Programming by demonstration enables users to easily personalize their applications, automating repetitive tasks simply by executing a few examples. We formalize programming by demonstration as a machine learning problem: given the changes in the application state that result from the user's demonstrated actions, learn the general program that maps from one application state to the next. We present a methodology for learning in this space of complex functions. First we extend version spaces to learn arbitrary functions, not just concepts. Then we intro- duce the version space algebra, a method for composing simpler version spaces to construct more complex spaces. Finally, we apply our version space algebra to the text-editing domain and describe an implemented system called SMARTedit that learns repetitive text-editing procedures by example. We evaluate our approach by measuring the number of examples required for the system to learn a procedure that works on the remainder of examples, and by an informal user study measuring the eort users spend using our system versus performing the task by hand. The results show that SMARTedit is capable of generalizing correctly from as few as one or two examples, and that users generally save a significant amount of eort when

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