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A prefix grammar is a context-free grammar whose nonterminals generateprefix-free languages. A prefix grammar $G$ is an ordinal grammar if thelanguage $L(G)$ is well-ordered with respect to the lexicographic ordering. Itis known that from a finite system of parametric fixed point equations one canconstruct an ordinal grammar $G$ such that the lexicographic order of $G$ isisomorphic with the least solution of the system, if this solution iswell-ordered. In this paper we show that given an ordinal grammar, one cancompute (the Cantor normal form of) the order type of the lexicographic orderof its language, yielding that least solutions of fixed point equation systemsdefining algebraic ordinals are effectively computable (and thus, theirisomorphism problem is also decidable).

The ordinal generated by an ordinal grammar is computable