Context-free word problem semigroups

fellowship SFRH/BPD/121469/2016. The second author was supported by the ‘Investigador FCT’ fellowship IF/ 01622/2013/CP1161/CT0001. For the first and second authors, this work was partially supported by FCT projects UID/MAT/00297/2019. PTDC/MHC-FIL/2583/2014 and PTDC/MAT-PUR/31174/2017. This work was started during a visit by the third author to the Universidade Nova de Lisboa, which was supported by the exploratory project IF/01622/2013/ CP1161/CT0001 attached to the second author’s research fellowship.This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the notions of word-hyperbolicity and automaticity. Second, a study is made of whether these classes are closed under applying certain semigroup constructions, including direct products and free products, or under regressing from the results of such constructions to the original semigroup(s) or monoid(s).authorsversionpublishe