The parallel composition of uniform processes with data

Abstract

A general basis for the definition of a finite but unbounded number of parallel processes is the equation S(n, dt) = P (O, get(O, dt))< eq(n, 0) .(P(n, get(n, dt)) II S(n -1, dt)). In this formula eq(n,O) is an equality test, and get(n, dt) denotes the n-th data element in table dt. We derive a linear process equation with the same behaviour as Sen, dt), and show that this equation is well-defined, provided one adopts the principle CL-RSP from [4]. In order to demonstrate the strength of our result, we use it for the analysis of a standard example. We show that n + 1 concatenated buffers form a queue of capacity n + 1.

Cones and Foci for Protocol Verification Revisited

“…Linear process equations [6] constitute a restricted class of µCRL specifications in some kind of linear format. Algorithms have been developed to transform µCRL specifications into this linear format [19,24,35]. In a linear process equation, the states of the associated labeled transition system are data objects.…”

Analysis of Timed Processes with Data Using Algebraic Transformations

“…Many of the axioms are taken from, or inspired by [11,16]. The axioms say that ≤ is a total order on the Time domain, and 0 is the least element.…”

Abstraction of parallel uniform processes with data

“…Groote and van Wamel [12] defined an equation that models the parallel composition of N such processes, it uses a data type DTable to store the values of parameters d of each process. It defines tables indexed by natural numbers, and each element has the data type D. Based on their definitions, we specify a different representation that is more appropriate for performing abstractions.…”

“…Algorithms have been developed to transform µCRL specifications into this linear format. In particular, Groote and van Wamel [12] derived an LPE for the parallel composition of an arbitrary but finite number of uniform processes with data.…”

“…Considering a distributed system composed of an arbitrary but finite number of uniform processes with data, we develop a general framework and its formal requirements for safely abstracting the system by performing abstract interpretation of data, based on [12,19]. Moreover, we present two abstraction patterns, which fulfill the requirements and can be embedded in the general framework.…”