Showing papers by "Johan Håstad published in 1994"
TL;DR: It is proved that if $n$ is a power of 2, then there is a threshold function on inputs that requires weights of size around $2^{(n\log n)/2-n}$.
Abstract: It is proved that if $n$ is a power of 2, then there is a threshold function on $n$ inputs that requires weights of size around $2^{(n\log n)/2-n}$. This almost matches the known upper bounds.
152 citations
TL;DR: It is shown that for almost all oracles A, IP A ≠ PSPACE A, and the IPP = PSPACE result holds for all oracle worlds.
59 citations
TL;DR: Symmetric Boolean functions in AC 0 can be computed by unbounded fan-in circuits with the following properties: if the optimal depth of AC 0 -circuits is d, the depth is at most d + 2, the number of wires is almost linear, and theNumber of gates is subpolynomial.
Abstract: It is well known which symmetric Boolean functions can be computed by constant depth, polynomial size, unbounded fan-in circuits, i.e., which are contained in the complexity class AC 0 . This result is sharpened. Symmetric Boolean functions in AC 0 can be computed by unbounded fan-in circuits with the following properties. If the optimal depth of AC 0 -circuits is d , the depth is at most d + 2, the number of wires is almost linear, namely n log O (1) n , and the number of gates is subpolynomial (but superpolylogarithmic), namely 2 O (log δ n ) for some δ
23 citations
TL;DR: It is proved that any Turing machine that recognizes LT requires time close to T(n) for most inputs, thus forming an average time hierarchy.
14 citations
23 May 1994
TL;DR: Finite strings of characters drawn from an arbitrary, ordered alphabet are considered, here the common assumption that entire strings can be compared in constant time is replaced by the more conservative assumption that only single characters can be compmed in constantTime.
Abstract: ( ;iven n strings arranged in alphabetical order, how many characters must we probe to determine whether a k-character query string is present? If k is a constant, we can solve i IIe problem with @(log n) probes by means of binary search, .Ind this is optimal, but what happens for larger values of k? The question 1s a fundamental one; we are simply askiiig for the complexity of searching a dictionary for a string, ~vhere the common assumption that entire strings can be compared in constant time is replaced by the more conservative assumption that only single characters can be compmed in constant time. For s&iciently long strings, the latter assumption seems more realistic. At first glance the problem may appear easy — some liind of generalized binary search should do the trick. However, closer acquaintance with the problem reveals a surprising, intricacy. 13eing slightly more precise, we consider finite strings of characters drawn from an arbitrary, ordered alphabet.
9 citations
06 Jul 1994
TL;DR: Some of the recent results in proving that approximating some NP-hard optimization problems remains NP- hard are surveyed.
Abstract: We survey some of the recent results in proving that approximating some NP-hard optimization problems remains NP-hard. This is a survey paper and it contains no new results.
3 citations