Semigroups with a Context-Free Word Problem
The word problem is of fundamental interest in group theory and has been widely studied. One important connection between group theory and theoretical computer science has been the consideration of the word problem as a formal language; a pivotal result here is the classification by Muller and Schupp of groups with a context-free word problem. Duncan and Gilman have proposed a natural extension of the notion of the word problem as a formal language from groups to semigroups and the question as to which semigroups have a context-free word problem then arises. Whilst the depth of the Muller-Schupp result and its reliance on the geometrical structure of Cayley graphs of groups suggests that a generalization to semigroups could be very hard to obtain we have been able to prove some results about this intriguing class of semigroups.
KeywordsWord Problem Formal Language Cayley Graph Regular Language Simple Semigroup
Unable to display preview. Download preview PDF.
- 1.Anīsīmov, A.V.: Certain algorithmic questions for groups and context-free languages. Kibernetika (Kiev) (2), 4–11 (1972)Google Scholar
- 5.Clifford, A.H., Preston, G.B.: The algebraic theory of semigroups.Vol. I. Mathematical Surveys, vol. 7. American Mathematical Society, Providence (1961)Google Scholar
- 6.Clifford, A.H., Preston, G.B.: The algebraic theory of semigroups. Vol. II. Mathematical Surveys, vol. 7. American Mathematical Society, Providence (1967)Google Scholar
- 10.Harrison, M.A.: Introduction to formal language theory. Addison-Wesley Publishing Co., Reading (1978)Google Scholar