Abstract
Kobayashi et al. recently proposed a method for verification of higher-order tree transducers called HMTTs. An HMTT can be considered as a higher-order, functional tree-processing program. The goal of the HMTT verification is to check whether a given HMTT satisfies a given input/output specifications. Kobayashi et al.'s algorithm abstracts tree data using automata that represents input/output specifications and reduces an HMTT verification problem to a higher-order model checking problem. Their method cannot, however, determine whether a given HMTT verification problem actually has a counterexample when a corresponding higher-order model-checking problem has a counterexample. We propose a method of generating a counterexample of an HMTT verification problem from a counterexample of a corresponding higher-order model-checking problem. We also propose a method of refining an abstraction by splitting the states of automata when counterexamples do not exist. We have implemented the method and report the effectiveness of the method.
