Towards Action-Refinement in Process Algebras

AbstractWe present a simple process algebra which supports a form of refinement of an action by a process and address the question of an appropriate equivalence relation for it. The main result of the paper is that an adequate equivalence can be defined in a very intuitive manner. In fact we show that it coincides with the timed-equivalence proposed by one of the authors. We also show that it can be characterized equationally

Split-2 Bisimilarity has a Finite Axiomatization over CCS with<br> Hennessy&#39;s Merge

This note shows that split-2 bisimulation equivalence (also known as timed equivalence) affords a finite equational axiomatization over the process algebra obtained by adding an auxiliary operation proposed by Hennessy in 1981 to the recursion, relabelling and restriction free fragment of Milner's Calculus of Communicating Systems. Thus the addition of a single binary operation, viz. Hennessy's merge, is sufficient for the finite equational axiomatization of parallel composition modulo this non-interleaving equivalence. This result is in sharp contrast to a theorem previously obtained by the same authors to the effect that the same language is not finitely based modulo bisimulation equivalence

Action Contraction

The question we consider in this paper is: “When can a combination of fine-grain execution steps be contracted into an atomic action execution”? Our answer is basically: “When no observer can see the difference.” This is worked out in detail by defining a notion of coupled split/atomic simulation refinement between systems which differ in the atomicity of their actions, and proving that this collapses to Parrow and Sjödin’s coupled similarity when the systems are composed with an observer

Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice

This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well

A categorical view of action refinement in models of concurrency

We define a categorical characterization of refinement and show that refinement definitions for various models of concurrency can be captured be our view

Scalable reaction network modeling with automatic validation of consistency in Event-B

Constructing a large biological model is a difficult, error-prone process. Small errors in writing a part of the model cascade to the system level and their sources are difficult to trace back. In this paper we extend a recent approach based on Event-B, a state-based formal method with refinement as its central ingredient, allowing us to validate for model consistency step-by-step in an automated way. We demonstrate this approach on a model of the heat shock response in eukaryotes and its scalability on a model of the ErbB signaling pathway. All consistency properties of the model were proved automatically with computer support.</p

Free shuffle algebras in language varieties

AbstractWe give simple concrete descriptions of the free algebras in the varieties generated by the “shuffle semirings” LΣ := (P(Σ∗),+,., ⊗, 0,1), or the semirings RΣ := (R(Σ∗),+,., ⊗,∗,0,1), where P(Σ∗) is the collection of all subsets of the free monoid Σ∗, and R(Σ∗) is the collection of all regular subsets. The operation x ⊗ y is the shuffle product

Decomposition orders : another generalisation of the fundamental theorem of arithmetic

We discuss unique decomposition in partial commutative monoids. Inspired by a result from process theory, we propose the notion of decomposition order for partial commutative monoids, and prove that a partial commutative monoid has unique decomposition iff it can be endowed with a decomposition order. We apply our result to establish that the commutative monoid of weakly normed processes modulo bisimulation definable in ACPe with linear communication, with parallel composition as binary operation, has unique decomposition. We also apply our result to establish that the partial commutative monoid associated with a well-founded commutative residual algebra has unique decompositio