Parallel Programming: State Diagram Example

• Enter into state S0 into the superstate S1 through event 1 and yields action a1.
• When entering into superstate S1, we must go through state S12, with action a7 to enter and action a3 to exit.
  • If action a3 yields an event e9, which yielded action a9, we enter into state S13, causing action a6 and action a12 to exit.
    • If action a12 yields an event e5, we will get action a5 and we hit the superstate S1 and begin again to state S2.
    • If action a12 yields an event e9, we will use action a1 an enter state S112 (under the S11 superstate) with an entry of an action a11.
      • Event e2 acts on S112, to get action 2 which enters the superstate S11.
        • Entering into the superstate through state S112 we get an exit criterion of action a14 and we end.
        • If exiting state S112 we do event e1 and action a1 we are sent back to state S12 to start again.
        • If we exit state S112 we do event e3 and action a3 which is used to enter into state S1 follow 1.a.
  • If action a3 in state S12 yields event e4 and action a4, we enter the superstate S11. Entering super state S11 this way we enter into state S111 with an entry action of a8.
    • We then carry out event e9 and action a1 to get to state S112. If this happens follow 1.a.i.2.

LSAT Conditionals and CS Conditionals

In the past few months, I have been studying for the LSAT exam. Yes, I am contemplating Law School.  Law school will be a topic for another day.  However, I came across a few points that are extremely interesting and could spark discussion in the computer science field.  In the field of computer science, we have a thing called Loops in our coding languages.  One of the most common loops is called an IF-THEN loops, which is one of many conditional phrases. However, the LSAT has made me realized that there is more to the IF-THEN conditional statements in the LSAT, and here is why (Teti et al., 2013):

1. If X then Y (Simple IF-THEN loop)
2. If not Y then not X (This is the contra-positive of 1)
3. X If and only if Y means X and Y
4. X Unless Y means if not X then Y

where X here is the sufficient variable whereas Y is the necessary variable. The phrase “If” can be substituted for “All,” “Any,” “Every,” and “When” (Teti et al., 2013). Whereas the phrase for “then” can be substituted for the phrase “only,” or “only if.” Remember, that a conditional phrase like the ones above can introduce a relationship between the variables, but it doesn’t establish anything concrete. A sufficient variable (X) is enough to guarantee Y, but Y is not enough on its own to guarantee X.

Subsequently, with any Loop, we have to look at conjunctive “and” or disjunctive “or” statements.

1. Both X and Y = X + Y
2. Either X or Y = X or Y
3. Not both X or Y = X or Y
4. Neither X or Y = X + Y

We should note that an “or” statement can also allow for the possibility of both (Teti et al., 2013). Additionally, the LSAT adds some nuance to the conditional phrase by adding an “EXCEPT” clause.  For instance (Teti et al. 2013):

1. Must be true EXCEPT = Could be false
2. Could be true EXCEPT = Must be false
3. Could be false EXCEPT = Must be true
4. Must be false EXCEPT = Could be true

The LSAT views these loops, conjunctive, disjunctive, and conditional phrases a bit more nuance than computer scientists do and maybe we can combine some of this nuance in future coding to get more nuance code and results.

Though some people may state that this whole post is overkill and why do we have to look into such nuance. Each one of the above bullets is necessary and has value. It has been created in the lexicon for a particular reason. We can easily decompose each of these, and then map these out in simpler terms with a programming language. However, to sufficiently capture these nuance characteristics of these conditional phrases, we can create really nasty pieces of convoluted code.

Resources:

• Teti, T., Teti, J., and Riley, M. (2013). The Blueprint for LSAT Logic Games. Blueprint LSAT Preparation.