Related papers: A PBPO+ Graph Rewriting Tutorial
We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative in a natural sense. Notably,…
Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional…
Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a…
Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of…
We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…
In this article, we define a doubling procedure for the bialgebra of specified Feynman graphs introduced in a previous paper \cite {DMB}. This is the vector space generated by the pairs $(\bar \Gamma, \bar \gamma)$ where $\bar \Gamma$ is a…
The Binary Polynomial Optimization (BPO) problem is defined as the problem of maximizing a given polynomial function over all binary points. The main contribution of this paper is to draw a novel connection between BPO and the field of…
Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…
The basic principle of graph rewriting is the stepwise replacement of subgraphs inside a host graph. A challenge in such replacement steps is the treatment of the patch graph, consisting of those edges of the host graph that touch the…
Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…
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…
We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a…
Group Relative Policy Optimization (GRPO) is widely used for training reasoning models, but updating all sampled completions in each group incurs substantial cost and can reinforce verbose reasoning trajectories. In this paper, we study…
In this paper, we utilize Isabelle/HOL to develop a formal framework for the basic theory of double-pushout graph transformation. Our work includes defining essential concepts like graphs, morphisms, pushouts, and pullbacks, and…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
Two algorithms are presented for "compiling" influence diagrams into a set of simple decision rules. These decision rules define simple-to-execute, complete, consistent, and near-optimal decision procedures. These compilation algorithms can…
A divide-and-conquer based approach for computing the Moore-Penrose pseudo-inverse of the combinatorial Laplacian matrix $(\bb L^+)$ of a simple, undirected graph is proposed. % The nature of the underlying sub-problems is studied in detail…
This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of typed…
Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…