  Here we propose a variant of the nondeterministic finite automaton with
translucent letters (NFAwtl) which, after reading and deleting a letter, does
not return to the left end of its tape, but rather continues from the position
of the letter just deleted. When the end-of-tape marker is reached, our
automaton can decide whether to accept, to reject, or to continue, which means
that it again reads the remaining tape contents from the beginning. This type
of automaton, called a non-returning finite automaton with translucent letters
or an nrNFAwtl, is strictly more expressive than the NFAwtl. We study the
expressive capacity of this type of automaton and that of its deterministic
variant. Also we are interested in closure properties of the resulting classes
of languages and in decision problems.
