Concepts of Concurrent Computation computation? Turing machines or - PowerPoint PPT Presentation

Introduction Process Calculi Chair of Software Engineering ◮ Question : Why do we need a theoretical model of concurrent Concepts of Concurrent Computation computation? ◮ Turing machines or the λ -calculus have proved to be useful models of Bertrand Meyer sequential systems Sebastian Nanz ◮ Abstracting away from implementation details yields general insights into programming and computation ◮ Process calculi help to focus on the essence of concurrent systems: Lecture 11: CCS interaction Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 2/44 Introduction Introduction The Calculus of Communicating Systems (CCS) Introductory Example: A Simple Process ◮ We study the Calculus of Communicating Systems (CCS) ◮ A coffee and tea machine may take an order for either tea or coffee, ◮ Introduced by [Milner 1980] accept the appropriate payment, pour the ordered drink, and ◮ Milner’s general model: terminate: ◮ A concurrent system is a collection of processes ◮ A process is an independent agent that may perform internal activities tea . coin . cup of tea . 0 + coffee . coin . coin . cup of coffee . 0 in isolation or may interact with the environment to perform shared activities ◮ We have the following elements of syntax: ◮ Milner’s insight: Concurrent processes have an algebraic structure ◮ Actions: tea , cup of tea , etc. ◮ Sequential composition: the dot “.” (first do action tea , then coin , ...) ◮ Non-deterministic choice: the plus “+” (either do tea or coffee ) P 1 op P 2 ⇒ P 1 op P 2 ◮ Terminated process: 0 ◮ This is why a process calculus is sometime called a process algebra Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 3/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 4/44

Introduction Syntax of CCS Introductory Example: Execution of a Simple Process ◮ When a process executes it performs some action, and becomes a new process a ◮ The execution of an action a is symbolized by a transition − → Syntax of CCS tea . coin . cup of tea . 0 + coffee . coin . coin . cup of coffee . 0 tea − → coin . cup of tea . 0 coin − → cup of tea . 0 cup of tea − → 0 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 5/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 6/44 Syntax of CCS Syntax of CCS Syntax of CCS The Terminal Process ◮ Goal : In the following we introduce the syntax of CCS step-by-step The simplest possible behavior is no behavior Terminal process We write 0 (pronounced “nil”) for the terminal or inactive process Basic principle 1. Define atomic processes that model the simplest possible behavior ◮ 0 models a system that is either deadlocked or has terminated 2. Define composition operators that build more complex behavior from ◮ 0 is the only atomic process of CCS simpler ones Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 7/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 8/44

Syntax of CCS Syntax of CCS Names and Actions Action Prefixing ◮ We assume an infinite set A of port names, and a set ¯ A = { ¯ a | a ∈ A} of complementary port names The simplest actual behavior is sequential behavior Action prefixing Input actions If P is a process we write When modeling we use a name a to denote an input action, i.e. the α. P receiving of input from the associated port a to denote the prefixing of P with the action α Output actions We use a co-name a to denote an output action, i.e. the sending of output to the associated port a ◮ α. P models a system that is ready to perform the action, α , and then behaves as P , i.e. Internal actions α α. P − → P We use τ to denote the distinguished internal action ◮ The set of actions Act is given by Act = A ∪ ¯ A ∪ { τ } Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 9/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 10/44 Syntax of CCS Syntax of CCS Example: Action Prefixing Process Interfaces Interfaces The set of input and output actions that a process P may perform in A process that starts a timer, performs some internal computation, and isolation constitutes the interface of P then stops the timer: ◮ The interface enumerates the ports that P may use to interact with go stop τ the environment go .τ. stop . 0 − → τ. stop . 0 − → stop . 0 − → 0 Example: The interface of the coffee and tea machine is: tea , coffee , coin , cup of tea , cup of coffee Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 11/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 12/44

Syntax of CCS Syntax of CCS Non-deterministic Choice Example: Non-deterministic Choice A more advanced sequential behavior is that of alternative behaviors Non-deterministic choice tea . coin . cup of tea . 0 + coffee . coin . coin . cup of coffee . 0 If P and Q are processes then we write tea − → coin . cup of tea . P + Q Note that: to denote the non-deterministic choice between P and Q ◮ prefixing binds harder than plus and ◮ the choice is made by the initial coffee / tea button press ◮ P + Q models a process that can either behave as P (discarding Q ) or as Q (discarding P ) Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 13/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 14/44 Syntax of CCS Syntax of CCS Process Constants and Recursion Example: Recursion (1) The most advanced sequential behavior is the recursive behavior Process constants A system clock, SC , sends out regular clock signals forever: A process may be the invocation of a process constant, K ∈ K SC def = tick . SC This is only meaningful if K is defined beforehand Recursive definition The system SC may behave as: If K is a process constant and P is a process we write tick tick tick . SC − → SC − → . . . K def = P to give a recursive definition of the behavior of K (recursive if P invokes K ) Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 15/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 16/44

Syntax of CCS Syntax of CCS Example: Recursion (2) Parallel Composition A fully automatic coffee and tea machine CTM works as follows: Finally: concurrent behavior CTM def Parallel composition = tea . coin . cup of tea . CTM + coffee . coin . coin . cup of coffee . CTM If P and Q are processes we write The system CTM may e.g. do: P | Q tea . coin . cup of tea . CTM + coffee . coin . coin . cup of coffee . CTM to denote the parallel composition of P and Q tea − → coin . cup of tea . CTM coin − → cup of tea . CTM ◮ P | Q models a process that behaves like P and Q in parallel: cup of tea − → CTM ◮ Each may proceed independently − α → . . . ◮ If P is ready to perform an action a and Q is ready to perform the complementary action a , they may interact This will serve drinks ad infinitum Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 17/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 18/44 Syntax of CCS Syntax of CCS Example: Parallel Composition Example: Parallel Composition Recall the coffee and tea machine: Recall the coffee and tea machine: CTM def CTM def = tea . coin . cup of tea . CTM + coffee . coin . coin . cup of coffee . CTM = tea . coin . cup of tea . CTM + coffee . coin . coin . cup of coffee . CTM Now consider the regular customer – the Computer Scientist, CS : Now consider the regular customer – the Computer Scientist, CS : CS def CS def = tea . coin . cup of tea . teach . CS = tea . coin . cup of tea . teach . CS + coffee . coin . coin . cup of coffee . publish . CS + coffee . coin . coin . cup of coffee . publish . CS ◮ CS must drink coffee to publish ◮ CS can only teach on tea Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 19/44 Bertrand Meyer Sebastian Nanz Concepts of Concurrent Computation 19/44