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On Relativizations of the P =? NP Question for Several Structures

2008
*
Electronical Notes in Theoretical Computer Science
*

*For*

*several*

*structures*, including

*structures*over

*the*reals, we construct oracles which imply that

*the*

*relativized*versions

*of*

*P*and

*NP*are equal or are not equal. ... This implies

*questions*like

*the*following

*for*any

*structures*K: Which relationships between

*the*

*relativized*versions

*of*

*P*K and

*NP*K will we obtain if we permit oracles

*for*machines over K? ...

*of*

*Relativized*Versions

*of*

*P*and

*NP*We shall present three kinds

*of*oracles Q 1 (= Q (K) 1 ), Q 2 (= Q (K) 2 ), and Q 3 (= Q 3 )

*for*

*several*

*structures*K, in order to get

*the*inequality between

*the*corresponding ...

##
###
Page 6317 of Mathematical Reviews Vol. , Issue 93k
[page]

1993
*
Mathematical Reviews
*

Summary: “We consider

*several**questions**on**the*computational power*of*PP,*the*class*of*sets accepted by polynomial time-bounded probabilistic Turing machines with two-sided unbounded error probability. ... Using well-known results*on**the*simulation*of*logspace-bounded Turing machines by sequences*of*branching programs we complete*the*separation*of**the*complexity classes L, NL, co-NL, ®L, AL =*P**for*oblivious ...##
###
Page 2054 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

*Several*corollaries provide more insight into

*the*

*structure*

*of*

*the*hierarchy

*of*polynomial time frequency classes. ...

*For*exam- ple, it is shown that

*P*is different from

*NP*iff its proper subclass EASYY, is also different from

*NP*. Finally,

*the*behavior

*of*these classes under

*relativization*is considered. ...

##
###
New developments in structural complexity theory

1990
*
Theoretical Computer Science
*

Hudmonis

doi:10.1016/0304-3975(90)90191-j
fatcat:b32wvwbx4jcw3jmuinbslhk2ii
*The*Polynomial Time Hierarchy, PH, is defined in terms*of**NP*and is essential in*the*classification*of*problems with more complex logical*structure*than*NP*. .E;=L7,'=A,*P*=*P*, Z:=*NP*, II;= coNP, ... Clearly,*P*and*NP*are*the*dominant complexity classes In computer science and*the**P*1*NP**question*is*the*most famous open problem in our field. l This research was supported by NSF Research Grants DCR ... S is many-*one*compiere*for**NP*if S is in*NP*and*for*all B in*NP*, B s z S. Many results in*structural*complexity theory are expressed in terms*of*sparse sets. ...##
###
Page 2927 of Mathematical Reviews Vol. , Issue 90E
[page]

1990
*
Mathematical Reviews
*

*The*paper under review is concerned with when this can be improved to

*P*= R. This

*question*ties into ... Furthermore, it is shown that E = NE implies that BH \

*P*has no capturable sets (these are subsets

*of*sparse

*NP*sets). (2)

*For*a set S

*of*natural numbers,

*the*counting class CPs is

*the*class

*of*sets accepted ...

##
###
Page 545 of Mathematical Reviews Vol. , Issue 90A
[page]

1990
*
Mathematical Reviews
*

It is shown that this

*question*is difficult, since there are*relativizations**for*which UP“ has no complete languages and other*relativizations**for*which*P*® 4 UP® #*NP** and UP” has complete languages. ... This paper shows an efficient parallel algorithm (*on*CREW*P*- RAM)*for**the*optimal parenthesization problems, a class*of*dy- namic programming problems such as optimization*of**the*multi- plication*of*n ...##
###
Oracles versus proof techniques that do not relativize
[chapter]

1990
*
Lecture Notes in Computer Science
*

However,

doi:10.1007/3-540-52921-7_54
fatcat:qsdgtlzrbnbfjgzjkutmddmsfi
*the*existence*of*nonrelativizing proof techniques seems to call this practice into*question*. ... Oracle constructions have long been used to provide evidence that certain*questions*in complexity theory cannot be resolved using*the*usual techniques*of*simulation and diagonalization. ... Acknowledgments: I thank Ron Book, Jack Lutz, Pekka Orponen, and Seinosuke Toda*for*some interesting discussions that took place at*the*Workshop in*Structural*Complexity Theory at*the*University*of*California ...##
###
Processing as a Source of Accessibility Effects on Variation

2014
*
Proceedings of the annual meeting of the Berkeley Linguistics Society
*

in that

doi:10.3765/bls.v31i1.891
fatcat:543hvfkswvf4payosdhkqzubym
*the**relativizer*(here that) can be omitted: 1 (1) This is*the*first president i (that) nobody voted*for*_ i . ... We link this finding to research*on**the*production and comprehension*of*relative clauses, and so integrate*the*observed accessibility effect into a uniform processing account*of**relativizer*variation ( ... > First Name > Definite*NP*> Indefinite*NP*Although past research*on**relativizer*variation has not invoked accessibility,*several*studies have shown that NSRC subjects higher*on**the*accessibility scale ...##
###
Processing as a Source of Accessibility Effects on Variation

2014
*
Proceedings of the annual meeting of the Berkeley Linguistics Society
*

in that

doi:10.3765/bls.v31i1.889
fatcat:6tbumuntbfahdbbxgtc6zkbhla
*the**relativizer*(here that) can be omitted: 1 (1) This is*the*first president i (that) nobody voted*for*_ i . ... We link this finding to research*on**the*production and comprehension*of*relative clauses, and so integrate*the*observed accessibility effect into a uniform processing account*of**relativizer*variation ( ... > First Name > Definite*NP*> Indefinite*NP*Although past research*on**relativizer*variation has not invoked accessibility,*several*studies have shown that NSRC subjects higher*on**the*accessibility scale ...##
###
Qualitative relativizations of complexity classes

1985
*
Journal of computer and system sciences (Print)
*

*The*principal result

*of*this paper is a "positive

*relativization*"

*of*

*the*open

*question*"

*P*= ?

*NP*n co-

*NP*." ...

*NP*

*questions*also, where @ is

*the*class

*of*languages L in

*NP*accepted by nondeterministic machines that operate in polynomial time and that have

*for*each input at most

*one*accepting computation. ... We will show, dependent

*on*a plausible conjecture about

*the*mathematical

*structure*

*of*

*the*class

*NP*, that NPCMm( ) yields a positive

*relativization*

*of*

*the*

*P*= ?

*NP*

*question*and so not

*of*

*P*= ? ...

##
###
Fixed-Polynomial Size Circuit Bounds

2009
*
2009 24th Annual IEEE Conference on Computational Complexity
*

Despite

doi:10.1109/ccc.2009.21
dblp:conf/coco/FortnowSW09
fatcat:ogzwc5rxirgkhmyb3krxo2xby4
*several*improvements*of*Kannan's result, we still cannot prove that*P**NP*does not have linear size circuits. ... We explore*questions*about fixed-polynomial size circuit lower bounds around and beyond*the*algebrization barrier. We find*several*connections, including ... They formalize a variant*of**relativization*called "algebrization", and show that essentially all known*structural*complexity results at*the*polynomial time level algebrize, while*several*important lower ...##
###
Page 2776 of Mathematical Reviews Vol. , Issue 80G
[page]

1980
*
Mathematical Reviews
*

There are

*several*results which consider problems related to*P*=*NP**relativized*by an oracle. Surprisingly little is known about*the**relativized*polynomial hierarchy. ... (*The*famous*P*=*NP*problem is, essentially,*the**question**of*whether*one*(= each)*of*these problems has an effi- cient algorithm.) These problems are said to be*NP*-complete. ...##
###
X' CONVENTION AND EXTENDED MINIMALITY

1992
*
English Linguistics
*

It is argued that, given

doi:10.9793/elsj1984.9.21
fatcat:2wvx7tz3qbduxn27h2k62fzau4
*the*X' Convention and*the*Minimality Condition, it is possible to produce a unified approach towards*the*three domains which supply*the*empirical foundation*for**the**Relativized*... Furthermore, to account*for**the*possibility*of**the*extraction*of*an element from*the*domain*of*a head governor, it is proposed that there are two kinds*of*minimality barrier: a weak minimality barrier ... In this section, we will turn to*the**question**of**NP*movement, examining how it might fit into*the*proposed framework. ...##
###
NONDETERMINISTICALLY SELECTIVE SETS

1995
*
International Journal of Foundations of Computer Science
*

We show that, assuming

doi:10.1142/s0129054195000214
fatcat:xdluoqt5bndexg3jvhpn2lwwoe
*P*6 =*NP*\coNP,*the*class*of**NP*-selective sets properly contains*the*class*of**P*-selective sets. ... We prove many*of*our results via a \*relativization*technique," by using*the*known properties*of**P*-selective sets. ... Acknowledgements We are grateful to Joel Seiferas*for*helpful discussions. ...##
###
Page 5892 of Mathematical Reviews Vol. , Issue 87j
[page]

1987
*
Mathematical Reviews
*

Summary: “We investigate

*the**structural*properties*of*sets in*NP*-—*P*and show that*the*computational difficulty*of*lower density sets in*NP*depends explicitly*on**the*relations between higher de- terministic ... In addition, we use*relativization*techniques to determine logical possibilities and lim- itations*of*these proof techniques, and exhibit*one**of**the*first natural*structural*differences between*relativized*...
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