Formal Aspects of Computing

, Volume 22, Issue 5, pp 537–545 | Cite as

Solutions of equations in languages

Open Access
Original Article


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.


Language Grammar Context-free Pushdown automaton Unguarded recursion 


Open Access

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Department of Computing ScienceUniversity of GroningenGroningenThe Netherlands

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