We shall discuss the word problem, the conjugacy problem, the generalized word problem and other algorithmic problems for groups generated by finite auotomata. Also we shall discuss the so-called L-type presentations of groups of finite automata. The last subject is related to the question about presentations of finitely generated subgroups in direct products.
Sponsored in part by the FCT approved projects POCTI 32817/99 and POCTI/MAT/37670/2001 in participation with the European Community Fund FEDER and by FCT through Centro de Matemática da Universidade do Porto. Also sponsored in part by FCT, the Faculdade de Ciências da Universidade do Porto, Programa Operacional Ciência, Tecnologia, Inovação do Quadro Comunitário de Apoio III, and by Caixa Geral de Depósitos.