Recognizable sets of series-parallel graphs admit regular grammar representations whose corresponding finite algebras are singly exponential in grammar size, yielding ExpTime-complete decision procedures for intersection and inclusion.
Proof.(1) Leta=⟨t p⟩p∈P ∈A P ∩FandGbe a P-graph such thath(G) =a
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Regular Grammars as Effective Representations of Recognizable Sets of Series-Parallel Graphs
Recognizable sets of series-parallel graphs admit regular grammar representations whose corresponding finite algebras are singly exponential in grammar size, yielding ExpTime-complete decision procedures for intersection and inclusion.