Related papers: Dichotomy Results for Fixed Point Counting in Bool…
The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this…
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
In this note, we discuss some fixed point theorems for contractive self mappings defined on a $G$-metric spaces. More precisely, we give fised point theorems for mappings with a contractive iterate at a point.
Holant problems are a general framework to study the algorithmic complexity of counting problems. Both counting constraint satisfaction problems and graph homomorphisms are special cases. All previous results of Holant problems are over the…
In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed…
A Boolean network (BN) with $n$ components is a discrete dynamical system described by the successive iterations of a function $f:\{0,1\}^n \to \{0,1\}^n$. This model finds applications in biology, where fixed points play a central role.…
In this paper, we study the learnability of the Boolean class of $d$-monotone functions $f:{\cal X}\to\{0,1\}$ from membership and equivalence queries, where $({\cal X},\le)$ is a finite lattice. We show that the class of $d$-monotone…
We determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted Boolean constraint satisfaction problem (or CSP) with any number of additional unary (i.e., arity 1)…
To each Boolean function F from {0,1}^n to itself and each point x in {0,1}^n, we associate the signed directed graph G_F(x) of order n that contains a positive (resp. negative) arc from j to i if the partial derivative of f_i with respect…
Let H stand for the set of homeomorphisms on [0,1]. We prove the following dichotomy for Borel subsets A of [0,1]: either there exists a homeomorphism f in H such that the image f(A) contains no 3-term arithmetic progressions; or, for every…
We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.
We study the complexity of enumerating the answers of Conjunctive Queries (CQs) in the presence of Functional Dependencies (FDs). Our focus is on the ability to list output tuples with a constant delay in between, following a linear-time…
In this note, we deal with the fixed points of an endofunctor $F: \mathcal{C} \longrightarrow \mathcal{C}$. Three classes of fixed points are introduced, and the case when $F$ is an endomorphism of a category with pretopology is…
We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a…
We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of complex-valued symmetric constraint functions F on Boolean variables. This extends and unifies all previous dichotomies for Holant problems on symmetric…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
Given a graph $G$, viewed as a loop-less symmetric digraph, we study the maximum number of fixed points in a conjunctive boolean network with $G$ as interaction graph. We prove that if $G$ has no induced $C_4$, then this quantity equals…
Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…
We study the complexity of approximately solving the weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, there is a classification known for the case in which the domain…
Cover's function counting theorem is a milestone in the theory of artificial neural networks. It provides an answer to the fundamental question of determining how many binary assignments (dichotomies) of $p$ points in $n$ dimensions can be…