Class: YPetri::Transition

Inherits:
Object
  • Object
show all
Defined in:
lib/y_petri/transition.rb

Overview

Transitions – little boxes in Petri net drawings – represent atomic operations on the Petri net’s marking.

Domain and codomin

Each transition has a domain (upstream places) and codomain (downstream places). Upstream places are those, whose marking affects the transition. Downstream places are those affected by the transition.

Action and action vector

Every transition action – the operation it represents. The action of non-stoichiometric transitions is directly specified by its action closure (whose output arity should match the codomain size.) For stoichiometric transitions, the action closure result must be multiplied by the transition’s stoichiometry vector. Timed transitions have rate closure. Their action can be obtained by multiplying their rate by Δtime.

Rate

In YPetri, marking is always considered a discrete number of tokens (as

    1. Petri has handed it down to us). Usefulness of floating point numbers

in representing larger amounts of tokens is acknowledged, but seen as a pragmatic measure, an implementation detail. There is no class distinction between discrete vs. continuous places / transitions. Often we see continuous transitions with their flux (flow rate) ditinguished from discrete stochastic transitions with their propensity (likelihood of firing in a time unit). In YPetri, flux and propensity are unified under a single term rate, and the choice between discrete and stochastic computation is a concern of the simulation, not of the object model.

Basic transition types

There are 4 basic transition types in YPetri:

  • TS – timed stoichiometric

  • tS – timeless stoichiometric

  • Ts – timed nonstoichiometric

  • ts – timeless nonstoichiometric

They arise by combining 2 qualities:

  1. Timedness: timed (T) / timeless (t)

  2. Stoichiometricity: stoichiometric (S) / nonstoichiometric (s)

Timedness

  • Timed transitions have rate closure, whose result is to be multiplied by Δtime.

  • Timeless transitions have action closure, whose result does not need to be multiplied by time.

Summary: Having vs. not having rate distinguishes the need to multiply the closure result by Δ time.

Stoichiometricity

  • TS transitions – rate vector = rate * stoichiometry vector

  • tS transitions – action vector = action * stoichiometry vector

  • Ts transitions – rate vector = rate closure result

  • ts transitions – action vector = action closure result

Summary: stoichiometricity distinguishes the need to multiply the rate/action closure result by stoichiometry.

Assignment action

Assignment transitions (_A_ transitions) are special transitions, that replace the codomain marking rather than modifying it – they assign new marking to their codomain, like we are used to from spreadsheets. Technically, this behavior is easily achievable with normal ts transitions, so the existence of separate A transitions is just a convenience, not a new type of a transition in the mathematical sense.

Functional / functionless transitions

Other Petri net implementation often distinguies between “ordinary” (vanilla as per C. A. Petri) and functional transitions, whose operation is governed by a function. In YPetri, transitions are generally functional, but there remains a possibility of creating vanilla (functionless) transitions by not specifying any rate / action, while specifying the stoichiometry. Action closure as per C. A. Petri is automatically constructed for these.

Defined Under Namespace

Modules: Arcs, Cocking, ConstructionConvenience, TypeInformation, Type_A, Type_T, Type_t, Types, UsableWithoutWorld

Constant Summary collapse

TYPES = 
{
  T: "timed",
  t: "timeless",
  S: "stoichiometric",
  s: "non-stoichiometric",
  A: "assignment",
  a: "non-assignment",
  TS: "timed stoichiometric",
  tS: "timeless stoichiometric",
  Ts: "timed nonstoichiometric",
  ts: "timeless nonstoichiometric"
}

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*args, &block) ⇒ Transition

Transition class represents many different kinds of Petri net transitions. It makes the constructor syntax a bit more polymorphic. The type of the transition to construct is mostly inferred from the constructor arguments.

Mandatorily, the constructor will always need a way to determine the domain (upstream arcs) and codomain (downstream arcs) of the transition. Also, the constructor must have a way to determine the transition’s action. This is best explained by examples – let us have 3 places A, B, C, for whe we will create different kinds of transitions:

TS (timed stoichiometric)

Rate closure and stoichiometry has to be supplied. Rate closure arity should correspond to the domain size. Return arity should be 1 (to be multiplied by the stoichiometry vector, as in all other stoichiometric transitions).

Transition.new stoichiometry: { A: -1, B: 1 },
               rate: -> a { a * 0.5 }

Ts (timed nonstoichiometric)

Rate closure has to be supplied, whose arity should match the domain, and output arity codomain.

tS (timeless stoichiometric)

Stoichiometry has to be supplied, action closure is optional. If supplied, its return arity should be 1 (to be multiplied by the stoichiometry vector).

ts transitions (timeless nonstoichiometric)

Action closure is expected with return arity equal to the codomain size:

Transition.new upstream_arcs: [A, C], downstream_arcs: [A, B],
               action_closure: proc { |m, x|
                                      if x > 0 then [-(m / 2), (m / 2)]
                                      else [1, 0] end
                                    }



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# File 'lib/y_petri/transition.rb', line 164

def initialize *args, &block
  check_in_arguments *args, &block # the big job
  extend( if timed? then Type_T
          elsif assignment_action? then Type_A
          else Type_t end )
  inform_upstream_places         # that they have been connected
  inform_downstream_places       # that they have been connected
  uncock                         # initialize in the uncocked state
end

Instance Attribute Details

#action_closure ⇒ Object (readonly) Also known as: action

For rateless transition, action closure must be present. Action closure input arguments must correspond to the domain places, and for timed transitions, the first argument of the action closure must be Δtime.



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# File 'lib/y_petri/transition.rb', line 229

def action_closure
  @action_closure
end

#codomain ⇒ Object (readonly) Also known as: codomain_arcs, codomain_places, downstream, downstream_arcs, downstream_places, action_arcs

Codomain, ‘downstream arcs’, or ‘action arcs’, is a collection of places, whose marking is directly changed by this transition’s firing.



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# File 'lib/y_petri/transition.rb', line 187

def codomain
  @codomain
end

#domain ⇒ Object (readonly) Also known as: domain_arcs, domain_places, upstream, upstream_arcs, upstream_places

Domain, or ‘upstream arcs’, is a collection of places, whose marking directly affects the transition’s action.



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# File 'lib/y_petri/transition.rb', line 177

def domain
  @domain
end

#rate_closure ⇒ Object (readonly) Also known as: rate, flux_closure, flux, propensity_closure, propensity

In YPetri, rate is a unifying term for both flux and propensity, both of which are treated as aliases of rate. The decision between discrete and continuous computation is a concern of the simulation. Rate closure arity should correspond to the transition’s domain.



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# File 'lib/y_petri/transition.rb', line 218

def rate_closure
  @rate_closure
end

#stoichiometry ⇒ Object (readonly)

Stoichiometry (implies that the transition is stoichiometric).



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# File 'lib/y_petri/transition.rb', line 197

def stoichiometry
  @stoichiometry
end

Instance Method Details

#inspect ⇒ Object

Inspect string for a transition.



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# File 'lib/y_petri/transition.rb', line 272

def inspect
  to_s
end

#place(id) ⇒ Object 



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# File 'lib/y_petri/transition.rb', line 283

def place id
  super rescue Place().instance( id )
end

#s ⇒ Object

Stoichiometry as a hash of pairs: { codomain_place_name_symbol => stoichiometric_coefficient }



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# File 'lib/y_petri/transition.rb', line 209

def s
  stoichio.with_keys { |k| k.name || k.object_id }
end

#stoichio ⇒ Object

Stoichiometry as a hash of pairs: { codomain_place_instance => stoichiometric_coefficient }



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# File 'lib/y_petri/transition.rb', line 202

def stoichio
  Hash[ codomain.zip( @stoichiometry ) ]
end

#to_s ⇒ Object

Conversion to a string.



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# File 'lib/y_petri/transition.rb', line 278

def to_s
  "#<Transition: %s>" %
    "#{'%s ' % name if name}(#{type})#{' id:%s' % object_id unless name}"
end

#transition(id) ⇒ Object 



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# File 'lib/y_petri/transition.rb', line 287

def transition id
  super rescue Transition().instance( id )
end

#zero_action ⇒ Object

Zero action.



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# File 'lib/y_petri/transition.rb', line 234

def zero_action
  codomain.map { 0 }
end