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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 ...doi:10.1016/j.entcs.2008.12.008 fatcat:cdr3pzdi75c33mjg2l2jdz6sta
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 ...
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. ...
Hudmonis 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. ...doi:10.1016/0304-3975(90)90191-j fatcat:b32wvwbx4jcw3jmuinbslhk2ii
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 ...
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 ...
Lecture Notes in Computer Science
However, 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 ...doi:10.1007/3-540-52921-7_54 fatcat:qsdgtlzrbnbfjgzjkutmddmsfi
in that 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 ...doi:10.3765/bls.v31i1.891 fatcat:543hvfkswvf4payosdhkqzubym
in that 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 ...doi:10.3765/bls.v31i1.889 fatcat:6tbumuntbfahdbbxgtc6zkbhla
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 = ? ...doi:10.1016/0022-0000(85)90053-4 fatcat:p2lwx45eb5h3bi6x2tllgpcsnq
Despite 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 ...doi:10.1109/ccc.2009.21 dblp:conf/coco/FortnowSW09 fatcat:ogzwc5rxirgkhmyb3krxo2xby4
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. ...
It is argued that, given 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. ...doi:10.9793/elsj1984.9.21 fatcat:2wvx7tz3qbduxn27h2k62fzau4
We show that, assuming 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. ...doi:10.1142/s0129054195000214 fatcat:xdluoqt5bndexg3jvhpn2lwwoe
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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