Actor Model - Message-passing Semantics - Unbounded Nondeterminism Controversy

Unbounded Nondeterminism Controversy

Arguably, the first concurrent programs were interrupt handlers. During the course of its normal operation, a computer needed to be able to receive information from outside (characters from a keyboard, packets from a network, etc.). So when the information arrived, execution of the computer was "interrupted" and special code called an interrupt handler was called to put the information in a buffer where it could be subsequently retrieved.

In the early 1960s, interrupts began to be used to simulate the concurrent execution of several programs on a single processor. Having concurrency with shared memory gave rise to the problem of concurrency control. Originally, this problem was conceived as being one of mutual exclusion on a single computer. Edsger Dijkstra developed semaphores and later, between 1971 and 1973, Tony Hoare and Per Brinch Hansen developed monitors to solve the mutual exclusion problem. However, neither of these solutions provided a programming-language construct that encapsulated access to shared resources. This encapsulation was later accomplished by the serializer construct ( and ).

The first models of computation (e.g. Turing machines, Post productions, the lambda calculus, etc.) were based on mathematics and made use of a global state to represent a computational step (later generalized in and see Event orderings versus global state). Each computational step was from one global state of the computation to the next global state. The global state approach was continued in automata theory for finite state machines and push down stack machines, including their nondeterministic versions. Such nondeterministic automata have the property of bounded nondeterminism; that is, if a machine always halts when started in its initial state, then there is a bound on the number of states in which it halts.

Edsger Dijkstra further developed the nondeterministic global state approach. Dijkstra's model gave rise to a controversy concerning unbounded nondeterminism. Unbounded nondeterminism (also called unbounded indeterminacy), is a property of concurrency by which the amount of delay in servicing a request can become unbounded as a result of arbitration of contention for shared resources while still guaranteeing that the request will eventually be serviced. Hewitt argued that the Actor model should provide the guarantee of service. In Dijkstra's model, although there could be an unbounded amount of time between the execution of sequential instructions on a computer, a (parallel) program that started out in a well defined state could terminate in only a bounded number of states . Consequently, his model could not provide the guarantee of service. Dijkstra argued that it was impossible to implement unbounded nondeterminism.

Hewitt argued otherwise: there is no bound that can be placed on how long it takes a computational circuit called an arbiter to settle (see metastability in electronics). Arbiters are used in computers to deal with the circumstance that computer clocks operate asynchronously with input from outside, e.g. keyboard input, disk access, network input, etc. So it could take an unbounded time for a message sent to a computer to be received and in the meantime the computer could traverse an unbounded number of states.

The Actor Model features unbounded nondeterminism which was captured in a mathematical model by Will Clinger using domain theory. There is no global state in the Actor model.