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Testing equivalence is a powerful means for expressing the security properties of cryptographic protocols, but its formal verification is a difficult task because of the quantification over contexts on which it is based. Previous articles have provided insights into using theorem-proving for the verification of testing equivalence of spi calculus specifications. This article addresses the same verification problem, but uses a state exploration approach. The verification technique is based on the definition of an environment-sensitive, labeled transition system representing a spi calculus specification. Trace equivalence defined on such a transition system coincides with testing equivalence. Symbolic techniques are used to keep the set of traces finite. If a difference in the traces of two spi descriptions (typically a specification and the corresponding implementation of a protocol) is found, it can be used to automatically build the spi calculus description of an intruder process that can exploit the difference.