CHAPTER 9' SYNTACTIC PATTERN CLASSIFIER

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CHAPTER 9. SYNTACTIC PATTERN CLASSIFIER

• Specification of a set of pattern primitives, a
  set of rules that governs their interconnection
  and a recognizer (automaton) whose structure is
  determined by the set of rules in the grammar.
• a finite set of variables called
  nonterminals
• a finite set of constants called
  terminals
• a set of rewriting rules called
  productions
• the starting symbol.

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• Example
• Automata as string recognizers
• a finite, nonempty set
  of states.
• a mapping from
  into the collection of all
• subsets of Q.
• the starting state.
• a set of final states.

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• Example Automaton
• and mapping given by
• The Automaton recognizes
• the string
• but rejects

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• Syntactic recognition of trees
• Tree grammar
• P is a set of productions of ,
  r is a ranking function that denotes the number
  of direct descendants of a node whose label is a
  terminal.
• Example
• Productions
• Ranking functions

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• Tree Automata
• A conventional finite automaton scans an
  input string symbol by symbol from left to right.
  
• A tree automaton begins simultaneously at
  each node on the frontier (the leaves taken in
  order from left to right) of an input tree and
  proceed along parallel paths toward the root.
• where Q a finite set of states, F a
  subset of Q, is a set of final states, a
  relation in such that m is a rank of
  k.
• Example with
  productions

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• The corresponding tree automaton
• Letting
• The tree automaton goes about recognizing a tree
  generated by the grammar

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• Example Photographs from bubble chamber events.

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