Search results
Results from the WOW.Com Content Network
An example of a non-transitive relation with a less meaningful transitive closure is "x is the day of the week after y". The transitive closure of this relation is "some day x comes after a day y on the calendar", which is trivially true for all days of the week x and y (and thus equivalent to the Cartesian square , which is " x and y are both ...
In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Every partial order and every equivalence relation is transitive. For example, less than and equality among real numbers are both transitive: If a < b and b < c then a < c; and if x ...
The relation is defined as the transitive closure of . That is, u ≍ v {\displaystyle u\asymp v} when there is a sequence u ≈ ⋯ ≈ v {\displaystyle u\approx \cdots \approx v} of vertices, starting with u {\displaystyle u} and ending with v {\displaystyle v} , such that each consecutive pair in the sequence is related by ≈ {\displaystyle ...
The Floyd–Warshall algorithm is an example of dynamic programming, and was published in its currently recognized form by Robert Floyd in 1962. [3] However, it is essentially the same as algorithms previously published by Bernard Roy in 1959 [4] and also by Stephen Warshall in 1962 [5] for finding the transitive closure of a graph, [6] and is closely related to Kleene's algorithm (published ...
The semantics for the common knowledge operator, then, is given by taking, for each group of agents G, the reflexive (modal axiom T) and transitive closure (modal axiom 4) of the , for all agents i in G, call such a relation , and stipulating that is true at state s iff is true at all states t such that (,).
The transitive closure of a DAG is the graph with the most edges that has the same reachability relation as the DAG. It has an edge u → v for every pair of vertices ( u , v ) in the reachability relation ≤ of the DAG, and may therefore be thought of as a direct translation of the reachability relation ≤ into graph-theoretic terms.
Various inequivalent definitions of Kleene algebras and related structures have been given in the literature. [5] Here we will give the definition that seems to be the most common nowadays. A Kleene algebra is a set A together with two binary operations + : A × A → A and · : A × A → A and one function * : A → A , written as a + b , ab ...
In matroid theory, the closure of X is the largest superset of X that has the same rank as X. The transitive closure of a set. [1] The algebraic closure of a field. [2] The integral closure of an integral domain in a field that contains it. The radical of an ideal in a commutative ring.