CasebyCase Problem Solving

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Case-by-Case Problem Solving

• Pei WangTemple University
• Philadelphia, USA

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Algorithmic Problem Solving

• Use a computer to solve a problem
• Problem is a class, solution is an algorithm
• e.g., sorting to quicksort
• Problem is an instance, solution is a result
• e.g., sort 3, 2, 4, 1 to 1, 2, 3, 4
• The former is done by human, the latter is done
  by computer following the algorithm

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No algorithm for it?

• What if the computer has no algorithm for a
  problem instance?
• Use a general-purpose algorithm
• e.g., state-space search
• Find an algorithm first
• e.g., machine learning

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Solving it without algorithm?!

• How about to directly solve the problem instance
  without following an algorithm?
• Nonsense! How can a computer run without
  algorithms?
• But this process can still be carried out by
  algorithms not defined for this problem. An
  algorithm for problem P is not an algorithm for
  problem Q, right?

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Case-by-case problem solving

• NARS represents a problem (instance) as an
  inference task, to be processed by a set of
  general-purpose inference rules
• Rule selection is knowledge-driven, rather than
  algorithm-guided
• Knowledge selection is context-sensitive
• Inference process is resource-restricted

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Scopes of input-output

• Each operation in NARS is controlled by certain
  algorithm, with fixed input-output mapping (see
  code)
• The lifelong experience of the system fully
  determines its lifelong behaviors (see examples)
• However, there is no function that maps problem
  to solution

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Properties of CPS

• CPS and APS are suitable for different
  (knowledge/resources) situations
• In CPS, the following notions are different
• Problem
• Solution
• Solvable problems
• Resource cost of a problem
• Scaling up