Related papers: On streams that are finitely red

We study rational streams (over a field) from a coalgebraic perspective. Exploiting the finality of the set of streams, we present an elementary and uniform proof of the equivalence of four notions of representability of rational streams:…

Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying…

We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…

We propose a novel approach to stream definition and manipulation. Our solution is based on two key ideas. Regular corecursion, which avoids non termination by detecting cyclic calls, is enhanced, by allowing in equations defining streams…

For certain families of fluid flow, a new conserved quantity -- stream-helicity -- has been established.Using examples of linked and knotted streamtubes, it has been shown that stream-helicity does, in certain cases, entertain itself with a…

Coinductive reasoning about infinitary structures such as streams is widely applicable. However, practical frameworks for developing coinductive proofs and finding reasoning principles that help structure such proofs remain a challenge,…

The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method.…

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…

Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. We propose a transformation from such a stream specification to a term rewriting system (TRS) in such a way…

We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation on the representations of two…

We propose a simple calculus for processing data streams (infinite flows of data series), represented by finite sets of equations built on stream operators. Furthermore, functions defining streams are regularly corecursive, that is, cyclic…

Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…

We consider arbitrarily long, but finite utility streams, and some appropriate axioms.

We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we…

Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…

This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an…

We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold…

Strong resilience properties of dynamical flow networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the inflow at a non-destination node gets split among its outgoing links is…

Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…

We study solutions to systems of stream inclusions of the form 'f in T(f)', where the nondeterministic transformer 'T' on omega-infinite streams is assumed to be causal in the sense that elements in output streams are determined by a finite…