History Monoid - Connection To Computer Science

Connection To Computer Science

The use of the word history in this context, and the connection to concurrent computing, can be understood as follows. An individual history is a record of the sequence of states of a process (or thread or machine); the alphabet is the set of states of the process.

A letter that occurs in two or more alphabets serves as a synchronization primitive between the various individual histories. That is, if such a letter occurs in one individual history, it must also occur in another history, and serves to "tie" or "rendezvous" them together.

Consider, for example, and . The union alphabet is of course . The elementary histories are, and . In this example, an individual history of the first process might be while the individual history of the second machine might be . Both of these individual histories are represented by the global history, since the projection of this string onto the individual alphabets yields the individual histories. In the global history, the letter can be considered to commute with the letters and, in that these can be rearranged without changing the individual histories. Such commutation is simply a statement that the first and second processes are running concurrently, and are unordered with respect to each other; they have not (yet) exchanged any messages or performed any synchronization.

The letter serves as a synchronization primitive, as its occurrence marks a spot in both the global and individual histories, that cannot be commuted across. Thus, while the letters and can be re-ordered past and, they cannot be reordered past . Thus, the global history and the global history both have as individual histories and, indicating that the execution of may happen before or after . However, the letter is synchronizing, so that is guaranteed to happen after, even though is in a different process than .