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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)
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)
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)
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)
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)
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)
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)
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)