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CIS 720

This document explores the principles of correctness in concurrent programming, focusing on interference freedom and synchronization techniques. It outlines the Concurrency rules that govern concurrent processes, ensuring they operate without interfering with each other. Key concepts include non-interference assertions, disjoint variable sets, and the use of global invariants to maintain correct program execution. Also discussed are techniques to avoid interference, highlighting the importance of careful process design in banking transactions and similar applications.

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CIS 720

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  1. CIS 720 Correctness of Concurrent Programs

  2. i := 1 max := A[1] do i < n  i = i + 1 if (max < A[i]) max = A[i] od

  3. Concurrency rule for all i, { Pi } Si { Qi } { P1 /\ …. /\ Pn} co S1 // …. // Snoc { Q1 /\ …. /\ Qn}

  4. x = 0; y = 1; x = 0; co co x = 1 x = x + 1 // // y = y + 1 x = x + 2 oc oc

  5. Interference freedom • Let abe a statement and C be an assertion. • NI(a, C) iff { pre(a) /\ C } a { C } • Execution of a does not invalidates (or interferes) with C.

  6. { Pi } Si { Qi }, for all I, are interference free if • For all i for all assertions C in proof outline of Si, for all actions a in Sj, i != j NI(a, C) holds

  7. Concurrency rule { Pi } Si { Qi } are interference free { P1 /\ …. /\ Pn} co S1 // …. // Snoc { Q1 /\ …. /\ Qn}

  8. x= 0; co x = x + 1 // x = x + 2 od

  9. Bank transactions co // Transfer(x,y,am): Auditor: ac[x] = ac[x] – am; total = 0; i = 0; ac[y] = ac[y] + am do i < n total = total + ac[i] i = i + 1 od oc

  10. Bank transactions co // Transfer(x,y,am): Auditor: if < !auditon  ac[x] = ac[x] – am; auditon = 1; total = 0; i = 0; ac[y] = ac[y] + am > [] do i < n <auditon && ( (x < i && y < i) ||(x > I && y > i)) total = total + ac[i]  ac[x] = ac[x] – am; ac[y] = ac[y] + am> i = i + 1 fi od auditon = 0 oc

  11. Techniques to avoid interference • Disjoint variables • If the write set of each process is disjoint from the read and write set of other processes, then the proof outlines will be interference free.

  12. Avoiding interference • Weakened assertions x= 0; co x = x + 1 // x = x + 2 od

  13. Avoiding interference • Global Invariants: Assume that every assertion in the proof outline of Pi is of the form I /\ L, where L refers to local variables of Pi or to variables that only Pi writes. - Then the proof outlines will be interference free.

  14. Concurrency rule for all i, { I} Si { I } { I} co S1 // …. // Sn { I}

  15. Avoiding interference • Synchronization

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