Properties of Commutative production system, Introduction to Decomposable production system

Properties of Commutative   production system

1. An irrevocable control regime can always be used in a commutative system because the application of a rule never needs to be taken back or undone.
2. No need of a mechanism for applying alternative sequence of rules .The rule that is applicable  to an earlier database is applicable to the current one as well.
3. In a commutative production system there may be a chance of having inappropriate rules. This inappropriate rule just delays but never prevents termination.

Decomposable production system

 In order to understand decomposable production system. Consider a system   which has initial database as (C,B,Z). The production rules are based on the following rules. C could be written as (D,L) ; C could be written as ( B,M) ; B could be written as (M,M) ; Z could be written as (B,B,M) i.e.,

R1 : C → ( D,L)

R2 : C → (B,M)

R3: B → (M,M)

R4: Z → (B,B,M)

 Here I’m looking for a termination condition where the database contains only M. If I start with  the complete C B Z I have 3 rewriting rules for C, B, Z so  my path would be 3 different distinct paths. I could write C or B or Z.

                                                            FIGURE  1

And each of them could take different paths. And what is important is to note that some path may lead to termination. But, some other path may not lead to termination . Instead of looking at C B Z as a complete single entity , the decomposable production system allows me to  look at C B Z as 3 different units of C B Z .This is because of the problem that  I get  when I look at it as 1 single unit as highlighted.