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This research by Prof. Dr. Holger Schlingloff investigates the challenges of parallelism, particularly with multicore processors and multithreading in C. It delves into synchronization issues that make parallel programming complex and error-prone. The study introduces new constructs to the language of while-programs, enabling clearer expression of parallel execution and atomic actions. Through illustrative examples and interleaving semantics, the work addresses deadlocks and invariants in parallel programs, contributing to safer and more reliable software verification methods.
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Software Verification 1Deductive Verification Prof. Dr. Holger Schlingloff Institut für Informatik der Humboldt Universität und Fraunhofer Institut für Rechnerarchitektur und Softwaretechnik
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
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
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;}}
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--}
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
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)
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: }
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;}
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
