Inverse monoids, trees and context-free languages

Stuart W. Margolis, John C. Meakin
1993 Transactions of the American Mathematical Society  
This paper is concerned with a study of inverse monoids presented by a set X subject to relations of the form e¡ = f¡, i € I, where e¡ and f¡ are Dyck words, i.e. idempotents of the free inverse monoid on X . Some general results of Stephen are used to reduce the word problem for such a presentation to the membership problem for a certain subtree of the Cayley graph of the free group on X . In the finitely presented case the word problem is solved by using Rabin's theorem on the second order
more » ... the second order monadic logic of the infinite binary tree. Some connections with the theory of rational subsets of the free group and the theory of context-free languages are explored. S is called E-unitary if and only if as is idempotent-pure (i.e. if aa = ea for some a £ S, e £ E(S), then a £ E(S)). There are many equivalent
doi:10.1090/s0002-9947-1993-1073775-x fatcat:5jhonep63verdc7hnzd4kxsqgm