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Samosa

Nested probable statements

Probable statements can be nested. Some examples would help understand how they work.

Single statement, nested probabilities

In such cases, probabilities are multiplied, starting from right to left.

Example 

<samosa>
("Hello world!") -> putout.   ?[40]... ?[80]...
</samosa>

In the example above, the probability of execution of the probable statement ("Hello world!") -> putout. ?[40]... (let’s call this event A) is 80% (as indicated by ?[80]... beside it.)

And further, the probability of execution of the statement ("Hello world!") -> putout. (let’s call this event B) is 40% provided that the probable statement ("Hello world!") -> putout. ?[40]... itself executes.

Hence, the effective probability of ("Hello world!") -> putout. executing can be expressed as P(B|A).

One can go on nesting probabilities like this. But remember, probabilities are nested from right to left.

Also, as mentioned before, the probabilities specified may not necessarily be constants. They can be expressions that are evaluated to an int at compile time.

Multiple statements, nested probabilities

Just like single probable statements, probable statements with alternatives can also be nested.

Example 

<samosa>

("nested3a") -> putout. ?[55] ("nested3b") -> putout. ?[70]
    ("nested2b") -> putout. ?[60]
         ("nested1b") -> putout.

</samosa>

Again, probabilities are nested from the right to left.

The above example will be easier to understand, if seen this way: (the snippet below is not actual code, just a pseudocode to make things easy to understand)

Let A signify the statement ("nested1b") -> putout.

Then, the top level probable statement is:
B ?[60] A

where B is:
    C ?[70] ("nested2b") -> putout.

    where C is:
        ("nested3a") -> putout. ?[55] ("nested3b") -> putout.

The above should have made things easier to understand :-)

In case it is still not that clear, here’s an attempt at an explanation:

First, the probability ?[60] is evaluated. Hence, 40% of the time, ("nested1b") -> putout. is executed. The rest 60% of the times:

  • The next probability, ?[70] is evaluated. 30% of times (after the first probability makes this statement run), ("nested2b") -> putout. gets executed. The rest 70% of the times:
    • The next probability, ?[55] is evaluated. So, 45% of times (after the previous nested probability statement makes this one run), the statement ("nested3b") -> putout. is executed, while for 55% of times, the statement ("nested3a") -> putout. gets executed.

Hopefully that served as a good explanation.

Mathematically, the probability of ("nested3a") -> putout. getting executed can be calculated by evaluating P(exec(C)|exec(B)|~exec(A)) (where exec(B) and so on denote the event of that statement executing, and ~exec(A) denotes the probability of that statement not executing.)