Overview

1. Ilias quiz
2. Summary:
   • (Resource) Deadlock
   • Lock Graphs
   • Lock Dependencies
3. Examples

Summary

(Resource) Deadlock

A group of threads, each of which is blocked trying to acquire a lock held by another.

Lock Graphs

Graph: nodes with (directed) edges between.

Lock graph of a given trace:

• Locks used in the trace are nodes.
• An edge $x \rightarrow y$ means that a thread acquires $y$ after acquiring and before releasing $x$ (“while holding $x$”).
• Deadlock prediction when there is a cycle in the graph: $x_1 \rightarrow x_2 \rightarrow \ldots \rightarrow x_n \rightarrow x_1$.

Efficient, but problematic false positives (cycles from a single thread, guard locks).

Lock Dependencies

Improves over lock graphs by accounting for threads and guard locks.

Lock dependencies of a given trace:

• A “lock dependency” $(t , x , \{y_1,\ldots,y_k\})$ denotes that thread $t$ acquires $x$ while holding locks $y_1,\ldots,y_k$.
• Deadlock prediction when:
  • Cycle among lock dependencies: $(t_a , x_a , LS_a = \{\ldots,x_b,\ldots\}) \rightarrow (t_b , x_b , LS_b = \{\ldots,x_c,\ldots\}) \rightarrow \ldots \rightarrow (t_z , x_z , LS_z = \{\ldots,x_a,\ldots\})$.
  • All from distinct threads: $t_a \neq t_b \neq \ldots \neq t_z$.
  • No guard locks: $LS_a \cap LS_b \cap \ldots \cap LS_z = \emptyset$.

Better than lock graphs, but still false positives (cross-thread critical sections)… We’re still searching for better solutions!

Examples

Example 1

     T1       T2     T3     T4

e1.  fork(T4)
e2.  fork(T3)
e3.  fork(T2)
e4.           acq(x)
e5.           acq(y)
e6.           wr(b)
e7.           rel(y)
e8.                  acq(y)
e9.                  wr(a)
e10.                 wr(b)
e11.                 rel(y)
e12.          acq(y)
e13.          rd(b)
e14.          rel(y)
e15.          rel(x)
e16.                        acq(x)
e17.                        acq(y)
e18.                        rd(a)
e19.                        rel(y)
e20.                        rel(x)
e21.                        wr(c)

Solution

Lock graph:

• $x \rightarrow y$

No cycle, so no deadlock predicted.

Lock dependencies:

• $(T2,y,\{x\})$
• $(T4,y,\{x\})$

No cycle, so no deadlock predicted.

True negative.

Example 2

     T1       T2     T3     T4

e1.  fork(T4)
e2.  fork(T3)
e3.  fork(T2)
e4.           acq(x)
e5.           acq(y)
e6.           wr(b)
e7.           rel(y)
e8.                  acq(y)
e9.                  wr(a)
e10.                 wr(b)
e11.                 rel(y)
e12.          acq(y)
e13.          rd(b)
e14.          rel(y)
e15.          rel(x)
e16.                        acq(y)
e17.                        acq(x)
e18.                        rd(a)
e19.                        rel(x)
e20.                        rel(y)
e21.                        wr(c)

Solution

Lock graph:

• $x \rightarrow y$
• $y \rightarrow x$

Cycle, so deadlock predicted.

Lock dependencies:

• $(T2,y,\{x\})$
• $(T4,x,\{y\})$

Cycle, so deadlock predicted.

False positive: last-write.

Example 3

     T1       T2     T3     T4

e1.  fork(T4)
e2.  fork(T3)
e3.  fork(T2)
e4.           acq(x)
e5.           acq(y)
e6.           wr(b)
e7.           rel(y)
e8.                  acq(z)
e9.                  wr(a)
e10.                 wr(b)
e11.                 rel(z)
e12.          acq(y)
e13.          rd(b)
e14.          rel(y)
e15.          rel(x)
e16.                        acq(z)
e17.                        acq(x)
e18.                        rd(a)
e19.                        rel(x)
e20.                        rel(z)
e21.                        wr(c)

Solution

Lock graph:

• $x \rightarrow y$
• $z \rightarrow x$

No cycle, no deadlock predicted.

Lock dependencies:

• $(T2,y,\{x\})$
• $(T4,x,\{z\})$

No cycle, no deadlock predicted.

Appears to be a false negative: ~~~ T1 T2 T3 T4

e1. fork(T4) e2. fork(T3) e3. fork(T2) e4. acq(x) e16. acq(z) e5. acq(y) e6. wr(b) e7. rel(y) e8. B-acq(z) e12. acq(y) e13. B-rd(b) e17. B-acq(x) ~~~ Not a resource deadlock: T2 not blocked on a lock acquire!