22 research outputs found
Reordering method and hierarchies for quantum and classical ordered binary decision diagrams
© Springer International Publishing AG 2017.We consider Quantum OBDD model. It is restricted version of read-once Quantum Branching Programs, with respect to “width” complexity. It is known that maximal complexity gap between determin-istic and quantum model is exponential. But there are few examples of such functions. We present method (called “reordering”), which allows to build Boolean function g from Boolean Function f, such that if for f we have gap between quantum and deterministic OBDD complexity for natural order of variables, then we have almost the same gap for function g, but for any order. Using it we construct the total function REQ which deterministic OBDD complexity is 2Ω(n/logn) and present quantum OBDD of width O(n2). It is bigger gap for explicit function that was known before for OBDD of width more than linear. Using this result we prove the width hierarchy for complexity classes of Boolean functions for quantum OBDDs. Additionally, we prove the width hierarchy for complexity classes of Boolean functions for bounded error probabilistic OBDDs. And using “reordering” method we extend a hierarchy for k-OBDD of polynomial size, for k = o(n/log3n). Moreover, we proved a similar hierarchy for bounded error probabilistic k-OBDD. And for deterministic and proba-bilistic k-OBDDs of superpolynomial and subexponential size
Separating the eraser Turing machine classes Le, NLe, co-NLe and Pe
AbstractBy means of exponential lower and polynomial upper bounds for read-once-only Ω-branching programs we separate the logarithmic space-bounded complexity classes Le, NLe, co-NLe and Pe for eraser Turing machines
Quantum Branching Programs and Space-Bounded Nonuniform Quantum Complexity
In this paper, the space complexity of nonuniform quantum computations is
investigated. The model chosen for this are quantum branching programs, which
provide a graphic description of sequential quantum algorithms. In the first
part of the paper, simulations between quantum branching programs and
nonuniform quantum Turing machines are presented which allow to transfer lower
and upper bound results between the two models. In the second part of the
paper, different variants of quantum OBDDs are compared with their
deterministic and randomized counterparts. In the third part, quantum branching
programs are considered where the performed unitary operation may depend on the
result of a previous measurement. For this model a simulation of randomized
OBDDs and exponential lower bounds are presented.Comment: 45 pages, 3 Postscript figures. Proofs rearranged, typos correcte
Классические и квантовые ветвящиеся программы
Классические и квантовые ветвящиеся программыбакалавриа
On Lower Bounds for Parity Branching Programs
Diese Arbeit beschaeftigt sich mit der Komplexität von parity Branching Programmen. Es werden superpolynomiale untere Schranken für verschiedene Varianten bewiesen, nämlich für well-structured graph-driven parity branching programs, general graph-driven parity branching programs und Summen von graph-driven parity branching programs