Case-by-Case Case-by-Case Problem Problem SolvingSolving

Pei WangTemple UniversityPhiladelphia, USA

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

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

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?”

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

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”

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

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