On ternary square-free circular words.
On the approximation of min split-coloring and min cocoloring.
On the binary expansion of irrational algebraic numbers
On the complexity of covering nodes by K node-disjoint cycles
On the complexity of infinite sequences. (Sur la complexité des suites infinies.)
On the complexity of the subgraph problem
On the computational complexity of centers locating in a graph
It is shown that the problem of finding a minimum -basis, the -center problem, and the -median problem are -complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal -center problem is also -complete.
On the computational complexity of (O,P)-partition problems
We prove that for any additive hereditary property P > O, it is NP-hard to decide if a given graph G allows a vertex partition V(G) = A∪B such that G[A] ∈ 𝓞 (i.e., A is independent) and G[B] ∈ P.
On the conjectures of Rauzy and Shallit for infinite words
We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy for infinite words on a finite alphabet. More precisely we show that a Rauzy-like conjecture is equivalent to Shallit's. In passing we correct a misprint in Rauzy's conjecture.
On the D0L Repetition Threshold
The repetition threshold is a measure of the extent to which there need to be consecutive (partial) repetitions of finite words within infinite words over alphabets of various sizes. Dejean's Conjecture, which has been recently proven, provides this threshold for all alphabet sizes. Motivated by a question of Krieger, we deal here with the analogous threshold when the infinite word is restricted to be a D0L word. Our main result is that, asymptotically, this threshold does not exceed the unrestricted...
On the decidability of semigroup freeness∗
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids....
On the decidability of semigroup freeness
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids. In 1991, Klarner, Birget and Satterfield proved the undecidability...
On the decidability of semigroup freeness∗
This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids....
On the difficulty of finding walks of length k
On the distributed decision-making complexity of the minimum vertex cover problem
On the distribution of characteristic parameters of words
For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.
On the distribution of characteristic parameters of words
For any finite word w on a finite alphabet, we consider the basic parameters Rw and Kw of w defined as follows: Rw is the minimal natural number for which w has no right special factor of length Rw and Kw is the minimal natural number for which w has no repeated suffix of length Kw. In this paper we study the distributions of these parameters, here called characteristic parameters, among the words of each length on a fixed alphabet.
On the distribution of characteristic parameters of words II
The characteristic parameters and of a word over a finite alphabet are defined as follows: is the minimal natural number such that has no repeated suffix of length and is the minimal natural number such that has no right special factor of length . In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal length of a repetition, among the words of each length on a given alphabet. In this paper...
On the distribution of characteristic parameters of words II
The characteristic parameters Kw and Rw of a word w over a finite alphabet are defined as follows: Kw is the minimal natural number such that w has no repeated suffix of length Kw and Rw is the minimal natural number such that w has no right special factor of length Rw. In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal length of a repetition, among the words of each length on a given alphabet....
On the energy and spectral properties of the he matrix of hexagonal systems
The He matrix, put forward by He and He in 1989, is designed as a means for uniquely representing the structure of a hexagonal system (= benzenoid graph). Observing that the He matrix is just the adjacency matrix of a pertinently weighted inner dual of the respective hexagonal system, we establish a number of its spectral properties. Afterwards, we discuss the number of eigenvalues equal to zero of the He matrix of a hexagonal system. Moreover, we obtain a relation between the number of triangles...