Generation and verification of plans with loops

This thesis studies planning problems whose solution plans are program-like structures that contain branches and loops. Such problems are a generalization of classical and conditional planning, and usually involve infinitely many cases to be handled by a single plan. This form of planning is useful in a number of applications, but meanwhile challenging to analyze and solve. As a result, it is drawing increasing interest in the AI community. In this thesis, I will give a formal definition of planning with loops in the situation calculus framework, and propose a corresponding plan representation in the form of finite-state automata. It turns out that this definition is more general than a previous formalization that uses restricted programming structures for plans. For the verification of plans with loops, we study a property of planning problems called finite verifiability. Such problems have the property that for any candidate plan, only a finite number of cases need to be checked in order to conclude whether the plan is correct for all the infinitely many cases. I will identify several forms of finitely-verifiable classes of planning problems, including the so-called one-dimensional problems where an unknown and unbounded number of objects need independent processing. I will also show that this property is not universal, in that finite verifiability of less restricted problems would mean a solution to the Halting problem or an unresolved mathematical conjecture. For the generation of plans with loops, I will present a novel nondeterministic algorithm which essentially searches in the space of the AND/OR execution trees of an incremental partial plan on a finite set of example instances of the planning problem. Two different implementations of the algorithm are explored for search efficiency, namely, heuristic search and randomized search with restarts. In both cases, I will show that the resulting planner generates compact plans for a dozen benchmark problems, some of which are not solved by other existing approaches, to the best of our knowledge. Finally, I will present generalizations and applications of the framework proposed in this thesis that enables the analysis and solution of related planning problems recently proposed in the literature, namely, controller synthesis, service composition and planning programs. Notably, the latter two require possiblynon-terminating execution in a dynamic environment to provide services to coming requests. I will show a generic definition and planner whose instantiation accommodates and solves all the three example applications. Interestingly, the instantiations are competitive with, and sometimes even outperform, the original tailored approaches proposed in the literature.

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