## The Mathematical Theory of Context Free Languages |

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acceptor arbitrary language bounded languages bounded set complete the proof context-free grammar context-free languages context-sensitive language defined determine for arbitrary deterministic deterministic language deterministic póla disjoint linear sets distinct symbols Exercise finite number finite set finite union function G is unambiguous grammar G gsm mapping gsm which maps Hence homomorphism induction inherently ambiguous languages initial subword integer L1 and L2 leftmost derivation Lemma Let G linear grammar linearly independent periods minimal n-tuple node name non-e words nonlanguage occurrence pola positive solution preserves regular sets production programming languages PROOF Let prove pushdown tape pushdown transducer recursively solvable recursively unsolvable right-linear semilinear set semilinear subset sequence sequential transducer set of words solvable to determine stratified and linearly suffices to show Suppose Ta(M Theorem tree union of linear union of sets unsolvable to determine variable wºw