  We investigated the computational power of a single mobile agent in an
$n$-node graph with storage (i.e., node memory). Generally, a system with
one-bit agent memory and $O(1)$-bit storage is as powerful as that with
$O(n)$-bit agent memory and $O(1)$-bit storage. Thus, we focus on the
difference between one-bit memory and oblivious (i.e., zero-bit memory) agents.
Although their computational powers are not equivalent, all the known results
exhibiting such a difference rely on the fact that oblivious agents cannot
transfer any information from one side to the other across the bridge edge.
Hence, our main question is as follows: Are the computational powers of one-bit
memory and oblivious agents equivalent in 2-edge-connected graphs or not? The
main contribution of this study is to answer this question under the relaxed
assumption that each node has $O(\log\Delta)$-bit storage (where $\Delta$ is
the maximum degree of the graph). We present an algorithm for simulating any
algorithm for a single one-bit memory agent using an oblivious agent with
$O(n^2)$-time overhead per round. Our results imply that the topological
structure of graphs differentiating the computational powers of oblivious and
non-oblivious agents is completely characterized by the existence of bridge
edges.
