Maximal Common Subsequence Algorithms

A common subsequence of two strings is maximal, if inserting any character into the subsequence can no longer yield a common subsequence of the two strings. The present article proposes a (sub)linearithmic-time, linear-space algorithm for finding a maximal common subsequence of two strings and also proposes a linear-time algorithm for determining if a common subsequence of two strings is maximal

Efficient algorithms for enumerating maximal common subsequences of two strings

We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a cubic-space data structure in cubic time to output each MCS in linear time. This data structure can be used to search for particular MCSs satisfying some condition without performing an explicit enumeration. Another prepares a quadratic-space data structure in quadratic time to output each MCS in linear time, and the other prepares a linear-space data structure in quadratic time to output each MCS in linearithmic time.Comment: 23 pages, 5 Postscript figure

Application of tensor network method to two dimensional lattice N=1\mathcal{N}=1 Wess-Zumino model

We study a tensor network formulation of the two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function without the sign problem, and basic ideas to obtain a tensor network for both fermion and scalar boson systems were already given in previous works. In addition to improving the methods, we have constructed a tensor network representation of the model including the Yukawa-type interaction of Majorana fermions and real scalar bosons. We present some numerical results.Comment: 8 pages, 4 figures, talk presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spai

Proper Learning Algorithm for Functions of k Terms under Smooth Distributions

AbstractIn this paper, we introduce a probabilistic distribution, called a smooth distribution, which is a generalization of variants of the uniform distribution such as q-bounded distribution and product distribution. Then, we give an algorithm that, under the smooth distribution, properly learns the class of functions of k terms given as Fk∘Tkn={g(f1(v), …, fk(v))|g∈Fk, f1, …, fk∈Tn} in polynomial time for constant k, where Fk is the class of all Boolean functions of k variables and Tn is the class of terms over n variables. Although class Fk∘Tkn was shown by Blum and Singh to be learned using DNF as the hypothesis class, it has remained open whether it is properly learnable under a distribution-free setting