P. Young, Juris Hartmanis: Fundamental contributions to isomorphism problems, Complexity Theory Retrospective (A. Selman, ed.), SpringerVerlag,  Home/Search   Document Not in Database   Summary   Related Articles   Check

....as discussed in this paper s sequel. 3. The Plan of This Paper In the early 1970s there was an interest among complexity theorists in axiomatically characterizing the natural complexity measures a problem that is still largely open and not quite abandoned. In commenting upon this work Young [You90] notes (in his footnote 6) that the contemporary understanding of what constitutes a natural complexity measure or class is based on two things: i) well understood, concrete, computational models and (ii) low complexity translations between these models which establish model equivalences, e.g. ....

P. Young, Juris Hartmanis: Fundamental contributions to isomorphism problems, Complexity Theory Retrospective (A. Selman, ed.), SpringerVerlag,

....Supported in part by ESPRIT II BRA EC project 3075 (ALCOM) and by Acci on Integrada Hispano Alemana 131 B z Supported by NSF grant CCR 9207797. 1 isomorphism conjecture: namely that all NP complete sets are polynomialtime isomorphic. This conjecture has engendered a large amount of work (cf. [KMR90, You] for surveys) The isomorphism conjecture was made using the notion of NP completeness via polynomial time, many one reductions because that was the standard definition at the time. In [Coo] Cook proved that the Boolean satisfiability problem (SAT) is NP complete via polynomial time Turing ....

Paul Young, "Juris Hartmanis: Fundamental Contributions to Isomorphism Problems," in Complexity Theory Retrospective, Alan Selman, ed., Springer-Verlag (1990), 28-58. 15

....sets are p isomorphic, has led to a number of interesting investigations of the relations among completeness notions for reducibilities. For a survey of results about the Berman Hartmanis Conjecture and about similar statements for reducibilities stronger than p m reducibility, see [11] and [17], as well as the recent survey [1] Since, for a complexity class C closed under r reducibility, the r complete sets for C form an r degree, i.e. an r equivalence class, the comparison of the completeness notions is closely related to the more abstract question of the possible relations among ....

P. Young. Juris Hartmanis: fundamental contributions to isomorphism problems. In [16], 28--58.

....sets are p isomorphic, has led to a number of interesting investigations of the relations among completeness notions for reducibilities. For a survey of results about the Berman Hartmanis Conjecture and about similar statements for reducibilities stronger than p m reducibility, see [11] and [17], as well as the recent survey [1] Since, for a complexity class C closed under r reducibility, the r complete sets for C form an r degree, i.e. an r equivalence class, the comparison of the completeness notions is closely related to the more abstract question of the possible relations among ....

P. Young. Juris Hartmanis: fundamental contributions to isomorphism problems. In [16], 28--58.

....really interesting work in this direction has been done by [JY85, KLD86, KMR95] Q: Let me interrupt. You ll never get this article done on time if you are going to survey the entire field. Are there any surveys you can suggest A: Yes. Two very nice ones that spring to mind are [KMR90] and [Yo90]. Some exciting developments (such as [FFK96, JPY94, Ro95] are too recent to be mentioned in the surveys. Q: What does this have to do with factorization A: I m getting to that. In spite of the general feeling that the original BermanHartmanis conjecture is probably false, it was shown in ....

Paul Young, Juris Hartmanis: Fundamental Contributions to Isomorphism Problems, in Complexity Theory Retrospective, Alan Selman, ed., SpringerVerlag (1990), 28-58.

....projection of the integer determinant problem, in symbols, PERM 6 fop DET. This is true iff PERM 62 fop( Q (Mn (Z) Thus this result would imply among other things that NL does not contain #P, cf. vzG, Cai] 7. We conjecture that a low level version of the isomorphism conjecture [BH] [You] should hold: For the complexity classes C = NL, P, NP, all problems complete for C via first order projections are logspace isomorphic. 4 8. It would be very nice to consider more algebraic versions of the reductions we are using, i.e. perhaps some versions of these reductions that are ....

Paul Young (1990), Juris Hartmanis: Fundamental Contributions to Isomorphism Problems, in Complexity Theory Retrospective, Alan Selman, ed., Springer-Verlag, 28-58.

....means of efficient renaming procedures of strings, and thus, there is basically only one, unique NP complete set. This simple, plausible statement has attracted many brilliant scientists over the past two decades and has become a central research area in complexity theory. The reader may refer to [KMR90, You90, FFK92] for the current status of the isomorphism conjecture. What does this conjecture suggest First of all, P 6= NP, because finite sets are in P NP but not isomorphic to SAT. Second, more amusingly, sparse sets are not NPcomplete. For a language A, define the census function of A, cens A (n) to ....

P. Young. Juris Hartmanis: fundamental contributions to isomorphism problems. In A. Selman, editor, Complexity Theory Retrospective, pages 28--58. Springer-Verlag, 1990.

....conjecture is true [JY85] There are NP complete sets that cannot be isomorphic under commonly used distributions on instances [WB95] The isomorphism conjecture is an active research topic with considerable work on the subject. For the current status of the subject, see [Sel92, FFK92, KMR90, You90] We will not go into this any further in this article. 3.2 Mahaney s theorem As typical NP complete languages such as SAT are all exponentially dense, and polynomial time isomorphisms cannot change the density from exponential to polynomial, it follows from the isomorphism conjecture that no ....

P. Young. Juris Hartmanis: fundamental contributions to isomorphism problems. In A. Selman, editor, Complexity Theory Retrospective, pages 28--58. Springer-Verlag, 1990.

....essentially one and the same problem. However, there is now considerable doubt whether the BermanHartmanis isomorphism conjecture is true [JY85] The isomorphism conjecture is an active research topic with considerable work on the subject. For the current status of the subject, see [FFK92, KMR90, You90] We will not go into this any further in this article. 3.2 Mahaney s theorem As typical NP complete languages such as SAT are all exponentially dense, and polynomial time isomorphisms cannot change the density from exponential to polynomial, it follows from the isomorphism conjecture that no ....

P. Young. Juris Hartmanis: fundamental contributions to isomorphism problems. In A. Selman, editor, Complexity Theory Retrospective, pages 28--58. Springer-Verlag, 1990.

....In 1977 Berman and Hartmanis noticed that all NP complete sets that they knew of were polynomial time isomorphic, BH77] They made their now famous isomorphism conjecture: namely that all NP complete sets are polynomial time isomorphic. This conjecture has engendered a large amount of work (cf. [KMR90, You] for surveys) The isomorphism conjecture was made using the notion of NP completeness via polynomialtime, many one reductions because that was the standard definition at the time. In [Coo] A preliminary version of this work appeared in Proc. 10th Symposium on Theoretical Aspects of Computer ....

Paul Young, "Juris Hartmanis: Fundamental Contributions to Isomorphism Problems," in Complexity Theory Retrospective, Alan Selman, ed., SpringerVerlag (1990), 28-58.

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