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Pebble automaton : ウィキペディア英語版 | Pebble automaton In computer science, a pebble automaton is an extension of tree walking automata which allows the automaton to use a finite amount of "pebbles", used for marking tree node. The result is a model stronger than ordinary tree walking automata, but still strictly weaker than branching automata. ==Definitions==
A pebble automaton is a tree walking automaton with an additional finite set of fixed size containing pebbles, identified with . Besides ordinary actions, an automaton can put a pebble at a currently visited node, lift a pebble from the currently visited node and perform a test "is the i-th pebble present at the current node?". There is an important stack restriction on the order in which pebbles can be put or lifted - the i+1-th pebble can be put only if the pebbles from 1st to i-th are already on the tree, and the i+1-th pebble can be lifted only if pebbles from i+2-th to n-th are not on the tree. Without this restriction, the automaton has undecidable emptiness and expressive power beyond regular tree languages. The class of languages recognized by deterministic (resp. nondeterministic) pebble automata with n pebbles is denoted (resp. ). We also define and likewise .
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