
[1988] Proceedings. Structure in Complexity Theory Third Annual Conference
*

Finally, we show that

doi:10.1109/sct.1988.5282
dblp:conf/coco/BussH88
fatcat:tvrzntst7zggbb44g743uguysa
*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*. ...##
###
On truth-table reducibility to SAT

1991
*
Information and Computation
*

We show that polynomial time

doi:10.1016/0890-5401(91)90075-d
fatcat:rgymrlwjirbwrhdhdiclwayrga
*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*). ...##
###
The difference and truth-table hierarchies for NP

1987
*
RAIRO - Theoretical Informatics and Applications
*

Using Corollary 3.12 it follows that

doi:10.1051/ita/1987210404191
fatcat:u6ragzrbbndktbjjnoveibir74
*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 ...##
###
Probabilistic Autoreductions
[chapter]

2016
*
Lecture Notes in Computer Science
*

autoreducible with respect

doi:10.1007/978-3-662-49192-8_34
fatcat:mtudxhfu35hnlmuya5g2o562mm
*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. ...##
###
Bounded queries to SAT and the Boolean hierarchy

1991
*
Theoretical Computer Science
*

., Bounded queries

doi:10.1016/0304-3975(91)90160-4
fatcat:q5kfoes22jb3lk3hzwpntdywxa
*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. ...##
###
Semi-membership algorithms

1994
*
ACM SIGACT News
*

Acknowledgment s We are grateful

doi:10.1145/193820.193828
fatcat:hgefsctwpvgdjop25d6pkyp7zu
*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 . ...##
###
Learning Reductions to Sparse Sets
[chapter]

2013
*
Lecture Notes in Computer Science
*

We furthermore show that if

doi:10.1007/978-3-642-40313-2_23
fatcat:ocm23fh4lzfyppn3w2qp5q4nyq
*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. ...##
###
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

1995
*
Mathematical Systems Theory
*

Finally, most of

doi:10.1007/bf01303054
fatcat:vqvwvg4t5bccnhhs4gwn7pfn2i
*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. ...##
###
Open questions in the theory of semifeasible computation

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. ...

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

2006
*
Lecture Notes in Computer Science
*

(n) (where

doi:10.1007/11830924_36
fatcat:zdsx4z5asvbs3ka2crwaymplqy
*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. ...##
###
Open Questions in the Theory of Semifeasible Computation
[article]

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. ...

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

1982
*
Information and Control
*

Rather than restrict our attention

doi:10.1016/s0019-9958(82)80084-3
fatcat:m5mvoqsy7vc37einfmirb4rfdq
*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. ...##
###
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

2016
*
Computational Complexity
*

When

doi:10.1007/s00037-016-0124-0
fatcat:jbrp3snmjreknjbl24w2maqqbi
*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). ...
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