Solutions of equations in languages

Wim H. Hesselink (1)

1 Department of Computing Science

A context-free grammar corresponds to a system of equations in languages. The language generated by the grammar is the smallest solution of the system. We give a necessary and sufficient condition for an arbitrary solution to be the smallest one. We revive an old criterion to decide that a grammar has a unique solution. All this fits in an approach to search for a grammar for an arbitrary language that is given by other means. The approach is illustrated by the derivation of a grammar for a certain set of bit strings. The approach is used to give an elegant derivation of the grammar for a language accepted by a pushdown automaton.

Mots clés: Language; Grammar; Context-free; Pushdown automaton; Unguarded recursion

Wim H. Hesselink. Solutions of equations in languages. Formal Aspects of Computing, 2009, 22 (5), pp.537-545. ⟨10.1007/s00165-009-0123-x⟩. ⟨hal-00522856⟩