Abstract
We show the decidability of integer subgraph problems (ISPs) on context-free sets of graphs L(Γ) defined by hyperedge replacement systems (HRSs) Γ. Additionally, we give a very general characterization of ISPs to be decidable on a set L(Γ). An ISP ∏ consists of a property s ∏ and a mapping f ∏ . If J is a subgraph of a graph G, then s ∏ (G, J) is true or false, and f ∏ (G, J) is an integer. We show the decidability of the following problem: Let Π1,...,Π n be n ISPs that fulfill our characterization and let C be a set of conditions (i, o, j) that specify two ISPs Π i and Π j and a compare symbol o ∈ {=, ≠, <, ≤, >, ≥}. Given a context-free set of graphs L defined by a HRS, is there a graph G ∈ L that has n subgraphs J 1,...,J n such that \(s_{\prod _i }\)(G, J) holds true for i = 1,...,n and \(s_{\prod _i }\)(G, J i ) o \(s_{\prod _j }\)(G, J j ) for each condition (i, o, j)?
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Wanke, E. (1991). On the decidability of integer subgraph problems on context-free graph languages. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_86
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DOI: https://doi.org/10.1007/3-540-54458-5_86
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