Abstract
For a given polynomial-time computable honest function, the complexity of its “max” inverse function is compared with that of the other inverse functions. Two structural results are shown which suggest that the “max” inverse function is not the easiest.
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J. Balcázar, J. Diaz, and J. Gabarró,Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, New York (1988).
R. Beigel. NP-hard sets are P-superterse unless R = NP. Technical Report 88-04, Department of Computer Science, The Johns Hopkins University.
C. Bennett and J. Gill, Relative to a random oracleA, PA ≠ NPA ≠ co-NPA with probability 1,SIAM J. Comput. 10 (1981), 96–113.
S. Buss and L. Hay, On truth-table reducibility to SAT and the difference hierarchy over NP, inProc. 3rd Structure in Complexity Theory Conference, IEEE, New York (1988), pp. 224–233.
J. Grollmann and A. Selman, Complexity measures for public-key cryptosystems, inProc. 25th IEEE Symposium on Foundations of Computer Science, IEEE, New York (1984), pp. 495–503; the final version appeared inSIAM J. Comput. 17 (1988), 309–335.
J. Kadin, The polynomial hierarchy collapses if the Boolean hierarchy collapses, inProc. 3rd Structure in Complexity Theory Conference, IEEE, New York (1988), pp. 278–292.
M. Krentel, The complexity of optimization problems,J. Comput. System Sci. 36 (1988), 490–509.
R. Ladner, N. Lynch, and A. Selman, A comparison of polynomial time reducibilities,Theoret. Comput. Sci. 1 (1975), 103–123.
U. Schöning, Probabilistic complexity classes and lowness, inProc. 2nd Structure in Complexity Theory Conference, IEEE, New York (1987), pp. 2–8.
A. Selman, One-way functions in complexity theory, inProc. Mathematical Foundations of Computer Science 1990, Springer-Verlag, New York (1990), pp. 88–104.
A. Selman, A taxonomy of complexity classes of functions, submitted for publication.
S. Tang and O. Watanabe, On tally relativizations ofBP-complexity classes,SIAM J. Comput. 18 (1989), 449–462.
S. Toda, On polynomial time truth-table reducibility of intractable sets to p-selective sets,Math. Systems Theory 24 (1991), 69–82.
L. Valiant, Relative complexity of checking and evaluating,Inform. Process. Lett. 5 (1976), 20–23.
L. Valiant and V. Vazirani, NP is as easy as detecting unique solutions,Theoret. Comput. Sci. 47 (1986), 85–93.
K. Wagner, Bounded query computations, inProc. 3rd Structure in Complexity Theory Conference, IEEE, New York (1988), pp. 260–277.
O. Watanabe, A comparison of polynomial time completeness notions,Theoret. Comput. Sci. 54 (1987), 249–265.
O. Watanabe and S. Toda, Structural Analyses on the complexity of inverting functions, inProc. International Symposium SIGAL '90, Lecture Notes in Computer Science, Vol. 450, Springer-Verlag, New York (1990), pp. 31–38.
S. Zachos, Probabilistic quantifiers and games,J. Comput. System Sci. 36 (1988), 433–451.
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Watanabe, O., Toda, S. Structural analysis of the complexity of inverse functions. Math. Systems Theory 26, 203–214 (1993). https://doi.org/10.1007/BF01202283
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DOI: https://doi.org/10.1007/BF01202283