On the complexity of existence of homing sequences for nondeterministic finite state machines

Homing Sequence Derivation with Quantified Boolean Satisfiability

“…It suggests that computing homing sequence for NFSM is challenging. In fact, there are exponentially many input sequences of a given length, and for a NFSM the problem of checking whether an input sequence is homing is known to be-long to the PSPACE complexity class [9]. The complexity of checking if a given sequence is homing for nondeterministic machine is "hidden" in the costly operation of an i-successor [9] of a given state subset.…”

“…In fact, there are exponentially many input sequences of a given length, and for a NFSM the problem of checking whether an input sequence is homing is known to be-long to the PSPACE complexity class [9]. The complexity of checking if a given sequence is homing for nondeterministic machine is "hidden" in the costly operation of an i-successor [9] of a given state subset. Moreover, the higher is the nondeterminism degree of the machine, the slower is the check that for each state pair and each common output response at these states, the final state is unique.…”

Adaptive Homing is in P

“…For preset homing experiments for nondeterministic FSMs, Kushik et al [8] show that differently from deterministic FSMs a homing sequence does not necessarily exist for a complete reduced nondeterministic FSM and proposed an algorithm for deriving a preset homing sequence for a given observable nondeterministic FSM when such sequence exists. A tight upper bound on a shortest preset homing sequence is exponential with respect to to the number of FSM states while the problem of checking the existence of a preset homing sequence for nondeterministic FSMs (Homing problem) is PSPACEcomplete [10].…”