Regular Inference for State Machines Using Domains with Equality Tests

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 operation. Our extension consists of two phases. In the first phase we apply an existing inference technique for finite-state Mealy machines to generate a model for the case that the values are taken from a small data domain. In the second phase we transform this finite-state Mealy machine into an infinite-state Mealy machine by folding it into a compact symbolic form.