Abstract
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.
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Communicated by E.C.R. Hehner
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hesselink, W.H. Solutions of equations in languages. Form Asp Comp 22, 537–545 (2010). https://doi.org/10.1007/s00165-009-0123-x
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DOI: https://doi.org/10.1007/s00165-009-0123-x