Sampling a Two-way Finite Automaton

We study position sampling in a two-way nondeterministic finite automaton (2NFA) to measure information flow between state variables, based on the information-theoretic sampling technique proposed in [20]. We prove that for a 2NFA, the language generated by position sampling is regular. We also show that for a 2NFA, we can effectively find a vector of sampling positions that maximizes information flow in a run of the 2NFA. Finally, we give some language properties of sampled runs of 2NFAs augmented with restricted unbounded storage. We conduct preliminary experiments to identify information concentration in a subset of statements in a program.