TY - JOUR
T1 - Inverse monoids, trees, and context-free languages
AU - Margolis, Stuart W.
AU - Meakin, John C.
PY - 1993/1
Y1 - 1993/1
N2 - This paper is concerned with a study of inverse monoids presented by a set X subject to relations of the form ei=fi, iϵI, where ei and fi 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 sucha presentation to the membership problem for a certainsubtree 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 monadic logic of the infinite binary tree. Some connections with the theory of rational subsets of the free group and the theory ofcontext-free languages are explored.
AB - This paper is concerned with a study of inverse monoids presented by a set X subject to relations of the form ei=fi, iϵI, where ei and fi 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 sucha presentation to the membership problem for a certainsubtree 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 monadic logic of the infinite binary tree. Some connections with the theory of rational subsets of the free group and the theory ofcontext-free languages are explored.
UR - http://www.scopus.com/inward/record.url?scp=0000003262&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1993-1073775-X
DO - 10.1090/S0002-9947-1993-1073775-X
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
SN - 0002-9947
VL - 335
SP - 259
EP - 276
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 1
ER -