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CSP Communicating Sequential Processes Prabhaker Mateti

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CSP Overview Models distributed computing – primitives: send/receive only – no shared variables (across outer processes) Idealistic send/receive – no buffering – sending a value from one process and the receiving of that value in another process appears externally as one event

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CSP Synchronous Message Passing Send ! – ex: R ! (x*y + c) – to process R send the value of expression x*y + c – sender names the receiving process R – waits until receiver R is ready to receive Receive ? – ex: S ? v – receiver names the sender process S – names the receptacle v a variable declared to be a compatible type – waits until sender S is ready to send Deadlock is possible

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G1 S1 [] G2 S2 []...[] Gn Sn Gi must not have sends Gi can include at the tail a receive Example: val > 0; Y?P() Q – Suppose val = 0. The above input is not attempted. – Suppose val > 0, but Y is not ready to send. Then, we are not committed to perform this input. – Suppose val > 0, and Y is ready to send. Then, we perform this input, and execute Q.

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Additional CSP Notation NotationComments :=assignment C1; C2Sequential composition: C2 after C1 C1 || C2Simult parallel; not C1; C2 or C2;C1 C2 || C1Same as C1 || C2 if G1 S1 [] G2 S2 []...[] Gn Sn fiIf statement; Hoare used [ …]; [] is fat bar do G1 S1 [] G2 S2 []...[] Gn Sn odLoop; Hoare used *[ … ] Multiple Gi can be true; non-determinism SkipDo-nothing (no-op) statement ;Also used to end declarations

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Small Set of Integers Design a server that can provide the abstraction of a Small Set of Integers Make it as distributed as possible Make it as symmetric as possible Simplifying Assumptions – Finite, say 100 integers – any/all integers can be elements – query “have you got x” replied with Boolean – request “insert x”, no replies if duplicate, no problem if ran out of room, problem … but silently discard

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Small Set of Integers: Design An array S of 102 processes S(i: ) – each process holds an integer or is empty-handed – S(i) has an integer implies S(i-1) also has an integer integer of S(i-1) < integer of S(i) S(101) is a sink S(0) is the “receptionist”

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Small Set of Integers S(i: ) :: do n: integer; S(i-1)?has(n) S(0)!false [] n: integer; S(i-1)?insert(n) do m: integer; S(i-1)?has(m) if m <= n S(0)!(m = n) [] m > n S(i+1)!has(m) fi [] m: integer; S(i-1)?insert(m) if m < n S(i+1)!insert(n); n := m [] m = n skip [] m > n S(i+1)!insert(m) fiod

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Small Set of Integers: S(i) do n: integer; S(i-1)?has(n) S(0)!false [] n: integer; S(i-1)?insert(n) do m: integer; S(i-1)?has(m) if m <= n S(0)!(m = n) [] m > n S(i+1)!has(m) fi [] m: integer; S(i-1)?insert(m) if m < n S(i+1)!isrt(n); n := m [] m = n skip [] m > n S(i+1)!insert(m) fi od Each S(i) starts out empty handed Any has(whatever) is replied with false. The first inserted value is saved in n After the first insert, the process spends its life in the second loop. Note: we have no breaks or exits.

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Small Set of Integers: has(m) do n: integer; S(i-1)?has(n) S(0)!false [] n: integer; S(i-1)?insert(n) do m: integer; S(i-1)?has(m) if m ≤ n S(0)!(m = n) [] m > n S(i+1)!has(m) fi [] m: integer; S(i-1)?insert(m) if m < n S(i+1)!isrt(n); n := m [] m = n skip [] m > n S(i+1)!insert(m) fi od processes are arranged in a “row” – 0 index at left, 101 at right S(i-1)?has(m) (black color) implies – S(i) is not empty handed – S(i-1) does not have m n is the number S(i) is holding elements are sorted from l-to-r m = n: we have it m < n: no one else has m either reply to the receptionist S(0)

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Small Set of Integers: insert(m) do n: integer; S(i-1)?has(n) S(0)!false [] n: integer; S(i-1)?insert(n) do m: integer; S(i-1)?has(m) if m <= n S(0)!(m = n) [] m > n S(i+1)!has(m) fi [] m: integer; S(i-1)?insert(m) if m < n S(i+1)!isrt(n); n := m [] m = n skip [] m > n S(i+1)!insert(m) fi od no S(j) has m (j < i) Case m = n – request to insert a duplicate element – do nothing Case m > n – to be inserted m is higher – ask S(i+1) to insert m Case m < n – the number n held by S(i) is higher – ask neighbor S(i+1) to hold n – S(i) now holds m

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Small Set of Integers: S(0) and S(101) S(101) is a sink S(101) :: do S(100)?has(m) S(0)!false [] S(100)?insert(m) skip od S(0) is the “receptionist” S(0) :: do Client ?has(n) S(1)!has(n); if (i: l.. 100) S(i)? b Client ! b fi [] Client ? insert(n) S(1)?insert(n) od

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Small Set of Integers: Questions Does “distributed” mean “concurrent” and/or “parallel” How do we delete? Can we redesign this into a lossless set of integers?

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Matrix Multiplication

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[ M(i: 1..3,0) ::WEST || M(0, j: 1..3) ::NORTH || M(i: 1..3,4) ::EAST || M(4, j: 1..3) ::SOUTH || M(i: 1..3, j: 1..3)::CENTER ] Declarations omitted for clarity NORTH = do true M(1, j)!0 od EAST = do M(i,3)?x skip od CENTER = do M(i, j - 1)?x M (i, j+1)!x; M (i-1, j)?sum; M (i+1, j)!(A (i, j)*x+sum) od

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Sieve of Eratosthenes Print all primes less than – 2, 3, 5, 7, 11, 13, … Design – Use an array SIEVE of processes – SIEVE(i) filters multiples of i-th prime – sqrt(10000) processes are needed – SIEVE(0) and SIEVE(101)

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Sieve of Eratosthenes [SIEVE(i: ):: SIEVE( i - 1)?p; print ! p; mp := p; do SIEVE(i - 1)? m do m > mp --> mp := mp + p od; if m = mp --> skip [] m SIEVE(i + l)!m fi od || SIEVE(0):: print!2; n := 3; do n SIEVE(1)!n; n := n + 2 od || SIEVE(101):: do SIEVE(100)?n --> print ! n od || print:: do (i: ) SIEVE(i)?n -->.“print-the-number” n od ]

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Shared Variables Duality: variables v. processes – Provide a “shared variable” V as a process V – User processes do: V ! expequiv of V := exp V ? uequiv of u := V, u local to this process semaphores, by intention, are shared variables.

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Semaphores in CSP S:: val: integer; val := 0; /* or any +int */ do (i:I..100)X(i)?V() val := val + 1 II(i:l..100) val > 0; X(i)?P() val := val - 1 od Within the loop: (unnamed) processes these 200 processes share the integer val yet there is no mutex problem here; why? Array X of 100 client processes can do – S!P() or S!V()

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Buffered Message Passing CSP send/receive have no buffering == Synchronous Message Passing A Buffer process can be inserted between the (original) sender and (original) receiver. This gives a Semi Asynchronous Message Passing. – Sends do not block (until the Buffer becomes full)

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Modeling Remote Proc Call RPC client server ! proc5(e1, e2); server? proc5(r1, r2, r3) RPC Server do… [] client?proc4(…) … [] client?proc5(v1, v2) … client!proc5(e3, e4, e5) [] … od

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Fairness [ X:: Y!stop() ll Y:: c := true; do c; X?stop() c := false [] c n := n + 1 od ] Will/Must this terminate? We (programmers) should not assume fairness in the implementation

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Process Algebras mathematical theories of concurrency Events – on, off, valve.open, valve.close, mouse?(x,y), screen!bitmap Primitive processes – STOP (communicates nothing), – SKIP (represents successful termination) Event Prefix: e P Deterministic Choice Nondeterministic Choice Interleaving Interface Parallel Hiding has an entire book by Hoare

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CSP Implementations Occam is based on CSP – Machine Lang of Transputer CPU, 1990s – Andrews book, Section 10.x CSP in Java == JCSP Software Release at a/jcsp/ a/jcsp/ Communicating Process Architectures Conference == CPA CSP in Jython and Python, CPA 2009 Limbo, Newsqueak are prog langs from Bell Labs, included in the Inferno OS, 2004 Concurrent Event-driven Programming in occam-π for the Arduino, CPA 2011 Experiments in Multi-core and Distributed Parallel Processing using JCSP, CPA 2011 LUNA: Hard Real-Time, Multi- Threaded, CSP-Capable Execution Framework, CPA 2011

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CSP References C. A. R. Hoare, ``Communicating Sequential Processes,'' Communications of the ACM, 1978, Vol. 21, No. 8, – has an entire book by Hoare. – For now, do not read it (!!) Andrews, Chapter on Synchronous Message Passing. U of Kent, CSP for Java (JCSP),

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