On Pebble Automata

Abstract We look at two simple variations of space-bounded Turing machines (TM's): An off-line S(n) -space bounded TM where S(n) is below log n , which can use a pebble on the input tape, and a TM with two (or three) pebbles and no workspace. We show that in the former case, a pebble increases the recognition power of the device. The latter model(s) can accept large families of languages. For example, 2-pebble automata can accept languages accepted by deterministic checking stack automata, and 3-pebble automata can accept languages accepted by ‘stack-resetting’ two-way deterministic pushdown automata. Moreover, the pebble automata are halting (i.e., halt on all inputs).