Related papers: Set membership with two classical and quantum bit …
Designs of data structures for approximate membership queries with false-positive errors that support both insertions and deletions stipulate the following two conditions: (1) Duplicate insertions are prohibited, i.e., it is prohibited to…
We study the problem of storing the minimum number of bits required to answer next/previous larger/smaller value queries on an array $A$ of $n$ numbers, without storing $A$. We show that these queries can be answered by storing at most…
String-bit models are both an efficient way of organizing string perturbation theory, and a possible non-perturbative composite description of string theory. This is a summary of ideas and results of string-bit and superstring-bit models,…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
This paper studies the minimal dimension required to embed subset memberships ($m$ elements and ${m\choose k}$ subsets of at most $k$ elements) into vector spaces, denoted as Minimal Embeddable Dimension (MED). The tight bounds of MED are…
In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…
The modular subset sum problem consists of deciding, given a modulus $m$, a multiset $S$ of $n$ integers in $0..m-1$, and a target integer $t$, whether there exists a subset of $S$ with elements summing to $t \mod m $, and to report such a…
The subalgebra membership problem is the problem of deciding if a given element belongs to an algebra given by a set of generators. This is one of the best established computational problems in algebra. We consider a variant of this…
Ranking bit patterns -- finding the index of a given pattern in an ordered sequence -- is a major bottleneck scaling up numerical quantum many-body calculations, as fermionic and hard-core bosonic states translate naturally to bit patterns.…
We consider the problem of discovering overlapping communities in networks which we model as generalizations of Graph Packing problems with overlap. We seek a collection $\mathcal{S}' \subseteq \mathcal{S}$ consisting of at least $k$ sets…
We resolve the space complexity of single-pass streaming algorithms for approximating the classic set cover problem. For finding an $\alpha$-approximate set cover (for any $\alpha= o(\sqrt{n})$) using a single-pass streaming algorithm, we…
We address the problem of counting the number of strings in a collection where a given pattern appears, which has applications in information retrieval and data mining. Existing solutions are in a theoretical stage. We implement these…
We consider the problem of summarizing a multi set of elements in $\{1, 2, \ldots , n\}$ under the constraint that no element appears more than $\ell$ times. The goal is then to answer \emph{rank} queries --- given $i\in\{1, 2, \ldots ,…
A binary string representation of prime occurrences is a sequence of bits, where $1$ entries encode positions of prime numbers. This is a convenient representation for analysis of prime distribution, since it allows for application of a…
We consider the problem of learning an unknown partition of an $n$ element universe using rank queries. Such queries take as input a subset of the universe and return the number of parts of the partition it intersects. We give a simple…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…
Associative memories are devices storing information that can be fully retrieved given partial disclosure of it. We examine a toy model of associative memory and the ultimate limitations it is subjected to within the framework of general…
Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string over S. A "secondary index" for x answers alphabet range queries of the form: Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in [a_l;…
The combined Universal Probability M(D) of strings x in sets D is close to max M({x}) over x in D: their ~logs differ by at most D's information j=I(D:H) about the halting sequence H. Thus if all x have complexity K(x) >k, D carries >i bits…
The problem of memory checking considers storing files on an unreliable public server whose memory can be modified by a malicious party. The main task is to design an online memory checker with the capability to verify that the information…