1 / 34

Process Algebra

Process Algebra. Hossein Hojjat Formal Methods Lab University of Tehran. Introduction. The lambda calculus models the functional computation completely Lambda calculus is unique: There is only one way to observe a functional computation

Leo
Download Presentation

Process Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Process Algebra Hossein Hojjat Formal Methods Lab University of Tehran Advanced Topics in SE Spring 2006

  2. Introduction • The lambda calculus models the functional computation completely • Lambda calculus is unique: There is only one way to observe a functional computation • watch which output values yields when presented with different input values • But the concurrent computation is not neat as functional • There are many aspects to concurrent programming Advanced Topics in SE Spring 2006

  3. Introduction (cont.) • Concurrent systems can be described in terms of many different constructs • For creating processes • fork/wait • cobegin/coend, etc. • Exchanging information between processes • shared memory • rendezvous • message-passing • data flow, etc. Advanced Topics in SE Spring 2006

  4. Introduction (cont.) • For managing the shared resources • semaphores • monitors • transactions • This variability has rise to a large class of formal systems: Petri nets, event structures, actor model,… • In the process algebra approach every thing is considered to be a process Advanced Topics in SE Spring 2006

  5. Introduction (cont.) • We need not distinguish between • active components like senders and receivers • passive components such as communication media • All of the processes interact via synchronous message passing • This is the only basic mode of interaction Advanced Topics in SE Spring 2006

  6. Process Algebra • Process • A behavior of a system • A system is anything showing behavior • Software system, actions of a machine, etc. • Algebra • We take an algebraic/axiomatic approach in talking about processes • By using axioms, we can perform calculations with processes Advanced Topics in SE Spring 2006

  7. Process Algebra: Automata Theory Extension • An automata has a number of states and a number of transitions • There are some initial and final states • A behavior is a run: a path from initial state to final state • Two automata are equivalent when their languages are equal Advanced Topics in SE Spring 2006

  8. Process Algebra: Automata Theory Extension (cont.) • The automata model lacks the notion of interaction • During the execution from initial to final state, a system may interact with other systems • This is needed in modeling the reactive systems Advanced Topics in SE Spring 2006

  9. Well Known Process Algebras • In the early eighties, Milner introduced CCS, Hoare introduced CSP and Bergstra introduced ACP • π calculus: In 1989, Milner extended CCS to take full advantage of named channels • PEPA(Performance Evaluation Process Algebra): a stochastic process algebra • Ambient calculus: a process calculus used to describe and theorize about concurrent systems that include mobility Advanced Topics in SE Spring 2006

  10. CCS • The Calculus of Communicating Systems (or CCS) is a process calculus developed by Robin Milner • This lecture mainly focus on the CCS process algebra Advanced Topics in SE Spring 2006

  11. The language CCS • Processes are called agents, built from a set of actions • Actions can be: • Observable, represented by letters a, b, etc. • Unobservable (silent), marked by τ • Observable actions • a, b, … input actions • a, b,… output actions • Input action a and output action a are complementary Advanced Topics in SE Spring 2006

  12. The language CCS (cont.) • If a means the reception of message a from the “in” port, the action a denotes the writing of the message to the “out” port • The following identity describes how the complementation of messages works • a = a • The most basic operator is 0 (read nill) • Performs no action whatsoever Advanced Topics in SE Spring 2006

  13. Operations • Agents may be constructed by employing process algebraic operations on other agents • There are primarily five different methods of constructing agents • Action prefixing • Choice operator • Parallel composition • Restriction • Relabeling Advanced Topics in SE Spring 2006

  14. a → Action Prefixing • The most basic process constructor in CCS is action prefixing • If a is an action and P is a process, then a.P is a process • The "." here is called "action prefixing" and denotes sequentialization • P becomes active only after the action a has been performed • a.P P Advanced Topics in SE Spring 2006

  15. Example def Match =strike.0 def CM =coin.coffee.CM def Clock=tick.Clock Advanced Topics in SE Spring 2006

  16. Choice Operator • If P and Q are processes, then so is P + Q • The process P + Q has the initial capabilities of both P and Q • Choosing to perform initially an action from P will preempt the further executions of actions from Q, and vice versa Advanced Topics in SE Spring 2006

  17. CTM=coin.(coffee.CTM+ tea.CTM) Example • After having input a coin, the process CTM is willing to deliver either tea or coffee • It depends upon the customer’s choice tea coffee Advanced Topics in SE Spring 2006

  18. α α α α α τ α → → → → → → → Parallel Composition • Let Q and R be processes, (Q | R) is a process • The semantics of parallel composition: 1. If MM’, and N cannot perform α, then M | NM’ | N 2. If NN’ and M cannot perform α, then M | NM | N’ 3. If MM’, and NN’, then M | NM’ | N’ Advanced Topics in SE Spring 2006

  19. Example def CM =coin.coffee.CM def CS =pub.coin.coffee.CS CS | CM Advanced Topics in SE Spring 2006

  20. Communication • The computer scientist and coffee machine may communicate via the ports • Given two CCS expression P and Q, the process P | Q describes a system which • P and Q may proceed independently • May communicate via complementary ports Advanced Topics in SE Spring 2006

  21. Example CM CS coffee pub coffee CM | CS coin coin CM CS coffee pub coffee coin CM|CS|CS’ coin CS’ coffee pub coin Advanced Topics in SE Spring 2006

  22. α α → → Restriction • Let Q be a process and Σ be a set of visible actions, τ Σ. Then (Q) \ Σ is a process • If Q Q’ and α Σ, α Σ, then ((Q) \ Σ) ((Q’) \ Σ) • Process (Q) \ Σ is like Q, but it cannot execute actions in the set Σ or their complement actions • The scope of port names in Σ is restricted to Q Advanced Topics in SE Spring 2006

  23. Example CM CS ((CM|CS)\coin\coffee)|CS’ pub CS’ coffee pub coin Advanced Topics in SE Spring 2006

  24. m(α) → α → Relabeling • Let Q be an agent and Σ the set of its visible actions, τ Σ • Let Σ’ be a set of actions and let m: ΣU {τ }→ ΣU {τ’ } such that m(τ) = τ and α ≠ τ : m(α)=m(α). Then P ::= Q[m] is a process • If QQ’ then Q[m] Q’[m] • Process P is like Q, but it actions have obtained by mapping the actions Q through m Advanced Topics in SE Spring 2006

  25. Example VendingMachine =coin.item.VendingMachine def CokeMachine =VendingMachine[coke/item] def CoffeeMachine =VendingMachine[coffee/item] Advanced Topics in SE Spring 2006

  26. Algebraic Operator Precedence • 1. Restriction and relabeling “P\L” “P[f]” • 2. Action prefixing “α.P” • 3. Parallel composition “P|Q” • 4. Summation “P+Q” • Q: How is “R+a.P|b.Q\L” then to be read ? • A: “R+((a.P)|(b.(Q\L)))” ! tightest Advanced Topics in SE Spring 2006

  27. Semantics 1. Operational Semantics • Specifies the behavior of a programming language by defining a simple abstract machine for it 2. Denotational Semantics • Map programs to denotations • Denotations are abstract representations details 3. Axiomatic Semantics • Instead of first defining the behaviors of programs and then deriving laws from this definition, take the laws themselves as the definition of the language Advanced Topics in SE Spring 2006

  28. SOS • Structural Operational Semantics • Developed by Gordon Plotkin in 1981 • Represents computation by means of deductive systems • These systems turn the abstract machine into a system of logical interferences • With SOS semantics definitions are given by inference rules Advanced Topics in SE Spring 2006

  29. Inference • Inference rule consists of a conclusion that follows from a set of premises, possibly under control of some conditions premise1 premise2 … premisen condition conclusion Advanced Topics in SE Spring 2006

  30. α α.P P α α P P’ Q Q’ α α P | Q P’ | Q P | Q P | Q’ P P’ α P + Q P’ SOS of CCS • The prefix is the only axiom in the system • The parallel composition requires two symmetric rules: • So as choice operator: α α Q Q’ α P + Q Q’ Advanced Topics in SE Spring 2006

  31. SOS of CCS (cont.) • Communication may happen when compatible prefixes are allowed • Restriction and relabeling rule α α P P’ Q Q’ τ P | Q P’ | Q’ α P P’ α, α’  L α P \ L P’ \ L α P P’ f(α) P [ f ] P’ [ f ] Advanced Topics in SE Spring 2006

  32. Labeled transition system • SOS formally defines for each process term the labeled transition system that it stands for • A labeled transition system (LTS) is a triple (S, Act, →) consisting of • a set S of states • a set Act of (action) labels • a transition relation →  S×Act× S • if (s,α,s’)  → we write ss’ α Advanced Topics in SE Spring 2006

  33. Example • C0=is_0? . C0 + set_1 . C1 + set_0 . C0 • C1=is_1? . C1 + set_0 . C0 + set_1 . C1 set_1 C0 C1 set_0 is_0? set_1 is_1? set_0 Advanced Topics in SE Spring 2006

  34. Next session • simulation • bisimulation • branching bisimulation Advanced Topics in SE Spring 2006

More Related