Derandomization of probabilistic auxiliary pushdown automata classes

We extend Nisan's breakthrough derandomization result that BP_HL sube SC² (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_HLOGCFL) can be simulated by an SC² machine. This derandomization result improves a classical result by Cook (1979) that LOGDCFL sube SC² since LOGDCFL is contained in BP_HLOGCFL. We also present a simple circuit-based proof that BP_HLOGCFL is in NC ²