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Chapter 11: Problem 49

Describe how the problem of traveling from one city to another could be framed as a production system. What are the states? What are the productions?

Short Answer

Expert verified
States are the locations (cities) and conditions; productions are the travel actions (e.g., drive, fly) between cities.

Step by step solution

01

Understand the Problem

We need to frame the travel problem from one city to another as a production system. This involves identifying three key elements: states (situations), productions (actions or transformations), and a system control (how actions lead from one state to another).
02

Define the States

In this context, a 'state' represents a specific condition or position in the city network at a given time. States can include the current location (starting point city, intermediate city, or destination city) and other conditional factors like available routes or time.
03

Identify the Productions

'Productions' are the actions or rules that allow transitions from one state to another. In traveling, these are the means or actions like driving, taking a bus, or flying from one city to linked adjacent cities. Each action taken moves you from one state (e.g. 'in city A') to another state (e.g. 'in city B').
04

System Control Mechanism

This describes how the productions are applied in practice to transition from the start state to the goal state. It determines the sequence of actions ensuring efficient travel. For example, it could involve optimizing for the shortest path, cheapest travel, or least time-consuming route.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

State Transition
State transition in a production system is a fundamental concept. It refers to how a system moves from one state to another due to an action or rule being applied. Imagine you're traveling from City A to City B. Each location you are in, or could move to, is a "state." For instance, starting in City A is your initial state, while arriving in City B is your final state.

Between these, you may have several possible intermediate states, like stopping in City C or City D. In the context of traveling, transitioning involves:
  • Determining starting and destination states: The cities you begin and aim to reach.
  • Recognizing all possible intermediate states: Other cities or conditions you might pass through or face.
  • Understanding the rules for transitioning between states: Taking a bus, train, or flight, which changes your current state in the city network.
The idea is to plan your states so each transition efficiently leads you towards your goal state of reaching the destination city.
Control Mechanism
A control mechanism in a production system dictates how actions are taken to achieve efficient state transitions. In traveling between cities, it's not enough to just know the states and possible actions; you need a system to control which actions to take and when. This mechanism can prioritize different criteria based on the traveler's needs, such as:

  • Finding the shortest possible path to the destination: Ensures minimal travel distance.
  • Identifying the fastest route: Focused on reducing travel time significantly.
  • Choosing the least expensive travel option: Prioritizes budget-friendly solutions.
Having a control mechanism means planning and scheduling the sequence of activities in a way that best meets your travel priorities. Just like in a navigation app that suggests the fastest route or Google Maps optimizing for fewer transfers on public transit.
Problem Solving
Problem solving within a production system is the practical application of state transitions and control mechanisms combined. Traveling from one city to another is essentially a problem-solving task. The key here is to effectively define and manipulate your known variables:

  • Knowing your start and end points (state definition).
  • Understanding all potential routes and actions (production rules).
  • Applying methods to control these actions meaningfully (control mechanism).
The ultimate aim is to address the travel problem efficiently, meeting set goals such as minimum travel time, cost, or effort. Problem solving is a way to smartly navigate known and unknown factors during transition to achieve desired outcomes, showcasing the practical elegance of production systems in real-world scenarios.

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Most popular questions from this chapter

a. Suppose a search tree is a binary tree and reaching the goal requires eight productions. What is the largest number of nodes that could be in the tree when the goal state is reached if the tree is constructed with a breadth-first manner? b. Explain how the total number of nodes considered during the search could be reduced by conducting two searches at the same time-one beginning at the initial state while the other searches backward from the goal-until the two meet. (Assume that the search tree recording the states found in the backward search is also a binary tree and that both searches progress at the same rate.)

Analyze the game of checkers as a production system and describe a heuristic that could be used to determine which of two states is closer to the goal. How would the control system in this setting differ from that of a one-person game such as the eight-puzzle?

a. If the notation ( \(i, j)\), where \(i\) and \(j\) are positive integers, is used to mean "If the entry in the \(\mathrm{i}^{\text {th }}\) position in the list is greater than the entry in the \(j^{\text {th }}\) position, interchange the two entries," which of the following two sequences does a better job of sorting a list of length three? \((1,3)(3,2)\) \((1,2)(2,3)(1,2)\) b. Note that by representing sequences of interchanges in this manner, sequences can be broken into sub-sequences that can then be reconnected to form new sequences. Use this approach to describe a genetic algorithm for developing a program that sorts lists of length ten.

In contrast to the statement in the preceding problem, some birds, such as an ostrich or a robin with a broken wing, cannot fly. However, it would not seem reasonable to construct a deductive reasoning system in which all the exceptions to the statement "All birds can fly" are explicitly listed. How then do we as humans decide whether a particular bird can or cannot fly?

If a researcher uses computer models for studying the memorization capabilities of the human mind, do the programs developed for the machine necessarily memorize to the best of the machine's abilities? Explain.
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