DYNAMIC PROGRAMMING: FAST BUT OPTIMAL SEARCH

• The search space for vocabularies of hundreds of words can become unmanageable if we allow any word to follow any other word (often called the no-grammar case).
  
  
• Our rudimentary knowledge of language tells us that, in reality, only a small subset of the vocabulary can follow a given word hypothesis, but that this subset is sensitive to the given word (we often refer to this as "context-sensitive").
  
  
• In real applications, user-interface design is crucial (much like the problem of designing GUI's), and normally results in a specification of a language or collection of sentence patterns that are permissible.
  
  
• A simple way to express and manipulate this information in a dynamic programming framework is a via a state machine:
• For example, when you enter state C, you output one of the following words: {daddy, mommy}.
  
  
  If:
    state A: give
    state B: me
    state C: {daddy, mommy}
    state D: come
    state E: here
  
  
  With such a state machine, we can generate phrases such as:
  
  
  Daddy give me
  transitions: Start -> C -> A -> B -> Stop
  
  
• We can also use this technology to compare feature streams from two signals:
  
  
• The latter example is similar to an early approach to speech recognition denoted dynamic time-warping. Why might this be useful for speech recognition?