Chapter 7 - Symbolic Search

Abstract

This chapter studies symbolic versions for various search algorithms and takes binary decision diagrams to represent and explore sets of states efficiently. Known search refinements are tailored to this setting. The central challenge in scaling-up search is the state/space explosion problem , which denotes that the size of the state space grows exponentially in the number of state variables (problem components). In recent years, symbolic search techniques, originally developed for verification domains, have shown a large impact on improving AI search. The term symbolic search originates in the research area and has been chosen to contrast explicit-state search . The characteristic function of a state set can be much smaller than the number of states it represents. The main advantage of symbolic search is that it operates on the functional representation of both state and actions. This has a dramatic impact on the design of available search algorithms, as known explicit-state algorithms have to be adapted to the exploration of sets of states. Binary decision diagrams (BDDs) are selected as the appropriate data structure for characteristic functions. BDDs are directed, acyclic, and labeled graphs. Roughly speaking, these graphs are restricted deterministic finite automata, accepting the state vectors (encoded in binary) that are contained in the underlying set.