3 research outputs found
Translation from Classical Two-Way Automata to Pebble Two-Way Automata
We study the relation between the standard two-way automata and more powerful
devices, namely, two-way finite automata with an additional "pebble" movable
along the input tape. Similarly as in the case of the classical two-way
machines, it is not known whether there exists a polynomial trade-off, in the
number of states, between the nondeterministic and deterministic pebble two-way
automata. However, we show that these two machine models are not independent:
if there exists a polynomial trade-off for the classical two-way automata, then
there must also exist a polynomial trade-off for the pebble two-way automata.
Thus, we have an upward collapse (or a downward separation) from the classical
two-way automata to more powerful pebble automata, still staying within the
class of regular languages. The same upward collapse holds for complementation
of nondeterministic two-way machines.
These results are obtained by showing that each pebble machine can be, by
using suitable inputs, simulated by a classical two-way automaton with a linear
number of states (and vice versa), despite the existing exponential blow-up
between the classical and pebble two-way machines
Translation from classical two-way automata to pebble two-way automata
We study the relation between the standard two-way automata and
more powerful devices, namely, two-way finite automata equipped
with some additional “pebbles” that are movable along
the input tape, but their use is restricted (nested) in
a stack-like fashion. Similarly as in the case of the classical
two-way machines, it is not known whether there exists
a polynomial trade-off, in the number of states, between the
nondeterministic and deterministic two-way automata with
nested pebbles. However, we show that these two machine models
are not independent: if there exists a polynomial trade-off for
the classical two-way automata, then, for each ≥ 0,
there must also exist a polynomial trade-off for the two-way
automata with nested pebbles. Thus, we have an upward
collapse (or a downward separation) from the classical two-way
automata to more powerful pebble automata, still staying within
the class of regular languages. The same upward collapse holds
for complementation of nondeterministic two-way machines. These results are obtained by
showing that each pebble machine
can be, by using suitable inputs, simulated by a classical
two-way automaton (and vice versa), with only a linear number of
states, despite the existing exponential blow-up between the
classical and pebble two-way machines