We consider the problem of reachability on One-Counter Systems (OCSs) and Pushdown (PDSs). The has a well-known O(n3) bound both models, while is believed to be tight for PDSs. Here we establish new upper lower bounds OCSs restricted show that can solved (i) in O(nω⋅log2⁡n) time OCSs, (ii) O(n2) sparse PDSs when witness executions stack height bounded by log⁡n. Moreover, prove similar bounds.

We consider two natural problems about nondeterministic finite automata. First, given such an automaton M of n states, and a length `, does M accept a word of length `? We show that the classic problem of triangle-free graph recognition reduces to this problem, and give an O(nω(log n)1+ log `)-time algorithm to solve it, where ω is the optimal exponent for matrix multiplication. Second, provide...

A comprehensive mechanistic study conducted on the formation mechanism of five-fold twinned copper nanowires by heating copper(I) chloride with oleylamine at 170 °C is presented. Electron microscopy and UV-visible absorption spectra are used to analyze the growth mechanism of copper nanowires. High-resolution transmission electron microscopy and selected-area electron diffraction are used to in...

Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic path-matching problems and an algorithm for constructing basic path-matchings in Õ(nω) time, where n is the number of vertices and ω is the exponent for matrix multiplic...

The binding energy of the six quark system with strangeness s=-3 is investigated under the chiral SU(3) constituent quark model in the framework of RGM . The calculations of the single NΩ channel with spin S=2 and the single ∆Ω channel with spin S=3 are performed. The results show that both systems could be dibaryons and the interaction induced by the chiral field plays a very important role on...

We show an exponential separation between two well-studied models of algebraic computation, namely read-once oblivious algebraic branching programs (ROABPs) and multilinear depth three circuits. In particular we show the following: 1. There exists an explicit n-variate polynomial computable by linear sized multilinear depth three circuits (with only two product gates) such that every ROABP comp...

We construct a PCP for NTIME(2n) with constant soundness, 2npoly(n) proof length, and poly(n) queries where the verifier’s computation is simple: the queries are a projection of the input randomness, and the computation on the prover’s answers is a 3CNF. The previous upper bound for these two computations was polynomial-size circuits. Composing this verifier with a proof oracle increases the ci...

In the post-Newtonian (PN) regime, the time scale on which the spins of binary black holes precess is much shorter than the radiation-reaction time scale on which the black holes inspiral to smaller separations. On the precession time scale, the angle between the total and orbital angular momenta oscillates with nutation period τ, during which the orbital angular momentum precesses about the to...

We give the first representation-independent hardness result for agnostically learning halfspaces with respect to the Gaussian distribution. We reduce from the problem of learning sparse parities with noise with respect to the uniform distribution on the hypercube (sparse LPN), a notoriously hard problem in theoretical computer science and show that any algorithm for agnostically learning halfs...