Related papers: Moore machines duality
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…
This paper is concerned with the problem of state estimation for discrete-time linear systems in the presence of additional (equality or inequality) constraints on the state (or estimate). By use of the minimum variance duality, the…
The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability…
In this paper, we introduce the model of quantum Mealy machines and study the equivalence checking and minimisation problems of them. Two efficient algorithms are developed for checking equivalence of two states in the same machine and for…
We provide a simple proof for the necessity of conditions for discriminating with minimum error between a known set of quantum states.
This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text…
We show that Ore operators can be desingularized by calculating a least common left multiple with a random operator of appropriate order. Our result generalizes a classical result about apparent singularities of linear differential…
The aim of this paper is to analyze the MS transformation in the case of weak deviation of the condition for equal detunings, which in necessary for factorization towards set of two-state systems and set of decouple states. Some elements…
The Moore-Hodgson Algorithm minimizes the number of late jobs on a single machine. That is, it finds an optimal schedule for the classical problem $1~|\;|~\sum{U_j}$. Several proofs of the correctness of this algorithm have been published.…
This paper illustrates a technique for specifying the timing, logical operation, and compositional circuit design of digital circuits in terms of ordinary state machines with output (Moore machines). The method is illustrated here with…
Necessary and sufficient condition for the existence of a minimum uncertainty state for an arbitrary pair of observables is given.
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
We derive an analytic approximation for the concurrence of weakly mixed bipartite quantum states - typical objects in state of the art experiments. This approximation is shown to be a lower bound of the concurrence of arbitrary states.
We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is…
Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task…
We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.
We provide a solution of finding optimal measurement strategy for distinguishing between symmetric mixed quantum states. It is assumed that the matrix elements of at least one of the symmetric quantum states are all real and nonnegative in…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
Using the known necessary and sufficient conditions for minimum error discrimination (MED), first it is shown that a Helstrom family of ensembles is equivalent to these conditions and then by a convex combination of the initial states (the…
We describe a purely algebraic method for finding the best separable approximation to a mixed state of a composite 2x2 quantum system, consisting of a decomposition of the state into a linear combination of a mixed separable part and a pure…