Related papers: Nested Term Graphs (Work In Progress)
We study various representations for cyclic lambda-terms as higher-order or as first-order term graphs. We focus on the relation between 'lambda-higher-order term graphs' (lambda-ho-term-graphs), which are first-order term graphs endowed…
We study various representations for cyclic lambda-terms as higher-order or as first-order term graphs. We focus on the relation between `lambda-higher-order term graphs' (lambda-ho-term-graphs), which are first-order term graphs endowed…
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…
Nested conditions are used, among other things, as a graphical way to express first order formulas ruling the applicability of a graph transformation rule to a given match. In this paper, we propose (for the first time) a notion of…
Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis.…
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…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We…
We investigate the relationship between finite terms in {\lambda}-letrec, the {\lambda}-calculus with letrec, and the infinite {\lambda}-terms they express. We say that a lambda-letrec term expresses a lambda-term if the latter can be…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
The relationship between Term Graph Rewriting and Term Rewriting is well understood: a single term graph reduction may correspond to several term reductions, due to sharing. It is also known that if term graphs are allowed to contain…
In contrast to dyadic interactions, higher-order interactions may contain one another, with subgroups naturally embedded within larger groups. These containment patterns arise empirically in ecology, sociology, computer science and the…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Word-representable graphs are a subset of graphs that may be represented by a word $w$ over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices…
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…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…