Problem Solving in Problem Solving in Common LispCommon Lisp

Common Lisp

J.E. Spragg

May 1997

The Problem Space ModelThe Problem Space Model

People seem to handle adequately the notion of physical space.

It seems natural to extend our notions of physical space and use it as a topological metaphor for problems and problem solving.

The problem space model of problems and problem solving makes use of the ideas of location, shape, and distance that are so useful in reasoning about physical space.

Problem SpaceProblem Space

A problem space is a set of states that represent distinct configurations of the objects and relationships of the domain.

And a set of operators which define how to move between states.

Operators typically have parameters.

Defining a Problem SpaceDefining a Problem Space

Defining a problem in a given problem space requires two things: » an initial state» a goal

The initial state is a distinguished state that represents the starting point within the space.

The goal is a specification of the subset of the problem space which could serve as a solution to the problem.

Solving ProblemsSolving Problems

Solving a problem in this model is accomplished by finding a sequence of operators which, when applied to the initial state, allows one to reach a state satisfying the goal criterion.

In the Blocks World example, the solution is a sequence of transformations that represent a legal plan.

SearchSearch

It is easy to see why this is an attractive model of problem solving.

To solve a problem, all we have to do is define the problem space and then unleash a general-purpose search engine on it.

Classic Problem Solving Classic Problem Solving SystemsSystems

The design of a classic problem solver consists of two parts:» an interface for user-supplied problem

spaces, and a» search engine.

InterfaceInterface

The interface requires the ability to manipulate states and operators.

What kinds of manipulations are needed?» Goal detection: Ascertain whether a given state

satisfies the goal criterion.» State identity: Detect when two descriptions of

states refer to the same state.» State display: Produce a human readable

description of a given state.

The importance of goal detection is obvious.

State identity is important because we make no progress by re exploring already examined states.

Displaying states allows us to observe and debug system behaviour.

Expanding a StateExpanding a State

Identify what operators are available. Determine whether a given operator is

applicable to a particular state. Given a state and an operator applicable to it,

ascertain all the ways the operator can be instantiated on that state.

Figure out what new state results from applying an instantiated operator to a state.