202 research outputs found
A Finite Equational Base for CCS with Left Merge and Communication Merge
Using the left merge and communication merge from ACP, we present an equational base for the fragment of CCS without restriction and relabelling. Our equational base is finite if the set of actions is finite
On the Axiomatisation of Branching Bisimulation Congruence over CCS
In this paper we investigate the equational theory of (the restriction, relabelling, and recursion free fragment of) CCS modulo rooted branching bisimilarity, which is a classic, bisimulation-based notion of equivalence that abstracts from internal computational steps in process behaviour. Firstly, we show that CCS is not finitely based modulo the considered congruence. As a key step of independent interest in the proof of that negative result, we prove that each CCS process has a unique parallel decomposition into indecomposable processes modulo branching bisimilarity. As a second main contribution, we show that, when the set of actions is finite, rooted branching bisimilarity has a finite equational basis over CCS enriched with the left merge and communication merge operators from ACP
Process Algebras
Process Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems.
They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems.
Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external
experiments
Unique Parallel Decomposition for the Pi-calculus
A (fragment of a) process algebra satisfies unique parallel decomposition if
the definable behaviours admit a unique decomposition into indecomposable
parallel components. In this paper we prove that finite processes of the
pi-calculus, i.e. processes that perform no infinite executions, satisfy this
property modulo strong bisimilarity and weak bisimilarity. Our results are
obtained by an application of a general technique for establishing unique
parallel decomposition using decomposition orders.Comment: In Proceedings EXPRESS/SOS 2016, arXiv:1608.0269
Formal mechanization of device interactions with a process algebra
The principle emphasis is to develop a methodology to formally verify correct synchronization communication of devices in a composed hardware system. Previous system integration efforts have focused on vertical integration of one layer on top of another. This task examines 'horizontal' integration of peer devices. To formally reason about communication, we mechanize a process algebra in the Higher Order Logic (HOL) theorem proving system. Using this formalization we show how four types of device interactions can be represented and verified to behave as specified. The report also describes the specification of a system consisting of an AVM-1 microprocessor and a memory management unit which were verified in previous work. A proof of correct communication is presented, and the extensions to the system specification to add a direct memory device are discussed
On CSP and the Algebraic Theory of Effects
We consider CSP from the point of view of the algebraic theory of effects,
which classifies operations as effect constructors or effect deconstructors; it
also provides a link with functional programming, being a refinement of Moggi's
seminal monadic point of view. There is a natural algebraic theory of the
constructors whose free algebra functor is Moggi's monad; we illustrate this by
characterising free and initial algebras in terms of two versions of the stable
failures model of CSP, one more general than the other. Deconstructors are
dealt with as homomorphisms to (possibly non-free) algebras.
One can view CSP's action and choice operators as constructors and the rest,
such as concealment and concurrency, as deconstructors. Carrying this programme
out results in taking deterministic external choice as constructor rather than
general external choice. However, binary deconstructors, such as the CSP
concurrency operator, provide unresolved difficulties. We conclude by
presenting a combination of CSP with Moggi's computational {\lambda}-calculus,
in which the operators, including concurrency, are polymorphic. While the paper
mainly concerns CSP, it ought to be possible to carry over similar ideas to
other process calculi
On the Axiomatisability of Parallel Composition
This paper studies the existence of finite equational axiomatisations of the
interleaving parallel composition operator modulo the behavioural equivalences
in van Glabbeek's linear time-branching time spectrum. In the setting of the
process algebra BCCSP over a finite set of actions, we provide finite,
ground-complete axiomatisations for various simulation and (decorated) trace
semantics. We also show that no congruence over BCCSP that includes
bisimilarity and is included in possible futures equivalence has a finite,
ground-complete axiomatisation; this negative result applies to all the nested
trace and nested simulation semantics
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