Context-free grammars with cancellation properties

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Abstract

Given a context-free grammar G the Hotz monoid (group) of G is the quotient of the free monoid (group) on the alphabet by the relations defined by the productions. We study the language consisting of all words equal to the axiom in the Hotz monoid. We calculate the syntactic monoid of this language from the Hotz monoid by a general algebraic construction. This construction is simpler if the grammar is both right and left very-simple. In this case the Hotz monoid is embeddable in the Hotz group, which is free, and the syntactic monoid is a Rees quotient of the Hotz monoid. If in addition the grammar is not derivation-bounded, then the language generated is a generator of the family of context-free languages.

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