Derandomization of probabilistic auxiliary pushdown automata classes

We extend Nisan's breakthrough derandomization result that BP
_H
L sube SC
²
(1992) to bounded error probabilistic complexity classes based on auxiliary pushdown automata. In particular, we show that any logarithmic space, polynomial time two-sided bounded-error probabilistic auxiliary pushdown automaton (the corresponding complexity class is denoted by BP
_H
LOGCFL) can be simulated by an SC
²
machine. This derandomization result improves a classical result by Cook (1979) that LOGDCFL sube SC
²
since LOGDCFL is contained in BP
_H
LOGCFL. We also present a simple circuit-based proof that BP
_H
LOGCFL is in NC
²