1 / 46

Chapter 3 Structures and Strategies For Space State Search

Chapter 3 Structures and Strategies For Space State Search. Contents. Graph Theory Strategies for Space State Search Using the Space State to Represent Reasoning with the Predicate Calculus. The city of Königsberg. Leonhard Euler

dinh
Download Presentation

Chapter 3 Structures and Strategies For Space State Search

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 3 Structures and Strategies For Space State Search Contents • Graph Theory • Strategies for Space State Search • Using the Space State to Represent Reasoning with the Predicate Calculus Artificial Intelligence

  2. The city of Königsberg • Leonhard Euler • Problem: if there is a walk around the city that crosses each bridge exactly once? Artificial Intelligence

  3. Representations • Predicate calculus: connect(X, Y, Z) connect(i1, i2, b1) connect(i2, i1, b1) connect(rb1, i1, b2) connect(i1, rb1, b2) connect(rb1, i1, b3) connect(i1, rb1, b3) connect(rb1, i2, b4) connect(i2, rb1, b4) connect(rb2, i1, b5) connect(i1, rb2, b5) connect(rb2, i1, b6) connect(i1, rb2, b6) connect(rb2, i2, b7) connect(i2, rb2, b7) • Graph theory • Nodes • Linkes • Easy proof: the walk is impossible since all nodes have odd degrees Artificial Intelligence

  4. Graph of the Königsberg bridge system Artificial Intelligence

  5. A labeled directed graph Artificial Intelligence

  6. A rooted tree, exemplifying family relationships Artificial Intelligence

  7. Artificial Intelligence

  8. Finite State Machine (FSM) Artificial Intelligence

  9. Flip Flop FSM (a) The finite state graph for a flip flop and (b) its transition matrix. Artificial Intelligence

  10. Finite State Accepting Machine • Deterministic FSM: transition function for any input value to a state gives a unique next state • Probabilistic FSM: the transition function defines a distribution of output states for each input to a state Artificial Intelligence

  11. String Recognition • The finite state graph • The transition matrix for string recognition example Artificial Intelligence

  12. State Space and Search Artificial Intelligence

  13. State Space of the 8-Puzzle • generated by “move blank” operations •  -- up •  -- left •  -- down •  -- left Artificial Intelligence

  14. The travelling salesperson problem • Find the shortest path for the salesperson to travel, visiting each city and returning to the starting city Artificial Intelligence

  15. Search for the travelling salesperson problem. Each arc is marked with the total weight of all paths from the start node (A) to its endpoint. Artificial Intelligence

  16. An instance of the travelling salesperson problem with the nearest neighbour path in bold. Note this path (A, E, D, B, C, A), at a cost of 550, is not the shortest path. The comparatively high cost of arc (C, A) defeated the heuristic. Artificial Intelligence

  17. Strategies for State Space Search • Data-driven search – forward chaining • Begin with the given facts and a set of legal rules for changing states • Apply rules to facts to produce new facts • Repeat rules application until finding a path that satisfies the goal condition • Goal-driven search – backward chaining • Begin with the goal and a set of facts and legal rules • Search rules that generate this goal • Determine conditions of these rules  subgoals • Repeat until all conditions are facts Artificial Intelligence

  18. Data-driven Search State space in which data-directed search prunes irrelevant data and their consequents and determines one of a number of possible goals. Artificial Intelligence

  19. Goal-driven Search State space in which goal-directed search effectively prunes extraneous search paths. Artificial Intelligence

  20. Search and Backtrack • Search – find a path • Backtrack – when the path is dead, try others • Backtrack to the most recent node on the path having unexamined siblings • Continue toward to a new path • Like a recursion • Implemented in Prolog as an internal mechanism Artificial Intelligence

  21. Backtrack algorithm Artificial Intelligence

  22. Backtracking search of a hypothetical state space space. Artificial Intelligence

  23. A trace of backtrack on the previous graph Artificial Intelligence

  24. Depth-First and Breadth-First Search • Determine the order of nodes (states) to be examined • Depth-first search • When a state is examined, all of its children and their descendants are examined before any of its siblings • Go deeper into the search space where possible • Breadth-first search • When a state is examined, all of its children are examined after any of its siblings • Explore the search space in a level-by-level fashion Artificial Intelligence

  25. Graph for search examples Artificial Intelligence

  26. The breadth-first search algorithm Artificial Intelligence

  27. A trace of breadth-first search Artificial Intelligence

  28. The graph at iteration 6 of breadth-first search. States on open and closed are highlighted Artificial Intelligence

  29. Breadth-first search of the 8-puzzle, showing order in which states were removed from open Artificial Intelligence

  30. The depth-first search algorithm Artificial Intelligence

  31. A trace of depth-first search Artificial Intelligence

  32. The graph at iteration 6 of depth-first search. States on open and closed are highlighted Artificial Intelligence

  33. Depth-first search of 8-puzzle with a depth bound of 5 Artificial Intelligence

  34. Comparison between breadth- and depth-first search • Breadth-first • Always find the shortest path to a goal • High branching factor -- Combinatorial explosion • Depth-first • More efficient • May get lost Artificial Intelligence

  35. State Space Representation of Logical Systems • Representation • Logical expressions as states • Inference rules as links • Correctness • Soundness and completeness of predicate calculus inference rules guarantee the correctness of conclusions • Theorem Proof • State space search Artificial Intelligence

  36. State space graph of the propositional calculus • Letters as nodes • Implications as links • qp • rp • vq • sr • tr • su Artificial Intelligence

  37. And/or graph • Or – separate • And -- connected • And/or graph of expression q  r  p • And/or graph of the expression q  r → p Artificial Intelligence

  38. Artificial Intelligence

  39. And/or graph of a set of propositional calculus expressions. Artificial Intelligence

  40. And/or graph of part of the state space for integrating a function Artificial Intelligence

  41. The facts and rules of this example are given as English sentences followed by their predicate calculus equivalents: Artificial Intelligence

  42. The solution subgraph showing that Fred is at the museum. Artificial Intelligence

  43. Rules for a simple subset of English grammar are: Artificial Intelligence

  44. And/or graph for the grammar. Some of the nodes (np, art, etc) have been written more than once to simplify drawing the graph. Artificial Intelligence

  45. And/or graph searched by the financial advisor. Artificial Intelligence

  46. Parse tree for the sentence “The dog bites the man.” Artificial Intelligence

More Related