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- Stephen A. Fenner, Lance Fortnow, Ashish V. Naik, John D. Rogers
- IEEE Conference on Computational Complexity
- 1996

We look at the hypothesis that all honest onto polynomial-time computable functions have a polynomial-time computable inverse. We show this hypothesis equivalent to several other complexity conjectures including In polynomial time, one can nd accepting paths of nondeterministic polynomial-time Turing machines that accept. Every total multivalued… (More)

- Joan Feigenbaum, Lance Fortnow, Sophie Laplante, Ashish V. Naik
- Computational Complexity
- 1996

We study three types of self-reducibility that are motivated by the theory of program veriication. A set A is random-self-reducible if one can determine whether an input x is in A by making random queries to an A-oracle. The distribution of each query may depend only on the length of x. A set B is self-correctable over a distribution D if one can convert a… (More)

- Lane A. Hemaspaandra, Ashish V. Naik, Mitsunori Ogihara, Alan L. Selman
- SIAM J. Comput.
- 1994

Is there an NP function that, when given a satissable formula as input, outputs one satisfying assignment uniquely? That is, can a nondeterministic function cull just one satisfying assignment from a possibly exponentially large collection of assignments? We show that if there is such a nondeterministic function, then the polynomial hierarchy collapses to… (More)

- Ashish V. Naik, John D. Rogers, James S. Royer, Alan L. Selman
- Theor. Comput. Sci.
- 1998

sity, Chicago, IL 60604. The second author gratefully acknowledges a visiting scholar appointment to the University of Chicago that facilitated this work. Abstract The class NPkV consists of those partial, multivalued functions that can be computed by a nondeterministic, polynomial time-bounded transducer that has at most k distinct values on any input. We… (More)

- Jin-Yi Cai, Ashish V. Naik, D. Sivakumar
- STACS
- 1996

Recently a 1978 conjecture by Hartmanis Har78] was resolved CS95], following progress made by Ogi95]. It was shown that there is no sparse set that is hard for P under logspace many-one reductions, unless P = LOGSPACE. We extend the results to the case of sparse sets that are hard under more general reducibilities. Our main results are as follows. (1) If… (More)

We study the complexity of inverting many-one, honest, polynomial-time computable onto functions. Asserting that every polynomial-time computable, honest, onto function is in-vertible is equivalent to the following proposition that we call Q: For all NP machines M that accept , there exists a polynomial-time computable function g M such that for all x, g M… (More)

- Lane A. Hemaspaandra, Albrecht Hoene, +4 authors Jie Wang
- Int. J. Found. Comput. Sci.
- 1995

In this note, we study NP-selective sets (formally, sets that are selective via NPSVt functions) as a natural generalization of P-selective sets. We show that, assuming P 6 = NP \coNP, the class of NP-selective sets properly contains the class of P-selective sets. We study several properties of NP-selective sets such as self-reducibility, hardness under… (More)

- Ashish V. Naik, Kenneth W. Regan, D. Sivakumar
- STACS
- 1994

This paper furthers the study of quasi-linear time complexity initiated by Schnorr Sch76] and Gurevich and Shelah GS89]. We show that the fundamental properties of the polynomial-time hierarchy carry over to the quasilinear-time hierarchy. Whereas all previously known versions of the Valiant-Vazirani reduction from NP to parity run in quadratic time, we… (More)

This paper presents an analytical approach for scheduling crackdowns on street{corner drug markets. The crackdown scheduling problem is shown to be NP{Complete. A dynamic programming formulation is presented with an exponential time optimal algorithm. We then provide eecient optimal algorithms for several special cases and approximation algorithms for the… (More)

- Lane A. Hemaspaandra, Albrecht Hoene, +4 authors Jie Wang
- 1993

1 Some of these results appear in preliminary form in \Computing Solutions Uniquely Collapses the Polynomial Hierarchy" Abstract A set is P-selective Sel79] if there is a polynomial-time semi-decision algorithm for the set|an algorithm that given any two strings decides which is \more likely" to be in the set. This paper studies two natural generalizations… (More)