modelling reactive system Introduction mCRL2 (successor of )is a - - PowerPoint PPT Presentation

Introducing mCRL2 language for modelling reactive system

Introduction

• mCRL2 (successor of 𝜈𝐷𝑆𝑀)is a specification language

for describing concurrent discrete event systems.

• It is accompanied with a toolset for simulation, analysis

and visualization of behavior.

• The behavioral part of the language is based on

process algebra (Algebra of Communicating Processes) which is extended to include data and time.

• The data part of the toolset is based on abstract

equational data types.

• The toolset has been founded by Jan Friso Groote and

is currently developed at Eindhoven University of Technology.

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Philosophy

• Like in every process algebra, a fundamental concept in

mCRL2 is the process.

• Processes can perform actions and can be composed to

form new processes using algebraic operators.

• A system usually consists of several processes (or

components) in parallel.

• A process can carry data as its parameters. The state of a

process is a specific combination of parameter values.

• Every process has a corresponding state space or Labelled

Transition System (LTS) which contains all states that the process can reach, along with the possible transitions between those states.

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Specification

• An mCRL2 specification is a plain-text file

containing a model in the mCRL2 language.

• The first step in the mCRL2 analysis process is to

linearise this specification to obtain a Linear Process Specification (LPS).

• This is an mCRL2 specification from which all

parallelism has been removed.

• All that remains is a series of condition – action –

effect rules that specify how the system as a whole reacts to certain stimuli given its current state.

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Syntax

• The mCRL2 specification format requires only that an

init statement be present.

• It might be the case that a specification file contains

definitions for multiple processes; the init statement specifies which of these definitions (if any) is used. act a, b; proc P = a . P + b; init P;

• This specification defines the process that can do any

number of a actions, followed by a single b. After this, it terminates.

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Algebra

• Actions in mCRL2 can be synchronized using the

Synchronization operator a | b

• Deadlock or inaction 𝜀
• Alternative composition p + q
• Sequential composition p . q
• Conditional operator or if-then-else construct 𝑑 → 𝑞 ◊ 𝑟

where c is a boolean expression

• Parallel composition p || q yielding interleavings of the

actions in p and q

• communication operator 𝑏0| … |𝑏𝑜 ⟼ 𝑑 , which means

that every group of actions 𝑏0| … |𝑏𝑜 within a multi-action is replaced by c.

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Data & Time

• Summation

𝑞

𝑒:𝐸 used to quantify over a data

domain D

• At operator a@t indicating that multi-action a

happens at time t

• The mCRL2 language provides a number of built-

in datatypes (e.g., boolean, natural, integer) with predefined standard arithmetic operations

• And a datatype definition mechanism to declare

custom types (called also sorts).

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Vending Machine

act ins10, ins20, acc10, acc20, coin10, coin20, ret10, ret20 ;

• ptA, optC, chg10, chg20, putA, putC, prod,

readyA, readyC, out10, out20 ; proc User = ins10.( optA + ins10.( optC + chg20 ) + chg10 ).User + ins20.( optA.chg10 + optC + chg20 ).User ; Mach = acc10.( putA.prod + acc10.( putC.prod + ret20 ) + ret10 ).Mach + acc20.( putA.prod.ret10 + putC.prod + ret20 ).Mach ; init allow( { coin10, coin20, readyA, readyC, out10, out20, prod }, comm( { ins10|acc10 -> coin10, ins20|acc20 -> coin20, chg10|ret10 -> out10, chg20|ret20 -> out20,

• ptA|putA -> readyA, optC|putC -> readyC },

User || Mach ) ) ;

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LTS Semantic

• Behaviour can depend on the data that is exchanged.
• The semantics of processes is defined using a structural
• perational semantics, which associates with every

expression in the language a labelled transition system (LTS).

• Each edge is labelled with an action, which in turn can

have data parameters.

• The information contained in vertices is represented by

a process expression and a valuation of its data parameters, but is unobservable.

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LTS Graph

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