Related papers: Formalising the Double-Pushout Approach to Graph T…
Recent developments in applied algebraic topology can simplify and extend results in graphic statics - the analysis of equilibrium forces, dual diagrams, and more. The techniques introduced here are inspired by recent developments in…
This paper shows that generalizations of operads equipped with their respective bar/cobar dualities are related by a six operations formalism analogous to that of classical contexts in algebraic geometry. As a consequence of our…
In recent years the effectiveness of interactive theorem provers has increased to an extent that the bottleneck in the interactive process shifted to efficiency: while in principle large and complex theorems are provable (effectiveness), it…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
The `lifting` or `splitting-off` operation on graphs is performed by deleting two edges sv and sw having a common end s and adding a new edge between v and w. Such a lift is considered good if it preserves a certain local edge-connectivity…
We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental…
We are concerned with rigid analytic geometry in the general setting of Henselian fields $K$ with separated analytic structure, whose theory was developed by Cluckers--Lipshitz--Robinson. It unifies earlier work and approaches of numerous…
We report the current state of the graph isomorphism problem from the practical point of view. After describing the general principles of the refinement-individualization paradigm and proving its validity, we explain how it is implemented…
We introduce a termination method for the algebraic graph transformation framework PBPO+, in which we weigh objects by summing a class of weighted morphisms targeting them. The method is well-defined in rm-adhesive quasitoposes (which…
In a recent paper, the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, $n$-formality of a differential graded algebraic structure is equivalent to the existence of a chain-level lift of a…
Isabelle/HOL augments classical higher-order logic with ad-hoc overloading of constant definitions---that is, one constant may have several definitions for non-overlapping types. In this paper, we present a mechanised proof that HOL with…
Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
Building on work of Cai, F\"urer, and Immerman \cite{CFI92}, we show two hardness results for the Graph Isomorphism problem. First, we show that there are pairs of nonisomorphic $n$-vertex graphs $G$ and $H$ such that any sum-of-squares…
We present a generic and executable formalization of signature-based algorithms (such as Faug\`ere's $F_5$) for computing Gr\"obner bases, as well as their mathematical background, in the Isabelle/HOL proof assistant. Said algorithms are…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the…
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…
Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…
Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes.…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…