Of course it can. Reasoning is algorithmic in nature, and algorithms can be encoded as sufficiently large state transition tables. I don't buy into Searle's "it can't reason because of course it can't" nonsense.
We were talking about a "sufficiently large" table, which means that it can be larger than realistic hardware allows for. Any algorithm operating on bounded memory can be ultimately encoded as a finite state automaton with the table defining all valid state transitions.
