Related papers: State complexity of multiple catenation
We prove that, for any arbitrary finite alphabet and for the uniform distribution over deterministic and accessible automata with n states, the average complexity of Moore's state minimization algorithm is in O(n log n). Moreover this bound…
The density of state for a complex $N\times N$ random matrix coupled to an external deterministic source is considered for a finite N, and a compact expression in an integral representation is obtained.
The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. The goal of this…
Wu, Lou, Lai and Chang proposed a multi-exponentiation algorithm using binary complements and the non-adjacent form. The purpose of this paper is to show that neither the analysis of the algorithm given by its original proposers nor that by…
We consider the distinguishability of Gaussian states from the view point of continuous-variable quantum cryptography using post-selection. Specifically, we use the probability of error to distinguish between two pure coherent (squeezed)…
For fast computation of the Arnold complexity of length $2^{n}$ binary words we obtain an upper bound for the Shannon function $Sh(n)$
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *,…
We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…
A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition…
How to calculate the entanglement entropy between two subsystems for a mixed state has remained an important problem. In this paper, we provide a straightforward method, namely the subtraction approach, to solve this problem for generic…
Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where its entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number…
We introduce a formalism that connections entanglement witnesses and the distillation and activation properties of a state. We apply this formalism to two cases: First, we rederive the results presented in quant-ph/0104095 by Eggeling et…
In this paper, some issues concerning the Chinese remaindering representation are discussed. Some new converting methods, including an efficient probabilistic algorithm based on a recent result of von zur Gathen and Shparlinski…
We give a mathematical proof for an identification criterion by a probability measure for the ground state among an infinite number of available states, or a finitely truncated number with appropriate boundary conditions, in a quantum…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
We consider the problem of remote state preparation recently studied in several papers. We study the communication complexity of this problem, in the presence of entanglement and in the scenario of single use of the channel.
We present a new linked cluster expansion for calculating properties of multiparticle excitation spectra to high orders. We use it to obtain the two-particle spectra for systems of coupled spin-half dimers. We find that even for weakly…
The author proves variants of Buchstab's identity on sieve functions, refining the previous work on new iteration rules of Brady. The main tool used in the proof is a special form of combinatorial identities related to the binomial…
The structural study of entanglement in multipartite systems is hindered by the lack of necessary and sufficient operational criteria able to discriminate among the various entanglement properties of a given mixed state. Here, we pursue a…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…