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Showing papers by "Juris Hartmanis published in 1985"


Journal ArticleDOI
TL;DR: The paper exploits the recently discovered upward separation method and uses relativization techniques to determine logical possibilities, limitations of these proof techniques, and exhibits one of the first natural structural differences between relativized NP and CoNP.
Abstract: This paper investigates the structural properties of sets in NP-P and shows that the computational difficulty of lower density sets in NP depends explicitly on the relations between higher deterministic and nondeterministic time-bounded complexity classes. The paper exploits the recently discovered upward separation method, which shows for example that there exist sparse sets in NP-P if and only if EXPTIME ≠ NEXPTIME . In addition, the paper uses relativization techniques to determine logical possibilities, limitations of these proof techniques, and exhibits one of the first natural structural differences between relativized NP and CoNP .

107 citations


Book ChapterDOI
15 Jul 1985
TL;DR: It is shown that NP∩CoNP has ≤ m P - complete languages if and only if it has ≤ T P -complete languages.
Abstract: It is not known whether complete languages exist for NP∩CoNP and Sipser has shown that there are relativizations so that NP∩CoNP has no ≤ m P -complete languages In this paper we show that NP∩CoNP has ≤ m P -complete languages if and only if it has ≤ T P -complete languages Furthermore, we show that if a complete language L0 exists for NP∩CoNP and NP∩CoNP≠NP then the reduction of L(Nt) e NP∩CoNP cannot be effectively computed from Nt We extend the relativization results by exhibiting an oracle E such that PE≠NPE∩CoNPE≠NPE and for which there exist complete languages in the intersection For this oracle the reduction to a complete language can be effectively computed from complementary pairs of machines (Nt, Nj) such that L(Nt)=\(\overline {L(N_1 )} \) On the other hand, there also exist oracles F such that PF≠NPF∩CoNPF≠NPF for which the intersection has complete languages, but the reductions to the complete language cannot be effectively computable from the complementary pairs of machines In this case, the reductions can be computed from $$(N_t ,N_J , Proof that L(N_1 ) = \overline {L(N_1 )} ) $$

32 citations



Journal ArticleDOI
TL;DR: It is shown that for any axiomatizable, sound formal system F there exist instances of natural problems about context-free languages, lower bounds of computations and P versus NP that are not provable in F for any recursive representation of these problems.

15 citations


Proceedings Article
15 Jul 1985
TL;DR: In this paper, it was shown that NP∩CoNP has ≤ m P -complete languages if and only if it has ≤ T P-complete languages in the intersection.
Abstract: It is not known whether complete languages exist for NP∩CoNP and Sipser has shown that there are relativizations so that NP∩CoNP has no ≤ m P -complete languages. In this paper we show that NP∩CoNP has ≤ m P -complete languages if and only if it has ≤ T P -complete languages. Furthermore, we show that if a complete language L0 exists for NP∩CoNP and NP∩CoNP≠NP then the reduction of L(Nt) e NP∩CoNP cannot be effectively computed from Nt. We extend the relativization results by exhibiting an oracle E such that PE≠NPE∩CoNPE≠NPE and for which there exist complete languages in the intersection. For this oracle the reduction to a complete language can be effectively computed from complementary pairs of machines (Nt, Nj) such that L(Nt)=\(\overline {L(N_1 )} \). On the other hand, there also exist oracles F such that PF≠NPF∩CoNPF≠NPF for which the intersection has complete languages, but the reductions to the complete language cannot be effectively computable from the complementary pairs of machines. In this case, the reductions can be computed from $$(N_t ,N_J , Proof that L(N_1 ) = \overline {L(N_1 )} ) .$$

5 citations