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Imperative process algebra with abstraction

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 نشر من قبل Kees Middelburg
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English
 تأليف C.A. Middelburg




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This paper introduces an imperative process algebra based on ACP (Algebra of Communicating Processes). Like other imperative process algebras, this process algebra deals with processes of the kind that arises from the execution of imperative programs. It distinguishes itself from already existing imperative process algebras among other things by supporting abstraction from actions that are considered not to be visible. The support of abstraction opens interesting application possibilities of the process algebra. This paper goes briefly into the possibility of information-flow security analysis of the kind that is concerned with the leakage of confidential data. For the presented axiomatization, soundness and semi-completeness results with respect to a notion of branching bisimulation equivalence are established.



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In process algebras such as ACP (Algebra of Communicating Processes), parallel processes are considered to be interleaved in an arbitrary way. In the case of multi-threading as found in contemporary programming languages, parallel processes are actua lly interleaved according to some interleaving strategy. An interleaving strategy is what is called a process-scheduling policy in the field of operating systems. In many systems, for instance hardware/software systems, we have to do with both parallel processes that may best be considered to be interleaved in an arbitrary way and parallel processes that may best be considered to be interleaved according to some interleaving strategy. Therefore, we extend ACP in this paper with the latter form of interleaving. The established properties of the extension concerned include an elimination property, a conservative extension property, and a unique expansion property.
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The well-known process algebras, such as CCS, ACP and $pi$-calculus, capture the interleaving concurrency based on bisimilarity semantics. We did some work on truly concurrent process algebras, such as CTC, APTC and $pi_{tc}$, capture the true concur rency based on truly concurrent bisimilarities, such as pomset bisimilarity, step bisimilarity, history-preserving (hp-) bisimilarity and hereditary history-preserving (hhp-) bisimilarity. Truly concurrent process algebras are generalizations of the corresponding traditional process algebras. In this book, we introduce localities into truly concurrent process algebras, based on the work on process algebra with localities.
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In a previous paper, an ACP-style process algebra was proposed in which propositions are used as the visible part of the state of processes and as state conditions under which processes may proceed. This process algebra, called ACPps, is built on cla ssical propositional logic. In this paper, we present a version of ACPps built on a paraconsistent propositional logic which is essentially the same as CLuNs. There are many systems that would have to deal with self-contradictory states if no special measures were taken. For a number of these systems, it is conceivable that accepting self-contradictory states and dealing with them in a way based on a paraconsistent logic is an alternative to taking special measures. The presented version of ACPps can be suited for the description and analysis of systems that deal with self-contradictory states in a way based on the above-mentioned paraconsistent logic.
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