A recurring topic in interstellar exploration and the search for extraterrestrial intelligence (SETI) is the role of artificial intelligence. More precisely, these are programs or devices that are capable of performing cognitive tasks that have been previously associated with humans such as image recognition, reasoning, decision-making etc. Such systems are likely to play an important role in ... [Show full abstract] future deep space missions, notably interstellar exploration, where the spacecraft needs to act autonomously. This article explores the drivers for an interstellar mission with a computation-heavy payload and provides an outline of a spacecraft and mission architecture that supports such a payload. Based on existing technologies and extrapolations of current trends, it is shown that AI spacecraft development and operation will be constrained and driven by three aspects: power requirements for the payload, power generation capabilities, and heat rejection capabilities. A likely mission architecture for such a probe is to get into an orbit close to the star in order to generate maximum power for computational activities, and then to prepare for further exploration activities. Given current levels of increase in computational power, such a payload with a similar computational power as the human brain would have a mass of hundreds to dozens of tons in a 2050 – 2060 timeframe.