Search results for "Information Science"
showing 10 items of 3627 documents
Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time
2002
This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and mac…
Nondeterministic Unitary OBDDs
2017
We investigate the width complexity of nondeterministic unitary OBDDs (NUOBDDs). Firstly, we present a generic lower bound on their widths based on the size of strong 1-fooling sets. Then, we present classically “cheap” functions that are “expensive” for NUOBDDs and vice versa by improving the previous gap. We also present a function for which neither classical nor unitary nondeterminism does help. Moreover, based on our results, we present a width hierarchy for NUOBDDs. Lastly, we provide the bounds on the widths of NUOBDDs for the basic Boolean operations negation, union, and intersection.
Subgroups of $$SF(\omega )$$ S F ( ω ) and the relation of almost containedness
2016
The relations of almost containedness and orthogonality in the lattice of groups of finitary permutations are studied in the paper. We define six cardinal numbers naturally corresponding to these relations by the standard scheme of $$P(\omega )$$P(ź). We obtain some consistency results concerning these numbers and some versions of the Ramsey theorem.
Quantum Algorithms for Learning Symmetric Juntas via Adversary Bound
2014
In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function f on n variables that only depends on k variables, and, when restricted to them, equals some predefined function h. The task is to identify the variables the function depends on. This is a generalisation of the Bernstein-Vazirani problem (when h is the XOR function) and the combinatorial group testing problem (when h is the OR function). We analyse the general case using the adversary bound, and give an alternative formulation for the quantum query complexity of this problem. We construct optimal quantum query algorithms for the cases when h is the OR function (compl…
Time-Efficient Quantum Walks for 3-Distinctness
2013
We present two quantum walk algorithms for 3-Distinctness. Both algorithms have time complexity $\tilde{O}(n^{5/7})$, improving the previous $\tilde{O}(n^{3/4})$ and matching the best known upper bound for query complexity (obtained via learning graphs) up to log factors. The first algorithm is based on a connection between quantum walks and electric networks. The second algorithm uses an extension of the quantum walk search framework that facilitates quantum walks with nested updates.
The Phagocyte Lattice of Dyck Words
2006
We introduce a new lattice structure on Dyck words. We exhibit efficient algorithms to compute meets and joins of Dyck words.
Every triangle-free induced subgraph of the triangular lattice is(5m,2m)-choosable
2014
A graph G is (a,b)-choosable if for any color list of size a associated with each vertex, one can choose a subset of b colors such that adjacent vertices are colored with disjoint color sets. This paper proves that for any integer m>=1, every finite triangle-free induced subgraph of the triangular lattice is (5m,2m)-choosable.
A Motzkin filter in the Tamari lattice
2015
The Tamari lattice of order n can be defined on the set T n of binary trees endowed with the partial order relation induced by the well-known rotation transformation. In this paper, we restrict our attention to the subset M n of Motzkin trees. This set appears as a filter of the Tamari lattice. We prove that its diameter is 2 n - 5 and that its radius is n - 2 . Enumeration results are given for join and meet irreducible elements, minimal elements and coverings. The set M n endowed with an order relation based on a restricted rotation is then isomorphic to a ranked join-semilattice recently defined in Baril and Pallo (2014). As a consequence, we deduce an upper bound for the rotation distan…
Matchings in three Catalan lattices
2003
In this note we consider a series of lattices that are enumerated by the well-known Catalan numbers. For each of these lattices, we exhibit a matching in a constructive way.
Dyck paths with a first return decomposition constrained by height
2018
International audience; We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height k with a flat (resp. with no flats) at the maximal height. (C) 2018 Elsevier B.V. All rights reserved.KeywordsKeyWords Plus:STATISTICS; STRINGS