Related papers: Decomposition Theorems and Model-Checking for the …

A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…

We review work on `decomposition,' a property of two-dimensional theories with 1-form symmetries and, more generally, d-dimensional theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are…

We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite…

One of the main open problems of mathematical physics is to consistently quantize Yang-Mills gauge theory. If such a consistent quantization were to exist, it is reasonable to expect a ``Wightman reconstruction theorem,'' by which a Hilbert…

While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…

We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…

We investigate the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove: [1] a decomposition theorem for the module of derivations into free modules; [2] the existence of a…

We study the decidability and expressiveness issues of $\mu$-calculus on data words and data $\omega$-words. It is shown that the full logic as well as the fragment which uses only the least fixpoints are undecidable, while the fragment…

In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-known Hilbert space case (where it coincides with the…

Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited…

Let $G = (V,E)$ be a connected graph. A probability measure $\mu$ on $V$ is called "balanced" if it has the following property: if $T_\mu(v)$ denotes the "earth mover's" cost of transporting all the mass of $\mu$ from all over the graph to…

The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…

We present a new method, the Subdivision Construction, for proving the finite model property (the fmp) for broad classes of modal logics and modal rule systems. The construction builds on the framework of stable canonical rules, and…

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions…

This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

A key result in the theory of the modal mu-calculus is the disjunctive normal form theorem by Janin & Walukiewicz, stating that every mu-calculus formula is semantically equivalent to a so-called disjunctive formula. These disjunctive…

Let $\mu$ be a Borel measure on $R^d$ which may be non doubling. The only condition that $\mu$ must satisfy is $\mu(B(x,r))\leq C r^n$ for all $x\in R^d$, $r>0$, and for some fixed $0<n\leq d$. In this paper, we develop Littlewood-Paley…

As the second part of the treatise 'A General Theory of Concept Lattice', this paper speaks of the tractability of the general concept lattice for both its lattice structure and logic content. The general concept lattice permits a feasible…

We identify a subproblem of the model-checking problem for the epistemic \mu-calculus which is decidable. Formulas in the instances of this subproblem allow free variables within the scope of epistemic modalities in a restricted form that…