Search results for "computational complexity."
showing 10 items of 245 documents
NP-completeness of the hamming salesman problem
1985
It is shown that the traveling salesman problem, where cities are bit strings with Hamming distances, is NP-complete.
Graph connectivity and monadic NP
2002
Ehrenfeucht games are a useful tool in proving that certain properties of finite structures are not expressible by formulas of a certain type. In this paper a new method is introduced that allows the extension of a local winning strategy for Duplicator, one of the two players in Ehrenfeucht games, to a global winning strategy. As an application it is shown that graph connectivity cannot be expressed by existential second-order formulas, where the second-order quantification is restricted to unary relations (monadic NP), even, in the presence of a built-in linear order. As a second application it is stated, that, on the other hand, the presence of a linear order increases the power of monadi…
Dichotomies properties on computational complexity of S-packing coloring problems
2015
This work establishes the complexity class of several instances of the S -packing coloring problem: for a graph G , a positive integer k and a nondecreasing list of integers S = ( s 1 , ? , s k ) , G is S -colorable if its vertices can be partitioned into sets S i , i = 1 , ? , k , where each S i is an s i -packing (a set of vertices at pairwise distance greater than s i ). In particular we prove a dichotomy between NP-complete problems and polynomial-time solvable problems for lists of at most four integers.
Understanding Quantum Algorithms via Query Complexity
2017
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes. Query complexity is widely used for studying quantum algorithms, for two reasons. First, it includes many of the known quantum algorithms (including Grover's quantum search and a key subroutine of Shor's factoring algorithm). Second, one can prove lower bounds on the query complexity, bounding the possible quantum advantage. In the last few years, there have been major advances on several longstanding problems in the query complexity. In this talk, we su…
On Physical Problems that are Slightly More Difficult than QMA
2013
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We introduce new complexity classes consisting of problems that are solvable with a small number of queries to a QMA oracle and use these complexity classes to quantify the complexity of several natural computational problems (for example, the complexity of estimating the spectral gap of a Hamiltonian).
If P≠NP then some strongly noninvertible functions are invertible
2006
AbstractRabi, Rivest, and Sherman alter the standard notion of noninvertibility to a new notion they call strong noninvertibility, and show—via explicit cryptographic protocols for secret-key agreement (Rabi and Sherman attribute this protocol to Rivest and Sherman) and digital signatures (Rabi and Sherman)—that strongly noninvertible functions are very useful components in protocol design. Their definition of strong noninvertibility has a small twist (“respecting the argument given”) that is needed to ensure cryptographic usefulness. In this paper, we show that this small twist has a consequence: unless P=NP, some strongly noninvertible functions are invertible.
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.
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.