Abstract
In the present paper, a parallel presentation of the theories of abstract families of languages (AFL) and abstract families of deterministic languages (AFDL) is given. This is done by introducing two families of languages. One of them is the one-way nondeterministic family of languages (1NFL). A 1NFL is a family of languages closed under special marked substitution and inverse nondeterministic a-gsm mapping. The deterministic counterpart of 1NFL is 1DFL. It is shown that 1NFL and 1DFL are equivalent to AFL and AFDL, respectively. These families of languages are then used to characterize, side by side and with alternate proofs, the families of languages accepted by AFA and AFDA. Moreover, it is also shown that 1NFL and 1DFL can be used to characterize the families of languages accepted by a closed class of 1NBA and 1DBA, respectively.
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