Factoring a Synchronous Context-Free Grammar into an equivalent grammar with a smaller number of nonterminals in each rule enables more efficient strategies for synchronous parsing. We present an algorithm for factoring an n-ary SCFG into a k-ary grammar in time O(kn). We also show how to efficiently compute the exact number of k-ary parsable permutations of length n, and discuss asymptotic beh...

Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we solve two open problems related to them raised in Phys. Rev. Lett. 117, 150401 (2016). We first show that fundamentally bina...

It is well known that the k-ary n-cube has been one of the most efficient interconnection networks for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. Let (X,Y ) be a bipartition of a k-ary 2-cube (even integer k ≥ 4). In this paper, we prove that for any two healthy vertices u ∈ X, v ∈ Y , there exists a hamiltonian path from u to v in the faulty k-ar...

Modern question answering and summarizing systems have motivated the need for complex n-ary relation extraction systems where the number of related entities (n) can be more than two. Shortest path dependency kernels have been proven to be effective in extracting binary relations. In this work, we propose a method that employs shortest path dependency based rules to extract complex n-ary relatio...

Many theoretical models of parallel computation are based on overly simplistic assumptions on the performance of the interconnection network. For example they assume constant latency for any communication pattern or innnite bandwidth. This paper presents a case study based on the FFT transpose algorithm, which is mapped on two families of scalable interconnection networks, the k-ary n-trees and...

We consider perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). In this paper, a generalized concatenation construction for q-ary 1-perfect codes is presented that allows us to construct q-ary 1-perfect codes of length (q − 1)nm + n +m from the given q-ary 1-perfect codes of length n = (q1 − 1)/(q − 1) and m = (q2 − 1)/(q − 1), where s1, s2 are ...

A general mechanism for "breaking" commutativity in algebras is proposed: if the underlying set taken to be not a crisp set, but rather an obscure/fuzzy membership function, reflecting degree of truth that element belongs can incorporated into commutation relations. The special "deformations" and $\varepsilon $-commutativity are introduced such way equal degrees result "nondeformed" case. We al...