Deadlock 2026-10-14
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A group of participants cannot proceed because each waits for a resource whose release depends on another participant in the group. Consider two initially free mutex objects A and B. T1 acquires A then tries B; T2 acquires B then tries A. If each obtains its first mutex, both wait permanently for the other, with release reachable only after the second acquisition. Each mutex still enforces mutual exclusion.[ref]
Figure 1.
Reachable states for opposite mutex acquisition orders and for one shared lock ordering
. Details.
Each software thread performs four indivisible operations: acquire its first mutex, acquire its second, release the second, release the first. An unavailable acquisition blocks; neither participant releases early. A state records each participant's completed-operation count and both owners. Exhaustive exploration finds 19 reachable states with opposite orders, including exactly one nonterminal state with no enabled operation: both counts are , T1 owns A, and T2 owns B. Giving both participants the order A then B leaves 16 reachable states and no such blocked state. Unshown grid positions are unreachable. These are tiny sequential consistency models, without timeouts, cancellation, recursive acquisition or other resources.
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Past exam of the computer science course of the University of Oxford / 2015 / Concurrent programming / 3 / b / iii / Solution 2026-10-31
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A FIFO semaphore must reserve a released permit for the oldest waiter. Merely waking the oldest caller is insufficient if a newcomer can consume the permit first. Keep an explicit FIFO queue of private wait records, and transfer the permit directly to the oldest record. Each record has its own monitor, so releasing a permit wakes exactly its chosen recipient.
class FifoBinarySemaphore(initiallyAvailable: Boolean) extends Semaphore {
  private final class Waiter { var granted = false }
  private val queue = scala.collection.mutable.Queue[Waiter]()
  private var available = initiallyAvailable

  def down: Unit = {
    val mine: Option[Waiter] = synchronized {
      if (available) {
        assert(queue.isEmpty)
        available = false
        None
      } else {
        val w = new Waiter
        queue.enqueue(w)
        Some(w)
      }
    }
    mine.foreach { w =>
      var interrupted = false
      w.synchronized {
        while (!w.granted) {
          try { w.wait() }
          catch { case _: InterruptedException => interrupted = true }
        }
      }
      if (interrupted) Thread.currentThread().interrupt()
    }
  }

  def up: Unit = synchronized {
    if (queue.nonEmpty) {
      val w = queue.dequeue()
      // available stays false: this permit is reserved for w.
      w.synchronized {
        w.granted = true
        w.notify()
      }
    } else {
      require(!available, "unmatched binary-semaphore release")
      available = true
    }
  }
}
The wait loop is deliberately uninterruptible with interruption status restored after acquisition: abandoning a queued wait record would otherwise strand its reserved permit. A caller that acquires must still complete the buffer operation. granted is read and written under the wait record's own monitor. The persistent flag prevents a lost wake-up if up runs after registration but before the caller begins waiting. Spurious wakeups simply repeat the loop.
The outer monitor serializes registration and the FIFO queue. A caller either consumes a genuinely free permit when nobody is queued, or appends one record. up removes exactly the front record and leaves available false, even if its owner has not yet resumed. A newcomer must queue behind existing records instead of stealing the handoff. The outer-to-inner lock ordering in up is safe because waiting callers release the outer monitor before acquiring their private monitors; no caller holds a private monitor while trying to reacquire the outer one.
Now use the same buffer body as in (ii), replacing only the initialization of its two fields:
private val empty: Semaphore = new FifoBinarySemaphore(true)
private val full: Semaphore = new FifoBinarySemaphore(false)
This is a complete implementation when inserted in SemaphoreMemory: its write and read methods remain exactly the displayed methods. Pending writers obtain empty-slot permissions in registration order on empty; pending readers obtain full-slot permissions in registration order on full. Each handoff permits just one caller to access the slot, so
(1)
First-come-first-served means the order in which concurrent calls register under the monitor; two overlapping calls have no externally determined order. The guarantee is separate for the two kinds of caller. A global order combining reads and writes cannot be required: an initial read must wait while a later write supplies its value. Subject to eventual scheduling and the arrival of matching operations of the opposite kind, no registered caller is overtaken by a later caller of its own kind. The design avoids broadcast wakeups as well as barging.
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