Re: RTS graph and "temporal formulas"

[optikos@verizon.net]

On Wednesday, August 21, 2013 5:50:55 PM UTC-5, Emanuel Berg wrote:
> opt...@verizon.net writes:
> 
> > You turn to the Ada-language Usenet group for a question about
> > 1950s mathematics-nomenclature?  Oh well.  Instead of "get off
> > my lawn", I will point you in the right direction, which
> > generally leads away from here. :-)
> 
> The reason I posted here is that we had Ada in the course.

  But your professor utilized C-language's == as the logical comparison in the E->D transition's stimulus-constraint in 7b, not Ada's =.  :-)

> Thanks for the tutorial, very helpful. I will read those pages,
> only: the "x := 0" response transition doesn't have a stimuli.

  Transitions which lack a stimulus are always traversed.  The lack of stimulus is notated overtly as epsilon.  2 or more epsilon transitions egressing from the same state is an ambiguous type of FSA called an NFA.  But when there exists only one epsilon transition as the sole transition egressing from a state, then determinism is effectively preserved.

http://en.wikipedia.org/wiki/Nondeterministic_finite_automaton_with_%CE%B5-moves

> The state it comes from has one, so perhaps that should be used?

  Yes.  Epsilon in this idiomatic usage means always traverse this C->A transition when in state C.

> But then, the "A" state has a stimuli (x <= 10), and two outgoing
> transitions *with* stimuli (x < 5 and x > 11) - how should this be
> interpreted?

  Upon second look, your professor has utilized both Mealy stimulus-constraint nomenclature (with green logical comparisons as stimulus-constraints on the transitions of 7a) and Moore response-triggered nomenclature (with purple logical comparisons as characterizations of execution time of the software which executes upon entering a state).

  Please be very careful with your wording, because sloppy terminology is a major component in your confusion.  The contextual environment has stimuli; the FSA does not.  The FSA has Mealy-nomenclature stimulus-***constraints*** (i.e., green logical comparisons on transitions) against which incoming stimuli from the sensors are matched.  State A does not have a stimulus; state A has a Moore-nomenclature response (i.e., purple logical predicate as a characterization of the execution time of software executed upon entrance to State A).

  Decoder ring that your professor should have provided in the text of Problem 7 or in the class:
   green:  stimulus-constraint (input)
  purple:  [characterization of] response (output)
    blue:  [imperative instruction that implements] response (output)

> Last: the clocks - do they start at 0?

  Yes.  In a well designed FSA, there would be an overt pre-A initial state with epsilon transition whose response is x:=0 initialization-to-zero, analogous to the C->A transition reset-to-zero.

> Making a transition, that doesn't take any time, does it?

  That is where I am supplementing my prior posting (where I was hand-wavingly oblivious to your current situation at hand).  "Taking time" in a state is precisely what the purple logical comparisons are.  The usage of nearly the same nomenclature 1) for characterization of execution time of the software executed upon entry to a state [as output] and 2) for the stimulus-constraint [related to comparisons against input] differed only by color is an especially cryptic and unwise nomenclature that is inferior to the nomenclature of Mealy, Moore, or the modern math utilized in the Wikipedia articles to which I directed you.

Your professor appears to lump the time it takes to make a transition in with the purple execution-time chararterizations of the state into which the transition ingresses.  Conversely, your professor appears to assume that failed attempts to match the sensors' stimuli to each not-traversed transition egressing from the current state takes zero time (which is incorrect, because it does take time, unless the clock ticks relatively huge compared to the overhead of operating the FSA).

> -- 
> Emanuel Berg - programmer (hire me! CV below)
> computer projects: http://user.it.uu.se/~embe8573
> internet activity: http://home.student.uu.se/embe8573