An alternative to finite state machines

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An alternative to finite state machines
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Drawbacks of FSMs

• FSMs offer a lot of advantages, but
• natural graphical notation doesnt scale well (
  textual version isnt fun)
• very moded (OK for most small ITs, not good for
  larger things)
• Hard to deal with independent state information
  (cross product problem)

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Cross product example

• Suppose we wanted a handle that moved up and down

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Whats the right FSM controller?

• Assume simple (snap) feedback
• Ignore actions for now

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Whats the right FSM controller?

• Assume simple (snap) feedback
• Ignore actions for now

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Now suppose we wanted a clutched handle

• Clutch is a toggle button
• Handle only moves when clutch is in
• What would clutch machine look like?

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FSM controller for clutch
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FSM controller for clutch
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Putting these together

• Need a cross-product machine
• Merge first and last state of the handle machine,
  with the enabled state of the clutch machine
• (Analysis to figure out how to do this in general
  is tricky)

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The cross product machine
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The cross product machine
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The cross product machine

• A mess
• state explosion (this is a simple one)

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State explosion

• It gets worse
• Suppose we have N things that have to all happen
  once, but we dont care what order
• good UI gt dont impose unnecessary sequencing
• Best we can do is 2N states!

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What do we do about this?

• Could look at sets of independent FSMs running in
  parallel
• But interactions arent completely independent
• E.g. Doesnt hands all-of-N problem

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Propositional Production Systems

• AKA PPS
• Computationally equiv to FSM
• but looks very different
• states encoded implicitly
• does cross-product implicitly at RT
• exponential of states transitions in linear
  sized spec
• can do all-of-N in size O(N) spec

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PPS

• Primary concept field
• gets used in several ways
• basically a category
• Each field has a set of conditions that it may be
  in
• values the field may have

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PPS Fields

• color black, white, red
• size small, medium, large
• Conditions from a field make up a fixed finite
  set
• an enumeration
• doesnt allow e.g., integers (simple extension to
  do this)
• fields have an initial condition value

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Kinds of PPS fields

• Several kinds of PPS fields
• State Info fields
• normal fields
• Each independent part of system encoded in one
  field
• current state of system is indicated by the
  values across all the fields
• (this is how we solve the cross-product problem)

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State info field examples

• clutch eng, part_eng, part_diseng, diseng

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State info field examples

• clutch eng, part_eng, part_diseng, diseng

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State info field examples

• clutch eng, part_eng, part_diseng, diseng
• lever up, part_up, part_dn, dn

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State info field examples

• clutch eng, part_eng, part_diseng, diseng
• lever up, part_up, part_dn, dn

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Another kind of field input fields

• Serve the role of events
• One for each type of event
• use bullet () to distinguish input field
  condition names
• input mouse_down, mouse_up, mouse_move,
  keypress,

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Another kind of field input fields

• Additional fields for other info in event
• cntrlkey cntrl, nocontrl
• shiftkey shift, noshift
• leftbtn leftup, leftdn
• Small issue here with not having integers
  location time

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More parts of PPS

• Can do basic PPS with state info and input fields
  
• will see other types in a bit
• Second major part of PPS
• productions
• serves role of transitions
• how state changes based on current state and input

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Productions

• Form
• ltlist of conditionsgt ? ltlist of conditionsgt
• Think of as
• ltpre-conditionsgt ? ltpost-conditionsgt
• ltantecedentgt ? ltconsequencegt
• if you find ltthisgt to be true, make the system be
  like ltthatgt
• LHS may have state info input
• RHS may only have state info

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An example the clutched lever

• What are the state info fields?
• What are the input fields?

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An example the clutched lever

• handle_state up, part_up, part_dn, dn
• input press_top, press_clutch, press_bottom,
  press_other, release_top, release_clutch,
  release_bottom, release_other, enter_bottom,
  enter_top

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Productions for the lever
Release_any
Enter_bottom
Press_top
Press_bottom
Enter_top
Release_any
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Productions for the lever
Release_any
Enter_bottom
Press_top

• up, press_top ? part_up
• part_up, enter_bottom ? part_dn
• part_up, release_top ? up
• part_up, release_clutch ? up
• part_up, release_bottom ? up
• part_up, release_other ? up

Press_bottom
Enter_top
Release_any
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Productions for the lever
Release_any
Enter_bottom
Press_top
Press_bottom
Enter_top
Release_any
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Productions for the lever

• part_dn, release_top ? dn
• part_dn, release_clutch ? dn
• part_dn, release_bottom ? dn
• part_dn, release_none ? dn
• part_dn, enter_top ? part_up

Release_any
Enter_bottom
Press_top
Press_bottom
Enter_top
Release_any
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Productions for the lever
Release_any
Enter_bottom
Press_top
Press_bottom
Enter_top
Release_any
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Productions for the lever

• dn, press_bottom ? part_dn

Release_any
Enter_bottom
Press_top
Press_bottom
Enter_top
Release_any
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Productions for the lever

• up, press_top ? part_up
• part_up, enter_bottom ? part_dn
• part_up, release_top ? up
• part_up, release_clutch ? up
• part_up, release_bottom ? up
• part_up, release_other ? up
• part_dn, release_top ? dn
• part_dn, release_clutch ? dn
• part_dn, release_bottom ? dn
• part_dn, release_none ? dn
• part_dn, enter_top ? part_up
• dn, press_bottom ? part_dn

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Now the clutch part

• clutch eng, part_eng, part_diseng, diseng

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Clutch transitions

• One each of the form
• state, event ? new-state

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Putting this together with the clutch

• Just bunch the productions together!
• Well not quite.
• Whats the problem?

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Putting this together with the clutch

• Just bunch the productions together!
• Well not quite.
• Whats the problem?
• Not completely independent
• extra conditions
• can only move the handle when the clutch is in

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Putting this together with the clutch

• Put productions together, then add conditions
  under which the parts affect each other
• only move handle when clutch eng
• was up, press_top ? part_up
• now

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Putting this together with the clutch

• Put productions together, then add conditions
  under which the parts affect each other
• only move handle when clutch eng
• was up, press_top ? part_up
• now up, press_top, eng ? part_up
• etc. for others

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Note the big advantage of PPS

• Independent aspects are easier in PPS
• write them independently
• add just the connections (typically extra
  conditions)
• dont have to replicate anything

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Note

• We did these examples as translation from FSM
• After you get familiar it may be better to start
  in PPS
• Some things are easier to express
• e.g., all-of-N

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All-of-N interaction

• N1 n1_done, n1_not
• N2 n2_done, n2_not
• ...
• state running, done
• ltsomethinggt ? n1_done // or add n1 to LHS of
  existing
• ltsomethinggt ? n2_done
• n1_done, n2_done, ? done

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What about actions?

• Handled with an additional kind of field Action
  Field
• names prefixed with !
• can only be on RHS

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Action field examples

• feedback_actions !show_clutch_in,
  !slow_clutch_out, !show_hand_top, !show_hand_mid,
  !show_hand_bot, !show_grinding,
  !show_not_grinding,
• Have
• up, press_top, eng ? part_up
• Change how?

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Action field examples

• feedback_actions !show_clutch_in,
  !slow_clutch_out, !show_hand_top, !show_hand_mid,
  !show_hand_bot, !show_grinding,
  !show_not_grinding,
• up, press_top, eng ? part_up, !show_hand_mid,
  !show_not_grinding
• up, press_top, diseng ? up, !show_hand_mid,
  !show_grinding
• etc.

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Other field types query fields

• Predicate over some arbitrary (outside) condition
• Only on LHS
• Prefix names with ?
• This is how we deal with no ints
• position ?in_clutch, ?in_top, , ?in_none
• Also semantic tests
• password_auth ?pw_ok, ?pw_bad

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Other field types External events

• Basically just like input events, but from the
  rest of the system
• prefix with gt
• reactor_alarm gtnormal, gtwarm, gthot, gtmeltdown
• Can only appear on which side?

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Other field types External events

• Basically just like input events, but from the
  rest of the system
• prefix with gt
• reactor_core gtnormal, gtwarm, gthot, gtmeltdown
• Can only appear on LHS

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Implementing PPS

• Project 4
• due 10/14 at midnight

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Implementing PPS

• Just kidding

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Implementing PPS

• Wont talk about the details, but straight
  forward implementation
• only a little more complex that FSM
• includes things like only execute queries when
  you have to, etc.

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PPS summary

• Same power as FSM (what you can do in one, can do
  in other)
• Deals with cross-product issue
• independent parts makes it easier to do fewer
  modes
• generally easier expression
• But lost FSM graphical notation
• didnt scale to large things anyway

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