Recently, we showed that first-order model checking on nested pushdown trees can be done in doubly exponential alternating time with linear many alternations. Using the interpretation method of Compton and Henson we give a matching lower bound.

The Boolean formula value problem is in alternating log time and, more generally, parenthesis context-free languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value problem is complete for alternating log time under deterministic log time reductions. Consequently, i...

Given a string w and a pattern p, approximate pattern matching merges traditional sequence comparison and pattern matching by asking for the minimum diierence between w and a string exactly matched by p. We give an O(PN 2 (N + logP)) algorithm for approximately matching a string of length N and a context-free language speciied by a grammar of size P. The algorithm generalizes the Cocke-Younger-...

In this work, the matching problem between two free-form parametric surfaces, S 0 (u, v) and S 1 (u, v), has been considered in the context of a "rst stage of the metamorphosis process, which is de"ned as gradual and continuous transformation of one key shape into another. A method is presented to approximate the two reparametrization functions, r(u, v) and t(u, v), via a discrete sampled set o...

For a family of connected graphs A , spanning subgraph H graph G is called an -factor if each component isomorphic to some in . has perfect 2-matching such that either edge or cycle, i.e. { P 2 C i | ≥ 3}-factor said be covered if, for every e ∈ E ( ), there M belongs deleted − possesses 2-matching. In this paper, we first obtain respective new characterizations bipartite and non-bipartite by p...

Alternating automata play a key role in the automata-theoretic approach to specification, verification, and synthesis of reactive systems. Many algorithms on alternating automata, and in particular, their nonemptiness test, involve removal of alternation: a translation of the alternating automaton to an equivalent nondeterministic one. For alternating Büchi automata, the best known translation ...

In this paper, we consider the problem of finding a maximum weight 2-matching containing no cycle of length at most three in a weighted simple graph, which we call the weighted trianglefree 2-matching problem. Although the polynomial solvability of this problem is still open in general graphs, a polynomial-time algorithm is given by Hartvigsen and Li for the problem in subcubic graphs, i.e., gr...

We study M-alternating Hamilton paths, and M-alternating Hamilton cycles in a simple connected graph G on ν vertices with a perfect matchingM . Let G be a bipartite graph, we prove that if for any two vertices x and y in different parts of G, d(x)+d(y) ≥ ν/2+2, then G has an M-alternating Hamilton cycle. For general graphs, a condition for the existence of an M-alternating Hamilton path startin...

We consider discretization on overlapping non-matching grids for elliptic equations by using the Schwartz alternating (SA) method. We investigate also the dependence between the angle of partition of unity (PU) subspaces and the condition number of the stiffness matrix for a model problem. The aim of the paper is to find strategies to choose optimal or quasi-optimal partition of unity set of fu...