Deterministic moles cannot solve liveness

We examine the conjecture that no polynomial can upper bound the increase in the number of states when a one-way nondeterministic finite automaton (1nfa) is converted into an equivalent two-way deterministic finite automaton (2dfa). We study the problem of liveness, which admits 1nfas of polynomial size and is known to defy 2dfas of polynomial size if and only if the conjecture is true. We focus on moles, a restricted class of two-way nondeterministic automata that includes the 1nfas solving liveness. We show that, in contrast, 2dfa moles cannot solve liveness, irrespective of their size.