Reduction of Register Pushdown Systems with Freshness Property to Pushdown Systems in LTL Model Checking

Register pushdown system (RPDS) is an extension of pushdown system (PDS) that has registers for dealing with data values. An LTL model checking method for RPDS with regular valuations has been proposed in previous work; however, the method requires the register automata (RA) used for defining a regular valuation to be backward-deterministic. This paper proposes another approach to the same problem, in which the model checking problem for RPDS is reduced to that problem for PDS by constructing a PDS bisimulation equivalent to a given RPDS. This construction is simpler than the previous model checking method and does not require RAs deterministic or backward-deterministic, and the bisimulation equivalence clearly guarantees the correctness of the reduction. On the other hand, the proposed method requires every RPDS (and RA) to have the freshness property, in which whenever the RPDS updates a register with a data value not stored in any register or the stack top, the value should be fresh. This paper also shows that the model checking problem with regular valuations defined by general RA is undecidable, and thus the freshness constraint is essential in the proposed method.