Related papers: Lindenmayer graph languages, first-order theories …
Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
The study of graph queries in database theory has spanned more than three decades, resulting in a multitude of proposals for graph query languages. These languages differ in the mechanisms. We can identify three main families of languages,…
For any graph $G$ on $n$ vertices and for any {\em symmetric} subgraph $J$ of $K_{n,n}$, we construct an infinite sequence of graphs based on the pair $(G,J)$. The First graph in the sequence is $G$, then at each stage replacing every…
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In 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…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
We describe two formalisms for defining graph languages, and prove that they are equivalent: 1. Separator logic. This is first-order logic on graphs which is allowed to use the edge relation, and for every $n \in \{0,1,\ldots \}$ a relation…
We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent…
We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.
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…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
We investigate the descriptional complexity of limited propagating Lindenmayer systems and their deterministic and tabled variants with respect to the number of rules and the number of symbols. We determine the decrease of complexity when…