**Remark:**
Tannenbaum use the term semaphore *only*
for blocking solutions.
I will use the term for our busy waiting solutions.
Others call our solutions *spin locks*.

The entry code is often called P and the exit code V. Thus the critical section problem is to write P and V so that

loop forever P critical-section V non-critical-sectionsatisfies

- Mutual exclusion.
- No speed assumptions.
- No blocking by processes in NCS.
- Forward progress (my weakened version of Tanenbaum's last condition).

Note that I use indenting carefully and hence do not need (and sometimes omit) the braces {} used in languages like C or java.

A **binary semaphore** abstracts the TAS solution we gave
for the critical section problem.

- A binary semaphore S takes on two possible values ``open'' and ``closed''.
- Two operations are supported
- P(S) is
while (S=closed) {} S<--closed <== This is NOT the body of the while

where finding S=open and setting S<--closed is*atomic* - That is, wait until the gate is open, then run through and atomically close the gate
- Said another way, it is not possible for two processes doing P(S) simultaneously to both see S=open (unless a V(S) is also simultaneous with both of them).
- V(S) is simply S<--open

The above code is *not* real, i.e., it is *not* an
implementation of P. It is, instead, a definition of the effect P is
to have.

To repeat: for any number of processes, the critical section problem can be solved by

loop forever P(S) CS V(S) NCS

The only specific solution we have seen for an arbitrary number of processes is the one just above with P(S) implemented via test and set.

**Remark**: Peterson's solution requires each process to
know its processor number. The TAS soluton does not.
Moreover the definition of P and V does not permit use of the
processor number.
Thus, strictly speaking Peterson did not provide an implementation of
P and V.
He did solve the critical section problem.

To solve other coordination problems we want to extend binary semaphores.

- With binary semaphores, two consecutive Vs do not permit two subsequent Ps to succeed (the gate cannot be doubly opened).
- We might want to limit the number of processes in the section to 3 or 4, not always just 1.

Both of the shortcomings can be overcome by not restricting ourselves
to a *binary* variable, but instead define a
**generalized** or **counting** semaphore.

- A counting semaphore S takes on non-negative integer values
- Two operations are supported
- P(S) is
while (S=0) {} S--

where finding S>0 and decrementing S is*atomic* - That is, wait until the gate is open (positive), then run through and atomically close the gate one unit
- Another way to describe this atomicity is to say that it is not possible for the decrement to occur when S=0 and it is also not possible for two processes executing P(S) simultaneously to both see the same necessarily (positive) value of S unless a V(S) is also simultaneous.
- V(S) is simply S++

These counting semaphores can solve what I call the
*semi-critical-section problem*, where you premit up to k
processes in the section. When k=1 we have the original
critical-section problem.

initially S=k loop forever P(S) SCS <== semi-critical-section V(S) NCS

- Two classes of processes
- Producers, which produce times and insert them into a buffer.
- Consumers, which remove items and consume them.

- What if the producer encounters a full buffer?

Answer: It waits for the buffer to become non-full. - What if the consumer encounters an empty buffer?

Answer: It waits for the buffer to become non-empty. - Also called the
**bounded buffer**problem.- Another example of active entities being replaced by a data structure when viewed at a lower level (Finkel's level principle).

Initially e=k, f=0 (counting semaphore); b=open (binary semaphore) Producer Consumer loop forever loop forever produce-item P(f) P(e) P(b); take item from buf; V(b) P(b); add item to buf; V(b) V(e) V(f) consume-item

- k is the size of the buffer
- e represents the number of empty buffer slots
- f represents the number of full buffer slots
- We assume the buffer itself is only serially accessible. That is,
only one operation at a time.
- This explains the P(b) V(b) around buffer operations
- I use ; and put three statements on one line to suggest that a buffer insertion or removal is viewed as one atomic operation.
- Of course this writing style is only a convention, the enforcement of atomicity is done by the P/V.

- The P(e), V(f) motif is used to force ``bounded alternation''. If k=1 it gives strict alternation.

Busy wait | block/switch | |
---|---|---|

critical | (binary) semaphore | (binary) semaphore |

semi-critical | counting semaphore | counting semaphore |

Busy wait | block/switch | |
---|---|---|

critical | enter/leave region | mutex |

semi-critical | no name | semaphore |

A classical problem from Dijkstra

- 5 philosophers sitting at a round table
- Each has a plate of spaghetti
- There is a fork between each two
- Need two forks to eat

- The obvious solution (pick up right; pick up left) deadlocks.
- Big lock around everything serializes.
- Good code in the book.

The purpose of mentioning the Dining Philosophers problem without giving the solution is to give a feel of what coordination problems are like. The book gives others as well. We are skipping these (again this material would be covered in a sequel course). If you are interested look, for example, here.

**Homework:** 31 and 32 (these have short answers but are
not easy). Note that the problem refers to fig. 2-20, which is
incorrect. It should be fig 2-33.

- Two classes of processes.
- Readers, which can work concurrently.
- Writers, which need exclusive access.

- Must prevent 2 writers from being concurrent.
- Must prevent a reader and a writer from being concurrent.
- Must permit readers to be concurrent when no writer is active.
- Perhaps want fairness (e.g., freedom from starvation).
- Variants
- Writer-priority readers/writers.
- Reader-priority readers/writers.

Quite useful in multiprocessor operating systems and database systems. The ``easy way out'' is to treat all processes as writers in which case the problem reduces to mutual exclusion (P and V). The disadvantage of the easy way out is that you give up reader concurrency. Again for more information see the web page referenced above.