Related papers: A PBPO+ Graph Rewriting Tutorial
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…
Bidirected graphs are a common generalisation of directed graphs where arcs can also be incoming to both their incident nodes, or outgoing from both their incident nodes. Such arcs allow a walk to change direction. Some algorithms can…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…
We tackle the problem of data-structure rewriting including pointer redirections. We propose two basic rewrite steps: (i) Local Redirection and Replacement steps the aim of which is redirecting specific pointers determined by means of a…
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…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
In this paper, author uses set theory to construct a logic model of abstract figure from binary relation. Based on the uniform quantified structure, author gives two logic system for graph traversal and graph coloring respectively, moreover…
In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These…
We present a type system for strategy languages that express program transformations as compositions of rewrite rules. Our row-polymorphic type system assists compiler engineers to write correct strategies by statically rejecting non…
The paper presents a novel modular hybrid parallel robot for pancreatic surgery and its higher-order kinematics derived based on various formalisms. The classical vector, homogeneous transformation matrices and dual quaternion approaches…
Direct Preference Optimization (DPO) has been proposed as an effective and efficient alternative to reinforcement learning from human feedback (RLHF). However, neither RLHF nor DPO take into account the fact that learning certain…
We describe a simple parallel-friendly lightweight graph reordering algorithm for COO graphs (edge lists). Our ``Batched Order By Attachment'' (BOBA) algorithm is linear in the number of edges in terms of reads and linear in the number of…
The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this paper, we propose new reformulation techniques for…
We tackle the problem of simultaneous transformations of networks represented as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or parallel rewrite relations over complex structures such as graphs: (i) those which…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…