Given a convex polygon with n vertices, we study the problem of identifying a triangle with its smallest side as large as possible among all the triangles that can be drawn inside the polygon. We show that at least one of the vertices of such a triangle must coincide with a vertex of the polygon. We also propose an O(n2) time algorithm to compute such a triangle inside the given convex polygon.

Connectivity and diagnosability are important parameters in measuring the reliability and fault-tolerance of an interconnection network G. The g-extra conditional faulty set F is a faulty vertex set such that every component of G−F has at least g+1 vertices. The g-extra connectivity κg(G) of a connected graph G is the minimum cardinality of a g-extra conditional faulty set F of G such that G−F is disconnected

Let a,k∈ℕ. By 1a:=a and ka:=ak−1a, we denote the k th iterate of the exponential function x↦ax evaluated at a, also known as tetration. We demonstrate how an algorithm for evaluating tetration modulo natural numbers N could be used to compute the prime factorization of N and provide heuristic arguments for the efficiency of this reduction. Additionally, we prove that the problem of computing the squarefree

We bring into attention the interplay between model theory of committed graphs (1-regular graphs) and their palindromic characteristic in the domain of formal languages. We prove some model theoretic properties of committed graphs and then give a characterization of them in the formal language domain using palindromes. We show in the first part of the paper that the theory of committed graphs and the

Frequency-hopping sequences (FHSs) with favorite partial Hamming correlation properties are intensively needed in many synchronization and multiple-access systems. Strictly optimal FHS sets are a kind of FHS sets which has optimal Hamming correlation for any correlation window. In this paper, firstly we present simplified representations of the generalized Lempel–Greenberger bound on the partial Hamming

One of the most essential classes of problems related to formal languages is the membership problem (also called word problem), i.e., to decide whether a given input word belongs to the language specified, e.g., by a generative grammar. For context-free languages the problem is solved efficiently by various well-known parsing algorithms. However, there are several important languages that are not context-free

Two-dimensional general row jumping finite automata were recently introduced as an interesting computational model for accepting two-dimensional languages. These automata are nondeterministic. They guess an order in which rows of the input array are read and they jump to the next row only after reading all symbols in the previous row. In each row, they choose, also nondeterministically, an order in