Büchi context-free languages

Scattered Context-Free Linear Orderings

“…These can be assumed for the results of the paper, since there is an easy polynomial time transformation of a context-free grammar to a grammar over the alphabet {0, 1} that generates an isomorphic language (with respect to the lexicographic order) not containing ǫ, and each grammar not generating the empty word can be transformed in polynomial time into an equivalent grammar that contains no useless nonterminals or ǫ-rules or any left-recursive nonterminal. See [1,8].…”

On Context-Free Languages of Scattered Words

“…Context-free grammars generating arbitrary countable words were defined in [26,27]. Actually, two types of grammars were defined, context-free grammars with Büchi acceptance condition (BCFG), and context-free grammars with Muller acceptance condition (MCFG).…”

“…These grammars generate the Büchi and the Muller context-free languages of countable words, abbreviated as BCFLs and MCFLs. It is clear from the definitions in [26,27] that every BCFL is an MCFL. On the other hand, there exist MCFLs of even well-ordered words that are not BCFLs, for example the set of all countable well-ordered words over some alphabet.…”

“…This is due to the fact that the order type of every word in a BCFL of well-ordered words is bounded by the ordinal ω n , for some integer n depending on the language, cf. [26]. More generally, it was shown in [26] that for every BCFL L of scattered words there is an integer n such that the Hausdorff rank of every word in L is bounded by n. On the other hand, regarding MCFLs L of scattered words, two cases arise, cf.…”

“…[26]. More generally, it was shown in [26] that for every BCFL L of scattered words there is an integer n such that the Hausdorff rank of every word in L is bounded by n. On the other hand, regarding MCFLs L of scattered words, two cases arise, cf. [27].…”