Analyzing Languages of Actions for the Purpose of Synthesis

Introduction Researchers in a number of different communities have crafted representations of actions tailored to the perspectives and goals of their particular communities. It has become clear that these separate perspectives are inadequate for developing an autonomous intelligent system. This abstract will briefly describe how several of these perspectives can be productively combined. In particular, the following themes will be related: Planning requires representations of domain theories to be tractable. Theories for tasks in large, complex environments must be represented in a form that possesses a useful subgoal decomposition. Control Theory analyzes tasks with small state spaces and synthesizes controls for them. Dynamical Systems theory shows how complex behaviors can arise from the interaction of small, simple components. Computational Linguistics characterizes languages of actions as transformation semigroups acting on a state space. The structure of a language can be specified in terms of local coordinate systems, thus permitting language transformations to be specified as coordinate transformations. The key to combining these ideas is the development of a new decomposition method. Decomposition is the process of transforming a description of a system into a composition of descriptions of smaller systems. The purpose of decomposition is to express global properties as arising from the interaction of local properties. When this can be accomplished, then both analysis and synthesis can be performed far more cheaply, because they can be performed on small subsystems yet their results apply to the whole system. This permits the methods of control theory to be applied to large, complex systems. An especially important and useful case is when a system can be decomposed into the replication of a single small pattern. The field of dynamical systems has shown that replicated patterns occur throughout the physical world, and understanding such patterns is a prerequisite to understanding more complex patterns. By analyzing the local symmetries and invariants of such patterns, we can relate local and global properties. In particular, local controls can be composed to give valid global controls. By computing how these symmetries can be transformed into each other, the system inductively defines the class of tasks in which these properties are guaranteed to hold, i.e., it determines how the controls scale up. The Semigroup Structure of Languages of Actions We consider a task theory M = (Q, A, δ) consisting of a set A of actions defined as partial functions on a state space Q, together with a …