Search results for "abstract"
showing 10 items of 1959 documents
Span-Program-Based Quantum Algorithms for Graph Bipartiteness and Connectivity
2016
Span program is a linear-algebraic model of computation which can be used to design quantum algorithms. For any Boolean function there exists a span program that leads to a quantum algorithm with optimal quantum query complexity. In general, finding such span programs is not an easy task. In this work, given a query access to the adjacency matrix of a simple graph G with n vertices, we provide two new span-program-based quantum algorithms:an algorithm for testing if the graph is bipartite that uses $$On\sqrt{n}$$ quantum queries;an algorithm for testing if the graph is connected that uses $$On\sqrt{n}$$ quantum queries.
Using Search Algorithms for Modeling Economic Processes
2013
Abstract Economic issues are placed in formal practice, when is desired a modelling of the economic process, a manufacturing process, a device, etc. Each share of that economic process is denoted by a, b, c, d, these actions with defined time periods and action pairs are formed strings of the form, ab * cab * bc ., ab, bb, bc. so for them there are no other restrictions. If the graph is viewed as a system image, nodes representing components, then an immediate interpretation of an arc (xi, xj) are the component xi that is said to directly influence component xj. If nodes have the significance of possible states of a system when a spring (xi.xj) means that, the system can jump from state xi …
On the regularity of circular splicing languages : A survey and new developments
2009
Circular splicing has been introduced to model a specific recombinant behaviour of circular DNA, continuing the investigation initiated with linear splicing. In this paper we focus on the relationship between regular circular languages and languages generated by finite circular splicing systems. We survey the known results towards a characterization of the intersection between these two classes and provide new contributions on the open problem of finding this characterization. First, we exhibit a non-regular circular language generated by a circular simple system thus disproving a known result in this area. Then we give new results related to a restrictive class of circular splicing systems…
A Potential Field Function for Overlapping Point Set and Graph Cluster Visualization
2015
In this paper we address the problem of visualizing overlapping sets of points with a fixed positioning in a comprehensible way. A standard visualization technique is to enclose the point sets in isocontours generated by bounding a potential field function. The most commonly used functions are various approximations of the Gaussian distribution. Such an approach produces smooth and appealing shapes, however it may produce an incorrect point nesting in generated regions, e.g. some point is contained inside a foreign set region. We introduce a different potential field function that keeps the desired properties of Gaussian distribution, and in addition guarantees that every point belongs to a…
The branch set of a quasiregular mapping between metric manifolds
2016
Abstract In this note, we announce some new results on quantitative countable porosity of the branch set of a quasiregular mapping in very general metric spaces. As applications, we solve a recent conjecture of Fassler et al., an open problem of Heinonen–Rickman, and an open question of Heinonen–Semmes.
Unary Languages Recognized by Two-Way One-Counter Automata
2014
A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages. Up to our knowledge, the only known unary nonregular languages recognized by 2D1CAs are those formed by strings having exponential length, where the exponents form some trivial unary regular language. In this paper, we present some non-trivial subsets of these languages. By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear–space Turing machines. We also show …
Termination of a set of rules modulo a set of equations
2006
The problem of termination of a set R of rules modulo a set E of equations, called E-termination problem, arises when trying to complete the set of rules in order to get a Church-Rosser property for the rules modulo the equations. We first show here that termination of the rewriting relation and E-termination are the same whenever the used rewriting relation is E-commuting, a property inspired from Peterson and Stickel’s E-compatibility property. More precisely, their results can be obtained by requiring termination of the rewriting relation instead of E-termination if E-commutation is used instead of E-compatibility. When the rewriting relation is not E-commuting, we show how to reduce E-t…
Defining relations of minimal degree of the trace algebra of 3×3 matrices
2008
Abstract The trace algebra C n d over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n , d ⩾ 2 . Minimal sets of generators of C n d are known for n = 2 and n = 3 for any d as well as for n = 4 and n = 5 and d = 2 . The defining relations between the generators are found for n = 2 and any d and for n = 3 , d = 2 only. Starting with the generating set of C 3 d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C 3 d is equal to 7 for any d ⩾ 3 . We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8. The proofs are based …
Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics
2007
The original publication is available at www.springerlink.com ; ISBN 978-3-540-75519-7 ; ISSN 0302-9743 (Print) 1611-3349 (Online); International audience; We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, \ie surfaces of algebraic degree~2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the adjacency graph of the arrangement. Our implementation is {\em complete} in the sense that it can handle all kinds of…
Superiority Of One-Way And Realtime Quantum Machines
2012
In automata theory, quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to QFAs augmented with counters or stacks. In this paper, we focus on such generalizations of QFAs where the input head operates in one-way or realtime mode, and present some new results regarding their superiority over their classical counterparts. Our first result is about the nondeterministic acceptance mode: Each quantum model architecturally intermediate between realtime finite state automaton and one-way pushdown automaton (one-way finite automaton, realtime and one-way finite automata with one-counter, and realtime push…