A Congruence-Based Perspective on Finite Tree Automata

We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski’s style minimization algorithm for tree automata. First, we prove correct this method relying on the following fact: when the automata-based and the language-based congruences coincide, determinizing the automaton yields the minimal one. Such automata-based congruences, in the case of word automata, are defined using pre and post operators. Now we extend these operators to tree automata, a task that is particularly challenging due to the reduced expressive power of deterministic top-down (or equivalently co-deterministic bottom-up) automata. We leverage further our framework to offer an extension of the original result by Brzozowski for word automata.

An Extended Reweighted ℓ1 Minimization Algorithm for Image Restoration

This paper proposes an effective extended reweighted ℓ1 minimization algorithm (ERMA) to solve the basis pursuit problem minu∈Rnu1:Au=f in compressed sensing, where A∈Rm×n, m≪n. The fast algorithm is based on linearized Bregman iteration with soft thresholding operator and generalized inverse iteration. At the same time, it also combines the iterative reweighted strategy that is used to solve minu∈Rnupp:Au=f problem, with the weight ωiu,p=ε+ui2p/2−1. Numerical experiments show that this l1 minimization persistently performs better than other methods. Especially when p=0, the restored signal by the algorithm has the highest signal to noise ratio. Additionally, this approach has no effect on workload or calculation time when matrix A is ill-conditioned.

An accelerated majorization-minimization algorithm with convergence guarantee for non-Lipschitz wavelet synthesis model *

We consider a wavelet based image reconstruction model with the ℓ p (0 < p < 1) quasi-norm regularization, which is a non-convex and non-Lipschitz minimization problem. For solving this model, Figueiredo et al (2007 IEEE Trans. Image Process. 16 2980–2991) utilized the classical majorization-minimization framework and proposed the so-called Isoft algorithm. This algorithm is computationally efficient, but whether it converges or not has not been concluded yet. In this paper, we propose a new algorithm to accelerate the Isoft algorithm, which is based on Nesterov’s extrapolation technique. Furthermore, a complete convergence analysis for the new algorithm is established. We prove that the whole sequence generated by this algorithm converges to a stationary point of the objective function. This convergence result contains the convergence of Isoft algorithm as a special case. Numerical experiments demonstrate good performance of our new algorithm.

Direct Energy Minimization Algorithm for Numerical Simulation of Carbon Dioxide Injection

We discuss numerical simulation of carbon dioxide injection considered by oil and gas companies. Complex behavior of multicomponent reservoir fluids mixed with carbon dioxide may cause the occurrence of vapor-liquid-liquid equilibria (VLLE), salt precipitation in aquifers, pore-clogging, etc. We propose a simple algorithm for phase equilibria calculations based on the minimization of the multicomponent system free energy. This algorithm can be used to calculate phase separations and component partitioning between the phases under various conditions (critical region, two- and three-phase equilibria, etc.). We demonstrate the applicability of the proposed algorithm in a series of calculations. We consider binary and ternary mixtures that include carbon dioxide and hydrocarbons. We examine the algorithm in two- and three-phase equilibrium calculations and compare its performance with the popular iterative fugacity equilibration technique. We show that both calculation techniques give near-identical results for the considered mixtures. Thus, we show that the free energy minimization algorithm can be used interchangeably with the fugacity equilibration technique for calculating phase equilibria. This algorithm is applicable for VLLE calculations, which is important when considering multicomponent reservoir fluids that include carbon dioxide.