Finite State Machines and Automata

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Finite State Machines and Automata

• Marco Loog

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Finite State Machine / Automaton

• Model of behavior composed of states,
  transitions, and actions some output
• Configuration of AI building blocks for agent
  control

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Overview

• Finite state machines and automata
• Mealy and Moore machines
• Pros and cons
• Other forms
• Fuzzy
• Nondeterministic
• Probabilistic
• Hierarchical

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Before Proceeding...

• ...what the e does the author mean by things
  like ? and ??

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Formal Definition

• A finite state machine / automaton is a device,
  or a model of a device, which has a finite number
  of states it can be in at any given time It can
  operate on input to either make transitions from
  one state to another and / or to cause an output
  or action to take placeIt can only be in one
  state at any moment in time

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Finite State Automata
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Finite State Automata

• Computational models often used as recognizers or
  acceptors
• Consists of set of states connected by
  transitions
• Transitions are triggered by matching inputs

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More Formally...

• An FSA is a quadruple S,Q,d,F
• S alphabet
• consists of possible inputs
• Q set of states
• special states initial and accepting states
• d transition function defined over alphabet
• determines next state based on current input
• F accepting states
• After all input, if such state is active, input
  pattern is recognized as corresponding class

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Transition Function

• Start Character End------------------------------
  -------1 a 41 b 32 b 1etc.

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Transition Function

• In principle all possible transitions should be
  defined
• Easier to assume that nothing happens if
  transition not specified

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FSM vs. FSA

• FSA do not generate output until terminal state
  reached recognition or acceptation takes place
• FSM provides output after each input symbol has
  been processed
• Can be used for modeling states of NPC

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Mealy Machines

• FSM
• Outputs symbols based on each transition
• Superset of FSA
• To define them, we need a quintuple S,Q,Z,d,l
  instead of a quadruple S,Q,d,F
• S, Q, and d are the same as in FSA
• Z is an output alphabet replacing F
• l function similar to state transition function
  d, which maps (state,input) pairs to outputs

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A Mealy Machine
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Moore Machines

• Alternative to Mealy machines
• Instead of output at every transition, states
  determine output
• I.e., output provided by function l is only based
  on state and not (state,input)
• As a consequence output remains the same if
  state does not change

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A Moore Machine
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The Finite States of the Ghosts

• For example (hunting,power pill) ? hunted
• Taken from Designing an Online Computer Game
  ITU, CGII, fall 2002

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Some Pros

• Easy to implement, visualize, debug, etc.
• Theory is well understood which may help... even
  in practice!
• Seem to work well in games one of the most often
  used techniques

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Some Cons

• Can become complex for large machines
• Limited to certain problems
• Output is, in a sense, predictable and therefore
  not necessarily suited to create good behavior
• Scripting vs. emergence

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One More Con?

• Quake-style bots consider states run / wander /
  attack
• So before attacking, stop running?

• wander

• run

• attack

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Nondeterministic State Machines

• ... and / or automata
• ... and some variations
• Sometimes useful to use a state machine that may
  have more than one possible transition for each
  combination of current state and input

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Nondeterministic State Machines

• Sometimes useful to use a state machine that may
  have more than one possible transition for each
  combination of current state and input
• In NSMs, more than one possible state response
  and output sequence possible
• Can simplify modeling of NPCs make output less
  predictable / smoother transitions

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Fuzzy State Machines

• Extension of FSM based on fuzzy logic
• A Degree of membership for every state is defined
• NPC can run while being in attack state
• Potential problem with conflicting states
• May be used for smoother state transitions

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Fuzzy FSA

• Again based on a quadruple S,Q,d,F
• ...and now everything may be fuzzy
• E.g., one can be in several states at the same
  time
• Typically, one uses the possibilities of fuzzy
  states only indirectly alphabets
• d has to be adapted accordingly

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Fuzzy FSM

• Again based on a quintuple S,Q,Z,d,l
• Not surprisingly, similar remarks hold as for the
  fuzzy FSA...

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A Fuzzy FSM

• N.B. Graph visualizes only current state

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A Pro and a Con

• Fuzzy versions of FSA and FSM give more
  flexibility
• Risk of combinatorial explosion

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Nondeterministic State Machines Again?

• Both FSM and fuzzy FSM are fully deterministic?
• ... in the sense that knowing the state and the
  input, it can be determined what the next state
  should be
• For nondeterministic machines more than one next
  state may be defined for each situation

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Nondeterministic FSA and FSM

• Now d is defined to a be transition relation
  instead of mapping to a single state, i.e., d can
  map to a set of possible next states
• Basically, such nondeterministic versions of FSA
  and FSM are difficult to work with and it is
  rather unclear how to really benefit from them in
  games...
• As an additional remark deterministic and
  these nondeterministic models are equivalent in a
  certain sense

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Probabilistic State Machines

• So far, all models have in fact been
  deterministic!
• Sticking to this claim, probabilistic can also be
  considered deterministic... if fuzzy machines are
• Although there is something more to it...
• Well delve into the more rigorous Markov models
  in some later lectures

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Hierarchical State Machines

• HSMs are one solution to some flaws with normal
  FSMs
• Exploiting the fact that tasks can often be
  decomposed in increasingly detailed subtasks,
  applicability can be improved
• Hierarchies of FSMs are created

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Difficulties with FSM

• During any attacking or wandering behavior, run
  away if the enemy boss appears
• When a flash grenade is thrown, enter dodge mode
• The attack behavior consists of the task of
  finding, following and shooting at the enemy
• The camping behavior is independent from weapon
  management

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Difficulties with FSM

• During any attacking or wandering behavior, run
  away if the enemy boss appears
• Need or at least possibility to group together
  cluster states for attacking and wandering
• Resulting state is referred to as a superstate

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Difficulties with FSM

• When a flash grenade is thrown, enter dodge mode
• Possible need to express transition from any
  state
• Current behavior is overridden so-called general
  transitions

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Difficulties with FSM

• The attack behavior consists of the task of
  finding, following and shooting at the enemy
• Some behaviors in FSM can be defined as a
  combination of simpler states
• Implies hierarchy, maybe, in the most natural way

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Difficulties with FSM

• The camping behavior is independent from weapon
  management
• Independence of machine parts there may be no
  need to model all of this in one and the same FSM
• This last difficulty is not dealt with using
  HSMs

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Hierarchy

• Set of objects nested on multiple levels
• Can be represented as a tree

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Hierarchical State Machines

• Hierarchy can be seen as nested states or entire
  machines

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Nested States

• HSM allows states to be defined within states
  latter are superstates
• Approach allows abstraction of FSM
• E.g. transition between two hierarchy levels are
  interpreted as being connected to all nested
  states
• Cut-down on number of transitions

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Hierarchy of State Machines

• Instead of simplifications using superstates,
  hierarchy can be considered a functional
  decomposition
• Each nested state provides exclusive
  functionality
• In this, abstraction, refinement, and modularity
  play a role

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Abstraction

• During design / implementation, ignore finer
  details zoom out

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Refinement

• Gradually increase complexity of model by
  designing more and more detailed states zooming
  in
• If needed, refine large simple tasks i.e.,
  those modeled by one FSM

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Modularity

• Each FSM can be treated as a modular object and
  can be reused in any part of the hierarchy

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Advantages

• Modularity reduces the complexity of the design
• Can be done with graphical tools possibly a con
  as well
• Greatly advantageous for gradual refinement of
  behaviors

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Disadvantage

• Debugging can be difficult in large models but
  HSM still seem best suited for this complexity

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Next Weeks Topic

• Intelligent agents
• The real start of the course?

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