Consider language $ \mathtt{EQUALITY} = \{ a^nb^n \mid n \geq 0 \} $.
It is known that $ \mathtt{EQUALITY} $ cannot be recognized by any sublogarithmic-space alternating Turing machine (ATM) (Szepietowski, 1994). (There is an ATM using sublogarithmic space for members but not for all non-members!)
On the other hand, Freivalds (1981) showed that bounded-error constant-space probabilistic Turing machines (PTMs) can recognize $ \mathtt{EQUALITY} $ but only in exponential expected time (Greenberg and Weiss, 1986). Later, it was shown that no bounded-error $ o(\log\log n) $-space PTM can recognize a non-regular language in polynomial expected time (Dwork and Stockmeyer, 1990). My question is
whether poly-time sublogarithmic-space PTMs recognize $ \mathtt{EQUALITY} $ with bounded-error.