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34 Search Cc. Search Methods Ct, Blind State-space Search As discussed in Article 81, a problem in the state-space search Paradigm is defined by a triple (S, 0, G), where S Is a set of one or more initial states, 0 is a set of operators on states, and Gis a sat of goal states. The state space is commonly identified with a directed graph in which each node is a state and each are represents the application of an operator transforming a state to a successor state. A solution is a path from a start state to a goai state. Goal states may be defined either explicitly or as the set of states satisfying a given predicate. The search for a solution is conducted by making just enough of the state-space graph explicit to contain a solution path. If the order in which potential solution paths are considered is arbitrary, using no domain-specifte information to Judge where the solution is likely to lie, the search is called bind search. Although blind search is impracticabie for nontrivial problems, because of the jarge proportion of the state space it may explore, it Provides a useful foundation for the understanding of Aeuristic search techniques, discussed in Section C3. Several blind-search methods are described below; they differ from one another mainly in the order in which nodes are examined. in each case, it Is assumed that a procedure exists for finding ail the successors of a given node--that Is, all the states that can be reached from the current state by a single operator application. Such a procedure is said to expand the given node. The first three algorithms also make two other assumptions: (a) The state-space graph is a tree. The implication is that there is only one Start state (the root) and that the path from the start node to any other node is unique. Modifications to the search methods needed for a general directed graph are noted in Nilsson (1971) and in Article C3a, Basic Concepts in Heuristic Search. (b) Whenever a node is expanded, creating a node for each of its successors, the successor nodes contain pointers back to the parent noda. When a goal node is finally generated, this feature makes it possibla to trace the solution path. Breadth-first Search The breadth-first method expands nodes in order of thelr proximity to the start node, measured by the number of arcs between them. In other words, it considers every possible operator sequence of length 2 before any sequence of length n+1. Thus, although the search may be an extremely long one, it is guaranteed eventually to find the shortest Possibie solution sequence if any solution exists. 
