Fast-forward (FF) was the most successful automatic planner in the Fifth International Conference on Artificial Intelligence Planning and Scheduling (AIPS '00) planning systems competition. Like the well-known hsp system, FF relies on forward search in the state space, guided by a heuristic that estimates goal distances by ignoring delete lists. It differs from HSP in a number of important details. This article describes the algorithmic techniques used in FF in comparison to hsp and evaluates their benefits in terms of run-time and solution-length behavior. Humans have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples are parking a car, driving in city traffic, playing golf, cooking a meal, and summarizing a story. In performing such tasks, humans use perceptions of time, direction, speed, shape, possibility, likelihood, truth, and other attributes of physical and mental objects. Reflecting the bounded ability of the human brain to resolve detail, perceptions are intrinsically imprecise. In more concrete terms, perceptions are f-granular, meaning that (1) the boundaries of perceived classes are unsharp and (2) the values of attributes are granulated, with a granule being a clump of values (points, objects) drawn together by indistinguishability, similarity, proximity, and function. For example, the granules of age might be labeled very young, young, middle aged, old, very old, and so on. F-granularity of perceptions puts them well beyond the reach of traditional methods of analysis based on predicate logic or probability theory. The computational theory of perceptions (CTP), which is outlined in this article, adds to the armamentarium of AI a capability to compute and reason with perception-based information. The point of departure in CTP is the assumption that perceptions are described by propositions drawn from a natural language; for example, it is unlikely that there will be a significant increase in the price of oil in the near future. In CTP, a proposition, p, is viewed as an answer to a question, and the meaning of p is represented as a generalized constraint. To compute with perceptions, their descriptors are translated into what is called the generalized constraint language (GCL). Then, goal-directed constraint propagation is utilized to answer a given query. A concept that plays a key role in CTP is that of precisiated natural language (PNL). The computational theory of perceptions suggests a new direction in AI -- a direction that might enhance the ability of AI to deal with realworld problems in which decision-relevant information is a mixture of measurements and perceptions. What is not widely recognized is that many important problems in AI fall into this category.