(V,R)-Languages
Shi Hai-zhon · 2014
V is an alphabet.FVis a free semigroup on V.Ris a subset of FV.At first,we proposed a concept—(V,R)-semigroup and proved that graph-semigroup and digraph-semigroup are both(V,R)-smigroups.Second,we proposed a concept—hypergraph semigroup.The theories of hypergraphs and free semigroups are connected by the hypergraph semigroups.On this base,we proposed two concepts--(V,R)-languages and hypergraph language.The theories of hypergraphs and formal languages are connected by the hypergraph languages.Furthermore,we proved that the hypergraph language,undirected graph and digraph language are all(V,R)-languages.Third,we proved that the undirected graph language and the digrapg language are both regular languages,which answers the open problems in references ofundirected graph languagesanddigraph languages.(V,R-)semigroups and(V,R)-languages are new theories and methods of studying free semigroups and formal languages.