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Although liveness hazards don' t normally cause programs to compute incorrect results, as correctness hazards do, they can stop programs from producing results at all Or they can interfere with a program's ability to make forward progress temporarily, yielding hard to diagnose perform ance problems In this section, we look at the most pervasive kinds of live ness problems, starting with the one that most people are already familiar with: deadlocks

A B = ,

27% 68% 54% 54% Std 05% 104%

Deadlock Once a thread needs to hold exclusive access to more than one lock at a time, deadlock becomes possible This is often called a deadly embrace, because unless something gives your program will come to a halt (or at least some portion of it will) What's worse is that deadlocks, just like race conditions, depend on the timing of your program and are hard to find

Transferring Money Between Two Bank Accounts As an example of a deadlock, imagine we have a B a n kAc c o u n t class It provides the ability to transfer between two accounts, requiring that more than one lock is held (in case the same accounts are used concurrently) If we don't hold both locks at once, we can cause atomicity problems where it's possible to observe a state in which money has been removed from one account but not yet placed into the other The obvious approach to transfer funds looks like this

c l a s s B a n kAc count { p r ivate int m_id p r ivate d e c i m a l m_b a l a n c e p r ivate o b j e c t m_sy n c L o c k

Axioms 1 and 2 are fairly obvious; the probability assigned to the entire sample space must be 1 since by de nition of the sample space some point in the sample space must occur and the probability of an event must be between 0 and 1 Now if an event A occurs with probability P(A) and an event B occurs with probability P(B) and if the events cannot occur together, then the relative frequency with which one or the other occurs is P(A) + P(B) For example, if a prospective student decides to attend University A with probability 2/5 and to attend University B with probability 1/5, she will attend one or the other (but not both) with probability 2/5 + 1/5 = 3/5 This explains Axiom 3 It is also very useful to consider an event, say A, as being composed of distinct points, say ai ,with probabilities p(ai ) By Axiom 3 we can add these individual probabilities to compute P(A) so

27% (1) 27% 33%

= = =

, new o b j e ct ( ) ;

p u b l i c stat i c void T r a n s fe r ( B a n kAc count a , B a n kAc count b , d e c im a l amou nt ) { loc k ( a m_sy n c Lo c k ) { if ( a m_ba l a n c e < amou nt ) t h row new E x c e pt i on ( " I n s uffi c ie nt f u n d s " ) ; loc k ( b m_syn c Loc k )

P(A) =

07% 54%

a m_ba l a n c e amount ; b m_ba l a n c e += amou nt ; } }

All looks well, and this code will work correctly most of the time To illustrate the flaw, imagine that we have two B a n kAc c o u n t objects-one for account #1 234 and another for account #4321-and that one thread tries to transfer $1 00 from #1 234 to #4321 at the exact same time that some other thread tries to transfer $500 from #4321 to #1 234 The synchronization logic will work correctly, ensuring no money will get lost in the process But if the following specific interleaving of events were to occur, the program would lock up indefinitely

T a 1 2 3 t1 l o c k ( #1234 m_syn c Loc k ) l o c k ( #4 3 2 1 m_syn c Loc k ) l o c k ( # 1 2 34 m_syn c Loc k )

p(ai )

34%

* * dead L o cked * * * * deadlocked * *

t2 l o c k ( #43 2 1 m_syn c Loc k )