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.
TheEXPTIME-hard lower bound follows from theEXPTIME-hardness of the same problems for sets of terms represented by finite tree automata [8, Theorems 1.7.5 and 1.7.7]
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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.