We consider context-free languages equipped with the lexico-graphic ordering. We show that when the lexicographic ordering of a context-free language is scattered, then its Hausdorff rank is less than ω ω. As a corollary of this result we obtain that an ordinal is the order type of a well-ordered context-free language iff it is less than ω ω ω .

The prefix distance between two words x and y is defined as the number of symbols in x and y that do not belong to their longest common prefix. The relative prefix distance from a language L1 to a language L2, if finite, is the smallest integer k such that for every word in L1, there is a word in L2 with prefix distance at most k. We study the prefix distance between regular, visibly pushdown, ...

In this paper we consider a strict generalization of context-free processes, the pushdown processes, and show that this class of processes is 1) closed under parallel composition with nite state systems, and can 2) be model checked by means of an elegant adaptation of the higher order model checker introduced in BS92]. This shows the advantages of pushdown processes over context-free processes,...

Data-free quantization (DFQ) recovers the performance of quantized network (Q) without accessing real data, but generates fake sample via a generator (G) by learning from full-precision (P) instead. However, such generation process is totally independence Q, specialized as failing to consider adaptability generated samples, i.e., beneficial or adversarial, over resulting into non-ignorable loss...

Knowledge distillation has been widely used to produce portable and efficient neural networks which can be well applied on edge devices for computer vision tasks. However, almost all top-performing knowledge methods need access the original training data, usually a huge size is often unavailable. To tackle this problem, we propose novel data-free approach in paper, named Dual Discriminator Adve...

Machine-learning potentials are usually trained on the ground-state, Born-Oppenheimer energy surface, which depends exclusively atomic positions and not simulation temperature. This disregards effect of thermally-excited electrons, that is important in metals, essential to description warm dense matter. An accurate physical these effects requires nuclei move a temperature-dependent electronic f...