Preservation of unambiguity and inherent ambiguity in context-free languages

Various elementary operations are studied to find whether they preserve on ambiguity and inherent ambiguity of language (“language” means “context-free language”) The following results are established:<list><item>If <italic>L</italic> is an unambiguous language and <italic>S</italic> is a generalized sequential machine, then (a) <italic>S</italic>(<italic>L</italic>) is an unambiguous language if <italic>S</italic> is one-to-one on <italic>L</italic>, and (b) <italic>S</italic><supscrpt>-1</supscrpt>(<italic>L</italic>) is an unambiguous language. </item><item>Inherent ambiguity is preserved by every generalized sequential machine which is one-to-one on the set of all words. </item><item>The product (either left or right) of a language and a word preserves both unambiguity and inherent ambiguity. </item><item>Neither unambiguity nor inherent ambiguity is preserved by any of the following language preserving operations: (a) one state complete sequential machine; (b) product by a two-element set; (c) <italic>Init</italic>(<italic>L</italic>) = [<italic>u</italic> ≠ dur in <italic>L</italic> for some <italic>v</italic>]; (d) <italic>Subw</italic>(<italic>L</italic>) = [<italic>w</italic> ≠ durr in <italic>L</italic> for some <italic>u</italic>, <italic>v</italic>]. </item></list>