Related papers: Separations of sets
An abstract $(v_k,b_r)$-configuration is a pair of finite sets of cardinalities $v$ and $b$ with a relation on the product of the sets such that each element of the first set is related to the same number $k$ of elements from the second set…
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
In this work, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…
The basic distinction between already known algorithmic characterizations of matroids and antimatroids is in the fact that for antimatroids the ordering of elements is of great importance. While antimatroids can also be characterized as set…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…
An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these…
In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and…
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
This paper is concerned with a compositional approach for constructing abstractions of interconnected discrete-time stochastic control systems. The abstraction framework is based on new notions of so-called stochastic simulation functions,…
Learning structured representations of visual scenes is currently a major bottleneck to bridging perception with reasoning. While there has been exciting progress with slot-based models, which learn to segment scenes into sets of objects,…