Each context-free grammar can be transformed to a context-free grammar in Greibach normal form, that is, a con text-free grammar where each right-hand side of a prorfuction begins with a terminal symbol and the remainder of the right-hand side consists of nonterminal symbols. In this short paper we show that for a left-regular grammar G we can obtain a right-regular grammar G’ (which is by defi...

In this paper we define the concepts of co-medial algebra and regular algebra and we will show that for a regular co-medial algebra (A, f , g), there exist a commutative semigroup (A,+), such that the operations f , g have the linear representation on (A,+). As a consequence of above result, we have the linear representation of an n−ary medial groupoid with an regular element, which was obtaine...

Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for these three graphs the bound k ≤ (n − 1)/2 holds. This result implies that only one of a complem...

We present provably correct interactive algorithms for learn ing regular grammars from positive examples and membership queries A structurally complete set of strings from a language L G corresponding to a target regular grammar G implicitly speci es a lattice of nite state automata FSA which contains a FSA MG corresponding to G The lattice is compactly represented as a version space and MG is ...

We prove that if G and H are primitive strongly regular graphs with the same parameters and φ is a homomorphism from G to H, then φ is either an isomorphism or a coloring (homomorphism to a complete subgraph). Moreover, any such coloring is optimal for G and its image is a maximum clique of H. Therefore, the only endomorphisms of a primitive strongly regular graph are automorphisms or colorings...

We present provably correct interactive algorithms for learning regular grammars from positive examples and membership queries. A structurally complete set of strings from a language L(G) corresponding to a target regular grammar G implicitly speciies a lattice of nite state automata (FSA) which contains a FSA MG corresponding to G. The lattice is compactly represented as a version-space and MG...

The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex that has a neighbor in each of the other color classes. We prove that every d-regular graph with at least 2d vertices has b-chromatic number d + 1, that the b-chromatic number of an arbitrary d-regular graph with girth g = 5 is at least ⌊ d+...

In this note we introduce a new family of convex polyhedra which we call the family of generalized deltahedra or in short, the family of g-deltahedra. Here a g-deltahedron is a convex polyhedron in Euclidean 3-space whose each face is an edge-to-edge union of some triangles each being congruent to a given regular triangle. Steiner’s famous icosahedral conjecture (1841) says that among all conve...

The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex that has a neighbor in each of the other color classes. We prove that every d-regular graph with at least 2d vertices has b-chromatic number d + 1, that the b-chromatic number of an arbitrary d-regular graph with girth g = 5 is at least ⌊ d+...

The notions of int-soft filters, int-soft G-filters, regular int-soft filters, and MV-int-soft filters in residuated lattices are introduced, and their relations, properties, and characterizations are investigated. Conditions for an int-soft filter to be an int-soft G-filter, a regular int-soft filter, or an MV-int-soft filter are provided. The extension property for an int-soft G-filter is dis...