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Software Verification 1 Deductive Verification

Software Verification 1 Deductive Verification. Prof. Dr. Holger Schlingloff Institut für Informatik der Humboldt Universität und Fraunhofer Institut für Rechnerarchitektur und Softwaretechnik. Research is calling. Parallelism. increasing importance (multicore processors)

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Software Verification 1 Deductive Verification

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  1. Software Verification 1Deductive Verification Prof. Dr. Holger Schlingloff Institut für Informatik der Humboldt Universität und Fraunhofer Institut für Rechnerarchitektur und Softwaretechnik

  2. Research is calling...

  3. Parallelism • increasing importance (multicore processors) • in C, parallelism by multithreading • POSIX: pthread_create (name, function, args) • pthread_join, pthread_exit, ... • key issue: synchronization • hard to understand, error-prone

  4. Concept Language • we add the following new constructs to the language of while-programs • { 1 || 2 } or, more generally, { 1 || ... || n } • await (b) ; • semantics • parallel (interleaved) execution of the i • blocking wait until condition is satisfied; program fragment within await is noninterruptable • for simplicity, assignments are atomic actions

  5. Examples • int n=0; { for (int i = 0; i<100; i++) n++;|| for (int i = 0; i<100; i++) n--;} • int n=0; int l, r; {for (int i = 0; i<100; i++) {l=n; l++; n=l;}|| for (int i = 0; i<100; i++) {r=n; r--; n=r;}} • int n=0; {for (int i = 0; i<100; i++) await (1) {l=n; l++; n=l;}|| for (int i = 0; i<100; i++) await (1) {r=n; r--; n=r;}}

  6. More Examples • a=0; {a*=a; a-=5; || a=2*a+3; a=1-a;} • a=0; {a++; || a--;} • {a=0; a++; || a=0; a--} • a=0; {await (a>=0); a++; || await (a<=0); a--} • a=0; {await (a>=0) a++; || await (a<=0) a--}

  7. A realistic example a=n; b=0; c=1; { while (a!=n-k) {c=c*a; a--;} || while (b!=k) {b++; await (a+b<=n); c=c/b;} } program calculates binomial coefficient

  8. Interleaving Semantics • A state of the program consists of • an assignment of values to variables • a set of program counters (depending on the number of parallel components), and • SOS-rules for parallel programs • if (U,I,V) ⊨ b and (, V)* (skip,V’), then (await (b) , V) (skip,V’) • if (1, V) (1’,V’), then ({1 ||  2}, V) ({1’ || 2},V’)if (2, V) (2’,V’), then ({1 ||  2}, V) ({1 || 2’},V’)({skip || skip}, V) (skip,V) • In general, several possible executions! (tree of possibilities)

  9. A realistic example a=n; b=0; c=1; :{ 1: while (a!=n-k) { 2: c=c*a; 3: a--; } 4: || 1: while (b!=k) { 2: b++; 3: await (a+b<=n); 4: c=c/b; } 5: }

  10. Deadlocks • a=0; b=0;{await (a!=0) || await (b!=0)} • a=0; b=0;{await (a==1) b=1 || await (b==1) a=1} • prt=T; dsk=T;{await (prt) prt=F; await(dsk) dsk=F; foo; prt=T; dsk=T; || await (dsk) dsk=F; await(prt) prt=F; bar; prt=T; dsk=T;}

  11. Invariants for Parallel Programs • Assume  is a formula such that {}  {}for every subprogram  of { 1 || 2 }.Then {}{ 1 || 2 }{} • Example:a=0; : {a++; : || a--; :} : Invariant a==0+- (or, more explicit: (¬¬a==0  a==0  ¬a==1  ¬a==-1) ) • int n=0; { for (int i = 0; i<100; i++) n++;|| for (int j = 0; j<100; j++) n--;} Invariant n=i-j

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