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Register a new userOn infinite guarded recursive specifications in process algebra
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Added by
Kees Middelburg
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In most presentations of ACP with guarded recursion, recursive specifications are finite or infinite sets of recursion equations of which the right-hand sides are guarded terms. The completeness with respect to bisimulation equivalence of the axioms of ACP with guarded recursion has only been proved for the special case where recursive specifications are finite sets of recursion equations of which the right-hand sides are guarded terms of a restricted form known as linear terms. In this note, we widen this completeness result to the general case.
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In the case of multi-threading as found in contemporary programming languages, parallel processes are interleaved according to what is known as a process-scheduling policy in the field of operating systems. In a previous paper, we extend ACP with this form of interleaving. In the current paper, we do so with the variant of ACP known as ACP$_epsilon$. The choice of ACP$_epsilon$ stems from the need to cover more process-scheduling policies. We show that a process-scheduling policy supporting mutual exclusion of critical subprocesses is now covered.
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 actually 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.
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.
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning with coinductive types. We wish to implement GDTT with decidable type-checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-Lof type theory in which the identity type is replaced by abstract paths between terms. CTT provides a computational interpretation of functional extensionality, is conjectured to have decidable type checking, and has an implemented type-checker. Our new type theory, called guarded cubical type theory, provides a computational interpretation of extensionality for guarded recursive types. This further expands the foundations of CTT as a basis for formalisation in mathematics and computer science. We present examples to demonstrate the expressivity of our type theory, all of which have been checked using a prototype type-checker implementation, and present semantics in a presheaf category.
This paper concerns the relation between process algebra and Hoare logic. We investigate the question whether and how a Hoare logic can be used for reasoning about how data change in the course of a process when reasoning equationally about that process. We introduce an extension of ACP (Algebra of Communicating Processes) with features that are relevant to processes in which data are involved, present a Hoare logic for the processes considered in this process algebra, and discuss the use of this Hoare logic as a complement to pure equational reasoning with the equational axioms of the process algebra.
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