Search results for " Complexity"
showing 10 items of 623 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…
Application of kolmogorov complexity to inductive inference with limited memory
1995
A b s t r a c t . We consider inductive inference with limited memory[l]. We show that there exists a set U of total recursive functions such that U can be learned with linear long-term memory (and no short-term memory); U can be learned with logarithmic long-term memory (and some amount of short-term memory); if U is learned with sublinear long-term memory, then the short-term memory exceeds arbitrary recursive function. Thus an open problem posed by Freivalds, Kinber and Smith[l] is solved. To prove our result, we use Kolmogorov complexity.
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.
Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs
2014
In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …
The computational complexity of the criticality problems in a network with interval activity times
2002
Abstract The paper analyzes the criticality in a network with interval activities duration times. A natural generalization of the criticality notion (for a path, an activity and an event) for the case of network with interval activity duration times is given. The computation complexity of five problems linked to the introduced criticality notion is presented.
Periodicity and repetitions in parameterized strings
2008
AbstractOne of the most beautiful and useful notions in the Mathematical Theory of Strings is that of a Period, i.e., an initial piece of a given string that can generate that string by repeating itself at regular intervals. Periods have an elegant mathematical structure and a wealth of applications [F. Mignosi and A. Restivo, Periodicity, Algebraic Combinatorics on Words, in: M. Lothaire (Ed.), Cambridge University Press, Cambridge, pp. 237–274, 2002]. At the hearth of their theory, there are two Periodicity Lemmas: one due to Lyndon and Schutzenberger [The equation aM=bNcP in a free group, Michigan Math. J. 9 (1962) 289–298], referred to as the Weak Version, and the other due to Fine and …
Quantum Finite Automata and Logics
2006
The connection between measure once quantum finite automata (MO-QFA) and logic is studied in this paper. The language class recognized by MO-QFA is compared to languages described by the first order logics and modular logics. And the equivalence between languages accepted by MO-QFA and languages described by formulas using Lindstrom quantifier is shown.
Minimal Morse flows on compact manifolds
2006
Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.
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.
Balls into non-uniform bins
2014
Balls-into-bins games for uniform bins are widely used to model randomized load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-to-peer (P2P) networks, which are not able to perfectly balance the load over the bins. While previous evaluations try to find strategies for uniform bins under non-uniform bin selection probabilities, this paper investigates heterogeneous bins, where the "capacities" of the bins might differ significantly. We show that heterogeneous environments can even help to distribute the load more eve…