ON THE DECIDABILITY OF INTEGER SUBGRAPH PROBLEMS ON CONTEXT-FREE GRAPH LANGUAGES

We show the decidability of integer subgraph problems (ISPs) on context-free sets of graphs L(GAMMA) defined by hyperedge replacement systems (HRSs) GAMMA. Additionally, we give a very general characterization of ISPs to be decidable on a set L(GAMMA). An ISP PI consists of a property S-PI and a mapping f-PI. If J is a subgraph of a graph G, then s-PI(G, J) is true or false, and f-PI(G, J) is an integer. We show the decidability of the following problem: Let PI-1,...,PI-n be n ISPs that fulfill our characterization and let C be a set of conditions (i, o, j) that specify two ISPs PI-i and PI-j and a compare symbol o is-an-element-of { =, not-equal, <, less-than-or-equal-to, >, greater-than-or-equal-to}. Given a context-free set of graphs L defined by a HRS, is there a graph G is-an-element-of L that has n subgraphs J1,...,J(n) such that s-PI-i(G, J) holds true for i = 1,...,n and s-PI-i(G, J(i)) o s-PI-j(G, J(j)) for each condition (i, o, j)?