Lec13_FXStudy_Interference - Illinois Institute of...

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Interference CS 536 Notes, Lecture 13, Mon Nov 29, 2010 A. Why Shared memory parallel programs can interfere with each other. We want to Fnd a way to guarantee that combining sequential threads won’t cause interference. B. Outcomes After this lecture, you should Know what will be covered on the ±inal Exam. Know how to check for interference between the correctness proofs of the sequential threads of a shared memory parallel program. A. Final Exam Study Guide ±inal Exam: Monday December 6, 7:30 – 9:30 pm. Comprehensive exam (All percentages ²5%): 10% Quiz 1 material 10% Midterm (but not Quiz 1) material 30% Quiz 2 material 50% material since Quiz 2. This include expanding a partial proof outline to a full proof outline. Material Since Quiz 2 Given a partial proof outline, expand it to a full proof outline. Given a partial proof outline of a loop, Fnd a loop bound and give the extra conditions needed to show termination. (Or, expand the whole thing into a full outline.) Below, each starred section will have roughly the same number of points on the exam. Rough = anywhere from 5 to 15 points. ±ind an invariant By replacing a constant by a variable. Hint: Check manifest constants (e.g. 2) and named constants (does it change during the run of the program?) By dropping a (single) conjunct. Hint: Don’t forget that iterated relation tests are conjunctions: (a = b = c) is equivalent to (a = b b = c) . By adding a disjunct (our example took “=” to “ ”). Illinois Institute of Technology Notes for Lecture 13 CS 536: Science of Programming - 1 of 10 - © James Sasaki, 2010
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Array Assignments wp ( b[ e ]:= e , P ) involves substitution P [ e / b[ e ] ], which involves e [ e / b[ e ] for a general expression e . Calculating P [ e / b[ e ] ]: Easy case: e doesn’t contain b : then P [ e / b[ e ] ] is just P . Example: ( y[5] x )[ e / b[ e ] ] is y[5] x . Fairly easy case: e doesn’t contain b and P contains b[ e ] . (Note: the same subscript as on the l.h.s. of the assignment.) Then replace the b[ e ] inside P by e . Example: ( 2 * b[z+1] y )[ e / b[z+1] ] is 2 *( e ) y . General case: ( b[ e ] )[ e / b[ e ] ] is if e ₃′ = e then e else b[ e ₃′ ] fi , where e ₃′ is e [ e / b[ e ] ]. Example: ( y + b[y] z )([ b[y/2] / b[z+1] ]) is (y + (if y = z+1 then b[y/2] else b[y] fi) z) It can be helpful to statically simplify predicates involving conditional expressions. E.g., we can replace if B then e else e fi by just e . Evaluation Graphs for Parallel Programs; Disjoint Parallel Programs
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Lec13_FXStudy_Interference - Illinois Institute of...

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