Random walks on semaphore codes and delay de Bruijn semigroups

Random walks on semaphore codes and delay de Bruijn semigroups

Identifying Codes on Directed De Bruijn Graphs

For a directed graph G, a t-identifying code is a subset S ⊆ V (G) with the property that for each vertex v ∈ V (G) the set of vertices of S reachable from v by a directed path of length at most t is both non-empty and unique. A graph is called t-identifiable if there exists a t-identifying code. This paper shows that the de Bruijn graph ~ B(d, n) is 1and 2-identifiable and examines conditions ...

Title and Subtitle Identifying Codes on Directed De Bruijn Graphs

For a directed graph G, a t-identifying code is a subset S ⊆ V (G) with the property that for each vertex v ∈ V (G) the set of vertices of S reachable from v by a directed path of length at most t is both nonempty and unique. A graph is called t-identifiable if there exists a tidentifying code. This paper shows that the de Bruijn graph ~ B(d, n) is t-identifiable for n ≥ 2t−1, and is not t-iden...

De Bruijn cycles for covering codes

A de Bruijn covering code is a q-ary string S so that every qary string is at most R symbol changes from some n-word appearing consecutively in S. We introduce these codes and prove that they can have length close to the smallest possible covering code. The proof employs tools from field theory, probability, and linear algebra. We also prove a number of “spectral” results on de Bruijn covering ...

De Bruijn Covering Codes for Rooted Hypergraphs

What is the length of the shortest sequence S of reals so that the set of consecutive n-words in S form a covering code for permutations on {1, 2, . . . , n} of radius R ? (The distance between two n-words is the number of transpositions needed to have the same order type.) The above problem can be viewed as a special case of finding a De Bruijn covering code for a rooted hypergraph. Each edge ...