Related papers: Parallel Hyperedge Replacement Grammars
There are many open questions surrounding the characterisation of groups with context-sensitive word problem. Only in 2018 was it shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is…
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…
We present a novel work-in-progress approach to the parsing of hypergraphs generated by context-free hyperedge replacement grammars. This method is based on a new LR parsing technique for positional grammars, which is also under active…
It is known that context-free grammars can be extended to generating graphs resulting in graph grammars; one of such fundamental approaches is hyperedge replacement grammars. On the other hand there are type-logical grammars which also…
It is known that hyperedge replacement grammars are similar to string context-free grammars in the sense of definitions and properties. Therefore, we expect that there is a generalization of the well-known Greibach normal form from string…
We prove that, for a finitely generated group hyperbolic relative to virtually abelian subgroups, the generalised word problem for a parabolic subgroup is the language of a real-time Turing machine. Then, for a hyperbolic group, we show…
This paper investigates complexity of the uniform membership problem for hyperedge replacement grammars in comparison with other mildly context-sensitive grammar formalisms. It turns out that the complexity of this problem depends on how…
We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free…
We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an…
We prove that the generalised word problem of a finitely generated subgroup of a finitely generated virtually free group is context-free, that a hyperbolic group must be virtually free if it has a torsion-free quasiconvex subgroup of…
Many physical theories, including notably string theory, require non-abelian higher gauge fields defining higher holonomy. Previous approaches to such higher connections on categorified principal bundles require these to be fake flat. This…
We study the full language of quasigeodesics in Cayley graphs, with fixed error constants. We show that, given a non-virtually-cyclic nilpotent group or Baumslag--Solitar group, and any finite generating set, such languages fail to be…
We present a method for generating random hypergraphs in context-free hypergraph languages. It is obtained by adapting Mairson's generation algorithm for context-free string grammars to the setting of hyperedge replacement grammars. Our…
Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…
In this paper we have defined the language theoretical properties of Parallel languages and series parallel languages. Parallel languages and Series parallel languages play vital roles in parallel processing and many applications in…
L systems generalise context-free grammars by incorporating parallel rewriting, and generate languages such as EDT0L and ET0L that are strictly contained in the class of indexed languages. In this paper we show that many of the languages…
We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems.…
Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We…
Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. Recent work at the intersection of formal language theory and graph theory has found that a Hyperedge Replacement Grammar (HRG)…
Natural language definitions possess a recursive, self-explanatory semantic structure that can support representation learning methods able to preserve explicit conceptual relations and constraints in the latent space. This paper presents a…