We present a new approach to motion rearrangement that preserves the syntactic structures of an input motion automatically by learning a context-free grammar from the motion data. For grammatical analysis, we reduce an input motion into a string of terminal symbols by segmenting the motion into a series of subsequences, and then associating a group of similar subsequences with the same symbol. ...

Equations of the form X = φ(X) are considered, where the unknown X is a set of natural numbers. The expression φ(X) may contain the operations of set addition, defined as S + T = {m + n | m ∈ S, n ∈ T}, union and intersection, as well as ultimately periodic constants. An equation with a non-periodic solution of exponential growth is constructed. At the same time it is demonstrated that no sets ...

We consider SCFG-basedMT systems that get syntactic category labels from parsing both the source and target sides of parallel training data. The resulting joint nonterminals often lead to needlessly large label sets that are not optimized for an MT scenario. This paper presents a method of iteratively coarsening a label set for a particular language pair and training corpus. We apply this label...

Context-free hypergraph grammars and boundary graph grammars of bounded nonterminal degree have the same power, both for generating sets of graphs and for generating sets of hypergraphs. Arbitrary boundary graph grammars have more graph generating power than context-free hypergraph grammars, but they have the same hypergraph generating power. To obtain these results, several normal forms for bo...