We consider variants of alternating auxiliary stack automata and characterize their computational power when the number of alternations is bounded by a constant or unlimited. In this way we get new characterizations of NP, the polynomial hierarchy, PSpace, and bounded query classes like co-DP=NL〈NP[1]〉 and 2P=P , in a uniform framework. c © 2002 Elsevier Science B.V. All rights reserved.

The non-negative matrix factorization (NMF) determines a lower rank approximation of a matrix where an interger "!$# is given and nonnegativity is imposed on all components of the factors % & (' and % )'* ( . The NMF has attracted much attention for over a decade and has been successfully applied to numerous data analysis problems. In applications where the components of the data are necessaril...

We consider infinite two-player games on pushdown graphs. For parity winning conditions, we show that the set of winning positions of each player is regular and we give an effective construction of an alternating automaton recognizing it. This provides a DEXPTIME procedure to decide whether a position is winning for a given player. Finally, using the same methods, we show, for any ω-regular win...

The nonemptiness problem for nondeterministic automata on infinite words can be reduced to a sequence of reachability queries. The length of a shortest witness to the nonemptiness is then polynomial in the automaton. Nonemptiness algorithms for alternating automata translate them to nondeterministic automata. The exponential blow-up that the translation involves is justified by lower bounds for...

This paper studies mathematical properties of reaction systems that was introduced by Enrenfeucht and Rozenberg as computational models inspired by biochemical reaction in the living cells. In particular, we continue the study on the generative power of functions specified by minimal reaction systems under composition initiated by Salomaa. Allowing degenerate reaction systems, functions specifi...

The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of 2n−1 permutations that pairwise generate the symmetric group Sn. There is no set of 2n−1 + 1 permutations having this property. For all sufficiently large integers n with n≡ 2 mod 4, there exists a set of 2n−2 even permutations that pairwise generate the alternating group An. The...

In order to completely separate objects with large sections of occluded boundaries in an image, we devise a new variational level set model for image segmentation combining the Chan-Vese elastica and landmark constraints. For computational efficiency, design its Augmented Lagrangian Method (ALM) or Alternating Direction Multiplier (ADMM) method by introducing some auxiliary variables, Lagrange ...

nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

Alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming problems. Recently, because of its significant efficiency and easy implementation in novel applications, ADM is extended to the case where the number of separable parts is a finite number. The algorithmic framework of the extended method consists of two phases. On each iteration it...

In the present study, a comprehensive and systematic strategy was described to evaluate the performance of several three-way calibration methods on a bio-analytical problem. Parallel factor analysis (PARAFAC), alternating trilinear decomposition (ATLD), self-weighted alternating trilinear decomposition (SWATLD), alternating penalty trilinear decomposition (APTLD) and unfolded partial least squa...