Chapter 4 Continued

Constraint satisfaction problems

• States are defined by the values of a set of variables; the goal test specifies constraints on the variables --- the objective is to find variable values that satisfy all constraints

• the order in which variables are assigned values does not matter --- the solution path does not matter
  Examples: cryptarithmetic, 8-queens problem,
  
  layout problems in general

Constraint propagation

• The best approach is to avoid making guesses on particular assignments until necessary. Constraints are propagated as far as possible to reduce the number of allowable guesses --- curtail the search.

• Constraint propagation arises from dependencies among constraints. E.g., in cryptarithmetic, 1 constraint may specify that N = E +1 and another that E = 2, by propagating these 2 constraints we get the additional restriction that N = 3

Constraint propagation continued

• constraint propagation terminates when: (1) a contradiction is dectected, or (2) no further changes can be made on the basis of current knowledge then search (guessing) begins

• Useful heuristics can help select the best guess to try first; these heuristics will be domain specific

Example problem: 8 queens

• Definition: place 8 queens on a chess board in such a way that none threatens any of the others (a queen threatens the squares in the same row, same column, and the same diagonal)

• Guess a solution: there are 4,426,165,368 possible guesses (the state space for the problem).

8 queens - constraint propagation

• 1st constraint: never put 2 queens in the same row; 16,777,216 possible guesses

• 2nd constraint: never put 2 queens in the same column; 40,320 possible guesses

• Now search for the configuration that satisfies the diagonal constraint; the leaves of the search tree are either solutions or dead ends

• Search is aided by good heuristics, e.g, the min-conflicts heuristic (book gives others)

Search as applied to constraint satisfaction problems

• The path to the solution does not matter. Could use best-first search guided by heuristic function to do the search (Why not A*?).

• Unfortunately the branching factor is large for most CSP’s and often CSP’s require searching to considerable depth --- space complexity becomes a problem!

Hill-Climbing Search

• Hill-climbing can be viewed as a varient of best-first search --- memory limited best-first search

• hill-climbing does not keep track of any previously encountered nodes except the best so far:
  current <= Make-Node(initial-state)
  
  loop
  node <= highest valued successor of current
  
  if value(node) < value(current) return current
  current <= node
  end loop

Why call it hill-climbing?

Simulated annealing

• Named after a metal-casting function technique: molten metal is gradually cooled; gradual temperature decrease results in even distribution of molecules

• Basic idea: instead of picking the best move, pick a random move; if it improves the current situation do it, otherwise take the move with some probability less than 1.0; probability decreases exponentially with badness of move.

Simulated annealing continued

• Define a temperature function that decreases with time. At each move, compute the current temp., t, and use t to determine the probability of taking a bad move. When t=0 you are doing hill-climbing.

Another constraint satisfaction problem: natural language processing (NLP)

• NLP can be viewed as a constraint satisfaction problem

• Four basic types of constraints: syntactic, semantic, discourse, and pragmatic

• Unfortunately even when all constraints are considered it is still not possible to avoid guessing and searching

Examples of natural language processing tasks

• Examples of natural language processing tasks
  communication with artificial agents in human language --- perhaps a distant goal
  
  text summarization
  machine translation

• What makes NLP so hard:
  The meaning of an utterance depends on both the language used in the utterance and the context in which it was spoken
  
  
  Language suffers from ambiguity

• As a result, NLP problems have:
  • require lots of world knowledge --- very large scale
  • huge state spaces and big branching factors

NLP continued

• What are the constraints in NLP?
  syntatic: derived from the grammar of the language; e.g., word order, number agreement
  semantic: derived from knowledge about entities that can exist in the world; e.g., the properties that objects that have --- semantic features and selectional restrictions
  discourse: derived from the structure of coherent discourse; e.g., new entities in a sentence must be introduced
  pragmatic: derived from context in general; e.g., the meaning of a sentence must be consistent with the social usage and speakers goals: Can you pass the salt?

A specific example

• Paper: “Lexical Disambiguation using Simulated Annealing,” Proc. DARPA Workshop on Speech and Natural Language, 1992.

• The NLP task: determine the correct meanings of the words in a sentence

• Constraints considered: semantic constraints as defined by the dictionary definitions of the words being considered

• search technique: simulated annealing

Summary of search techniques

• problem definition in terms of: states, goals and actions

• uniformed vs. informed search: information helps

• can compare strategies on the basis of: completeness, optimality, and time and space complexity

Some problems with state space search

• Every operator is equally important (maybe not for weighted links)

• Must construct unbroken sequences --- assumes the world is static

• Heuristic functions choose among states not actions

• Can’t modify actions or heuristics

• To overcome these we need more complete information --- Knowledge Representation