Abstract. Existing algorithms for regular inference (aka automata learning) allows to infer a finite state machine by observing the output that the machine produces in response to a selected sequence of input strings. We generalize regular inference techniques to infer a class of state machines with an infinite state space. We consider Mealy machines extended with state variables that can assume values from a potentially unbounded domain. These values can be passed as parameters in input and output symbols, and can be used in tests for equality between state variables and/or message parameters. This is to our knowledge the first extension of regular inference to infinite-state systems. We intend to use these techniques to generate models of communication protocols from observations of their input-output behavior. Such protocols often have parameters that represent node adresses, connection identifiers, etc. that have a large domain, and on which test for equality is the only meaningful...