SPACE-BOUNDED PROBABILISTIC GAME AUTOMATA

New results on the power of space-bounded probabilistic game automata are presented. Space-bounded analogues of Arthur-Merlin games and interactive proof systems, which are denoted by BC and BP respectively, for Bounded random game automata with Complete and Partial information, are considered. The main results are that BC-SPACE(s(n)) sub-set-or-equal-to BP-SPACE(log s(n)) for s(n) = OMEGA(n), union-c DTIME(2cs(n)) = BC-SPACE(s(n)) for s(n) = OMEGA(log n), where s(n) is space constructible. A consequence of these results is that any language recognizable in deterministic exponential time has an interactive proof that uses only logarithmic space. The power of games with simultaneous time and space bounds is also studied, and it is shown that any language in BC-TIME(t(n)) has an interactive proof that uses time polynominal in t(n) but space only logarithmic in t(n).