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.
Moreover, note that| |Sβ ⊎ S ♯| |1 =| |Sβ| |1+P s∈S π(lcm(π(s), π(s 0))− 1)
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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.