A Thread Algebra with Multi-Level Strategic Interleaving

Abstract

Abstract. In a previous paper we developed an algebraic theory about threads and a form of concurrency where some deterministic interleaving strategy determines how threads that exist concurrently are interleaved. The interleaving of different threads constitutes a multi-thread. Several multi-threads may exist concurrently on a single host in a network, several host behaviours may exist concurrently in a single network on the internet, etc. In the current paper we assume that the abovementioned kind of interleaving is also present at those other levels. We extend the theory developed so far with features to cover the multi-level case. We employ the resulting theory to develop a simplified, formal representation schema of the design of systems that consist of several multi-threaded programs on various hosts in different networks and to verify a property of all systems designed according to that schema.

Machine structure oriented control code logic

“…In [7], we show that the processes considered in BTA+REC can be viewed as processes that are definable over ACP [14].…”

Distributed strategic interleaving with load balancing

“…The transition rules for the postconditional composition operators on located threads constitute a trivial adaptation of the transition rules for the postconditional composition operators on unlocated threads. The transition rules for the deadlock at termination operator can be found in [7,8]. The transition rules for the cyclic distributed strategic interleaving operator, as well as the transition rules for the distributed strategic interleaving operators that will be introduced later in this paper, are similar to the transition rules for the strategic interleaving operator for cyclic interleaving found in [7,8].…”

“…The transition rules for the deadlock at termination operator can be found in [7,8]. The transition rules for the cyclic distributed strategic interleaving operator, as well as the transition rules for the distributed strategic interleaving operators that will be introduced later in this paper, are similar to the transition rules for the strategic interleaving operator for cyclic interleaving found in [7,8]. However, the transition rules for a distributed strategic interleaving operator are so much more involved that they might be called unreadable.…”

“…The following points illustrate why that point of view is untenable: (i) whether the interleaving of certain threads leads to deadlock depends on the interleaving strategy used; (ii) sometimes deadlock takes place with a particular interleaving strategy whereas arbitrary interleaving would not lead to deadlock and vice versa. We give demonstrations of (i) and (ii) in [7] and [5], respectively.…”

“…In [5], evidence of both (i) and (ii) is produced by the established connections of threads and services with processes as considered in an extension of ACP with conditions introduced in [4].…”