Weak Greibach Normal Form for Hyperedge Replacement Grammars

The hardest language for grammars with context operators

In 1973, Greibach ("The hardest context-free language", SIAM J. Comp., 1973) constructed a context-free language $L_0$ with the property that every context-free language can be reduced to $L_0$ by a homomorphism, thus representing it as an inverse homomorphic image $h^{-1}(L_0)$. In this paper, a similar characterization is established for a family of grammars equipped with operators for referring to the left context of any substring, recently defined by Barash and Okhotin ("An extension of context-free grammars with one-sided context specifications", Inform. Comput., 2014). An essential step …

论融合文法（Fusion Grammars）的可判定性与表达能力

On Decidability and Expressive Power of Fusion Grammars

本文研究融合文法的算法复杂度与表达能力，证明了几类融合文法的非空性、成员资格问题的可判定性及复杂度上界，提出相关证明技术，并证明保连接融合文法生成的语言满足Parikh定理、具有半线性性。

上下文无关图语言中的随机图生成

Random Graph Generation in Context-Free Graph Languages

本文将Mairson的上下文无关字符串文法生成算法适配到超边替换文法，提出一种在无歧义条件下以均匀随机方式、二次方时间生成随机超图的方法，并用生成项图的示例加以验证。

Learning Hyperedge Replacement Grammars for Graph Generation

The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate new realistic graphs. Our key insight is that a graph's clique tree encodes robust and precise information. We show that a Hyperedge Replacement Grammar (HRG) can be extracted from the clique tree, and we develop a fixed-size graph generation algorithm that can be used to produce new graphs of a specified size. In experiments on large real-world graphs, we sho…

超图Lambek文法的表达能力

Expressive Power of Hypergraph Lambek Grammars

本文证明了超图Lambek文法与带推导长度线性限制的双推出超图文法生成相同语言类，完整刻画了其表达能力，并推论其包含上下文超边替换文法。

验证由顶点替换图文法指定的参数化网络

Verifying Parameterized Networks Specified by Vertex-Replacement Graph Grammars

本文提出将顶点替换图文法的参数化可达性问题有效归约为超边替换文法问题，从而把现有HR验证技术扩展到团、多部图等稠密网络架构。

Grammars Based on a Logic of Hypergraph Languages

The hyperedge replacement grammar (HRG) formalism is a natural and well-known generalization of context-free grammars. HRGs inherit a number of properties of context-free grammars, e.g. the pumping lemma. This lemma turns out to be a strong restriction in the hypergraph case: it implies that languages of unbounded connectivity cannot be generated by HRGs. We introduce a formalism that turns out to be more powerful than HRGs while having the same algorithmic complexity (NP-complete). Namely, we introduce hypergraph Lambek grammars; they are based on the hypergraph Lambek calculus, which may be …

Modeling Graphs with Vertex Replacement Grammars

One of the principal goals of graph modeling is to capture the building blocks of network data in order to study various physical and natural phenomena. Recent work at the intersection of formal language theory and graph theory has explored the use of graph grammars for graph modeling. However, existing graph grammar formalisms, like Hyperedge Replacement Grammars, can only operate on small tree-like graphs. The present work relaxes this restriction by revising a different graph grammar formalism called Vertex Replacement Grammars (VRGs). We show that a variant of the VRG called Clustering-bas…

具有上下文无关以下复杂度的非交换线性逻辑片段

Non-commutative linear logic fragments with sub-context-free complexity

本文提出了Lambek演算片段对REG、LCFL和CFL类的新的描述复杂性刻画，首次将Lambek演算片段与证明复杂性REG和LCFL等同，并基于直接转换与结构归纳展示了最弱变体的CFL复杂性，确立了Cut消解定理在比较形式文法与矢列演算中的效用。

树可验证图文法

Tree-Verifiable Graph Grammars

本文提出树可验证图文法与可嵌入有界树宽，证明其语言可由 CMSO 定义、严格推广正则图文法，并对该图类给出完备刻画。

用于高效图识别的有限自动机

Finite Automata for Efficient Graph Recognition

本文在超边替换图文法框架下，将有限自动机从字符串提升到图，通过修改的幂集构造实现确定性化，并给出无需回溯识别图的充分条件。