CO1301 Games Concepts Week 16 Finite State Machines

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CO1301 - Games ConceptsWeek 16Finite State
Machines

• Gareth Bellaby

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References

• Rabin, Introduction to Game Development, chapter
  5.3 discusses Finite State Machines in the
  context of AI.

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Topics

• States
• Finite State Machines
• Alan Turing and Turing Machines

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States

• Assignment 2 used the idea of states.
• Having had some practical experience of working
  with states I want to look at some of the theory.
• States are a commonly used approach in computing.
• The diagrams I provided at the end of the
  assignment are state transition diagrams.

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States in the Assignment

• 1 Start of the game. Transition is "Distance to
  NPC".
• 2 Quest. Transition is "Distance to NPC".
• 3 Combat. Transition is " Monster defeated ".
• 4 Ring obtained. Transition is "Distance to NPC".
• 5 Quest Completed.

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States
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Usefulness of States

• States help us express complex behaviour or
  activity.
• Notice the complexity of what has been expressed.
  For example
• Dialogue is triggered when the player gets the
  quest.
• The dialogue is automatically triggered only the
  once.
• The treasure chest can only be opened after the
  player-character has visited the NPC.

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State Machines

• This is called a "state machine".
• A state is a unique set of properties.
• Particular instructions which be executed in
  response to particular input.
• State.
• Input
• Response.
• In combination they form a unique configuation,
  this particular state with this particular input
  will lead to that particular outcome.

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Why are states used?

• States describe the game extremely well.
• You were able to understand this aspect of the
  game mechanics.
• State Machines are flexible but also extremely
  powerful.
• A good way to implement the mechanics of a game
  (and other types of software).

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Why are states used?

• Aesthetically pleasing.
• The player experiences smooth gameplay.
• Unobtrusive. Typically a player will not perceive
  the existence of the state machine. Even if it is
  the case that they do, state machines are
  accepted approach.
• Also used extensively in AI. We'll do look at
  this again next year.
• Can provide strong signals to the player, i.e.
  what has happened, what to do next, etc.

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States

• A program will have many different state
  machines. For example, consider the assignment
  scenario. We have
• The state that the monster is in.
• The state that the treasure chest is in.
• Each of these things can be considered an object
  (or entity) within the program. This approach
  allows us to easily describe (and therefore
  implement) the life cycle of an object.

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States

• For example
• Monster is created.
• In an idle state.
• In a fighting state.
• Monster is destroyed.
• This insight leads on to Unified Modelling
  Language - UML. A design method used for Object
  Oriented Programming.

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States

• States are the basis of programming languages
  such as C. The program is in a particular
  state. An instruction changes the state of the
  program.
• With a language such as C computation is
  therefore described as states and instructions
  which change states.
• I have used the phrase "State Machines".
• Preferred terminology is "Finite State Machines"
  (FSMs)
• A state machine with a finite number of states.

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• Finite State Machines

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States

• Checking the current state of the game
• A FSM is a machine which models states,
  transitions between states and actions.

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FPS Monster

• Simple monster that reacts when the player comes
  into range and is in line-of-sight.

Attacking
No hit points
Attacks
Idle
Start
Dying
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Pac-Man Ghost (simplified)
Power Pill
Hunted
Power Pill
Eaten
Timer
Hunter
Resurrect
Start
Eaten
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Pac-Man Pac-Man (simplified)
Power Pill
Power Pill
Hunter
Timer
Hunted
Collision
Start
Dying
If lives gt 0
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• Alan Turing and Turing Machines

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Alan Turing

• English mathematician.
• 1912- 1954.
• Father of computer science. If any single
  individual can be said to have invented the
  computer I think that person is Turing.
• During Second World War worked at Bletchley Park,
  the location of Britain's codebreaking centre.
  Instrumental in the British efforts to decrypt
  the Engima device.
• "On computable numbers, with an application to
  the Entscheidungsproblem", (1936), Proceedings of
  the London Mathematical Society.
• "Computing Machinery and Intelligence", (1950).
  Computing machinery and intelligence, Mind.

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Alan Turing

• Attempting to clarify the foundations of
  mathematics.
• 1936 Turning defined a class of abstract
  machines now called Turing Machines.
• Wanted to make precise what is meant by a
  calculation (or an effectively computable
  function).

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Turing's Approach

• The approach taken by Turing was to consider
  computation as performed by a human and, by
  dismissing the extraneous and superfluous
  elements, to arrive at a description of the
  fundamental steps of computation.

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Turing Machine (1)

• TM is a universal algorithm device.
• Any calculation defined recursively by algorithm
  can be performed by TM.
• Any set defined by a recursive definition can be
  defined by a TM.

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Turing Machine (2)

• A finite alphabet of input and output symbols.
• A tape divided into a linear sequence of boxes.
  Each box contains one symbol. Tape can move in
  both directions.
• A tape head that can read from, and then write
  to, one box at a time.

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Turing Machine (3)

• A control or processing unit. The unit can assume
  one a finite number of states (finite state
  machine)
• A program rules or instructions which define the
  action of the machine when in a particular state
  reading a particular character. The permitted
  actions are to change state (or stay in the same
  state), write a particular symbol (could be the
  same the original symbol).

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Turing Machine (4)

Tape
Tape Head
Processor
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Turing Machine (5)

• Imagine a TM with the following program
• in state a, reading 1, write B (blank), move
  Right, go to state a
• in state a, reading B, write B, STOP, go to state
  b
• This is a program to erase the tape.

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Turing Machine (6)

Write 'B', move R
Write 'B', move R
Write 'B', STOP
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Universal TM

• A TM computes one particular function.
• Universal TM is one which can simulate any other
  machine.
• It takes as input a description of a particular
  machine in addition to a copy of the input tape.

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Turing's Thesis

• Turing's Thesis The class of effectively
  computable functions can be identified with the
  class of Turing machine computable functions.
• Universal TM comparable to a real computer.
• A binary alphabet is sufficient to construct a
  machine to compute any function.
• TM can perform all of the basic functions of
  computation (or calculation).

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States

• A Turing Machine has unlimited memory. Obviously
  memory is a consideration in the real world. A
  Finite State Machine is a Turing Machine but with
  limited memory.
• http//www.turing.org.uk/turing/scrapbook/tmjava.h
  tml
• http//ironphoenix.org/tril/tm/

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Halting Problem

• Turing's work arose out of his examination of
  Gödel's incompleteness theorem all consistent
  axiomatic formulations of number theory include
  undecidable propositions (can't be either proved
  or disproved).
• Halting problem the determination of whether a
  TM will come to a halt given a particular input
  program. This problem is undecidable.
• There are things computers cannot compute.