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

@article{Buss1988OnTR,
title={On truth-table reducibility to SAT and the difference hierarchy over NP},
author={Samuel R. Buss and Louise Hay},
journal={[1988] Proceedings. Structure in Complexity Theory Third Annual Conference},
year={1988},
pages={224-233}
}
• Published 14 June 1988
• Computer Science
• [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
It is shown that polynomial-time truth-table reducibility by 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 to SAT. It is proved that a constant number of rounds of parallel queries to SAT is equivalent to one round of parallel queries. It is shown that the infinite difference hierarchy over NP is equal to Delta p/2, and an oracle separating Delta p/2 from the class of predicates polynomial time…
On Truth-Table Reducibility to SAT
• Computer Science, Mathematics
Inf. Comput.
• 1991
Generalized theorems on relationships among reducibility notions to certain complexity classes
It is proved that, for a classK, reducibility notions of sets toK under polynomial-time constant-round truth-table reducible, polynometric-time log-Turing reducibles, logspace constant- round truth- table reducibilities, and logspace Turing reducibly are all equivalent.
Logical Characterizations of Bounded Query Classes I: Logspace Oracle Machines
If certain logics are of the same expressibility then the Polynomial Hierarchy collapses and some new complete problems for the complexity class LNP via projection translations are exhibited.
Nondeterministic Direct Product Reductions and the Success Probability of SAT Solvers
• Andrew Drucker
• Mathematics, Computer Science
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
• 2013
It is shown that if NP is not in coNP/poly then, for every PPT algorithm attempting to produce satisfying assigments to Boolean formulas, there are infinitely many instances where the algorithm's success probability is nearly-exponentially small.
Bounded Queries to SAT and the Boolean Hierarchy
• R. Beigel
• Computer Science, Mathematics
Theor. Comput. Sci.
• 1991
Restricted information from nonadaptive queries to NP
• Computer Science
Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference
• 1995
We investigate classes of sets that can be decided by bounded truth-table reductions to an NP set in which evaluators do not have full access to the answers to the queries but get only restricted
On the Power of Probabilistic Polynomial Time:PNP[log] ⊆ PP
• Computer Science, Mathematics
• 1988
We show that every set in the 0~ level of the polynomial hierarchy-every set polynomial­ time truth-table reducible to SAT~is accepted by a probabilistic polynomial-time Turing machine: pNP[log] ~
Logical Characterizations of Bounded Query Classes II: Polynomial-Time Oracle Machines
We have shown that the logics (±HP)*[FOS] and (±HP)1[FOS] are of the same expressibility, and both capture P∥ NP . This result gives us the weakest possible hint that it might be wiser to try and
On the power of probabilistic polynomial time: P/sup NP(log)/ contained in PP
• Computer Science
[1989] Proceedings. Structure in Complexity Theory Fourth Annual Conference
• 1989
It is shown that probabilistic time is closed under polynomial-time parity reductions. Therefore, every set polynomial-time truth-table reducible to SAT is accepted by a probabilistic polynomial-time
On Using Oracles That Compute Values
• Computer Science, Mathematics
STACS
• 1993
This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable

## References

SHOWING 1-10 OF 27 REFERENCES
Comparison of polynomial-time reducibilities
• Computer Science
STOC '74
• 1974
Comparison of the polynomial-time-bounded reducibilities introduced by Cook [1] and Karp] leads naturally to the definition of several intermediate truth-tableredcibilities, and it is noted that all redu cibilities of this type which do not have obvious implication relationships are in fact distinct in a strong sense.
A Comparison of Polynomial Time Reducibilities
• Computer Science
Theor. Comput. Sci.
• 1975
Bounded Query Classes
The Boolean hierarchy is generalized in such a way that it is possible to characterize P and O in terms of the generalization, and the class $P^{\text{NP}}[O(\log n)]$ can be characterized in very different ways.
Three results on the polynomial isomorphism of complete sets
• Mathematics
27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
• 1986
This paper proves three results relating to the isomorphism question for NP-complete sets, showing that no simple modification of the diagonalization argument used by Ko, Long and Du can be used to produce sets that are both EXPtime-complete w.r.t, polynomial many-one reducibility and not p-isomorphic.
The Boolean Hierarchy: Hardware over NP
• Computer Science
Computational Complexity Conference
• 1986
The structure of the boolean hierarchy and its relations with more common classes is emphasized: separation and immunity results, complete languages, upward separations, connections to sparse oracles for NP, and structural asymmetries between complementary classes.
Bounded query classes and the difference hierarchy
• Computer Science, Mathematics
Arch. Math. Log.
• 1989
A hierarchy of sets that are reducible toA based on bounding the number of queries toA that an oracle machine can make is defined, i.e. sets in a logarithmic way.
On the Boolean closure of NP
New machines whose computational power is bounded by that of alternating Turing machines making only one alternation are introduced whose polynomial time classes are exactly the levels of the Boolean closure of NP which can be defined in a natural way.
The complexity of optimization problems
The central result is that any FPSAT function decomposes into an OptP function followed by polynomial-time computation, and it quantifies "how much" NP-completeness is in a problem, i.e., the number of NP queries it takes to compute the function.
Theory of Recursive Functions and Effective Computability
Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.