Complete Search

Intelligence and the Future

  • Intelligence is partly about "thinking ahead"

  • A complicated problem is solved a piece at a time, or an action at a time. Steps interact

  • Looking ahead gets complicated fast

  • AI has spent a long time thinking about this problem, and has found some fairly fancy techniques

  • Ultimately P ≠ NP (probably), so must abstract or approximate

Computers Search Good

  • A computer can construct future states from current states quickly and perfectly

  • Humans are bad at this; "easy" AI might want to leverage this

  • Problems like route-finding, scheduling, planning, puzzle-solving, games, robotics have gone there

  • Pattern-matching, machine learning, etc can be augmented with search

State Spaces

  • A state is a situation. It is static in time

  • A state space is a graph of situations.

  • The neighbors of a state s in a state space are the graph edges — states that can be reached from s by some atomic action

Road Maps and State Spaces

  • In a fancy road map, the states are junctions on the map. The state space is literally the graph of roads and junctions

  • An AI could proceed heuristically toward the goal by always choosing the route that gets closer to it

  • Dead-ends and side-trips are a big problem, though

Search The Map

  • To find a short route, it's probably better to look at least a little ahead: traverse the graph a bit and see where you end up

  • Watch out for backtracking and loops: use a stop list

  • Ultimately, this is BFS / DFS / Dijkstra search

  • Problem is usually boring for modern computers

Combinatorial State Spaces

  • Consider a sliding tile puzzle: what is the state space?

    • State is particular puzzle configuration

    • Neighbors are states reachable by moving one tile: each state has 2-4 neighbors (corner, edge, central)

  • For an n × n puzzle, how many states? n^2! (Only half are reachable because parity.)

  • How big is this graph?

    2 2.40e1
    3 3.63e5
    4 2.09e13
    5 1.55e25
    6 3.72e41
    7 6.08e62
  • Won't be examining them all (or half of them)

Search Strategies

  • Keyed off some questions

    • How big is the space?

    • Need a best solution or just a good one?

    • Willing to use heuristics?

    • Need guarantees on solution (quality, existence)?

Stupid Search

  • Let's build a sliding-tile puzzle solver the dumb way

  • We will walk the state space randomly until we run into the answer


Stop Lists

  • Let avoid revisiting old states

  • We will use a stop list / closed list / tabu list of states we've already visited

    • Actually sets, not lists, but hey

    • There will be a lot: memory is a problem

Last modified: Wednesday, 9 October 2019, 10:58 AM