Intermittent Bounded Bypass in MUTEX Protocols

• Intermittent bounded bypass is a liveness property for MUTEX protocols that allows processes to ignore overtakes during a bounded number of designated write (interrupting) assignments.
• It refines fairness guarantees by counting overtakes only outside these critical intervals, addressing deficiencies in earlier bounded bypass formulations and ensuring eventual critical-section entry.
• Tight quantitative bounds are established for different register models, with atomic registers achieving n(n-1)-1 and safe/regular registers achieving n²-2 within n interrupting assignments.

to=arxiv_search.search d天天json {"^^^^^^^^2query2 OR title:\2^^^^^^^^"On the Notions of Bounded Bypass, and How to Make any Deadlock-Free MUTEX Protocol Satisfy One of Them\"","max_results":5,"sort_by":"submittedDate","sort_order":"descending"}ുവനന്തപുരം to=arxiv_search.search ＿一本道json {"^^^^^^^^2query2 \"bounded bypass\" OR \"post-doorway bounded bypass\" OR mutex bounded bypass","max_results":^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2query2^^^^,"sort_by":"submittedDate","sort_order":"descending"} to=arxiv_search.search 亚历山大发json {"^^^^^^^^2query2 Concurrent Broadcasts for Intermittent Channels with Bounded Capacities\" OR id:(&&&^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^&&&)","max_results":5,"sort_by":"submittedDate","sort_order":"descending"} to=arxiv_search.search 天天中彩票官网json {"^^^^^^^^2query2 Sharing of Fast Kernel-Bypass I/O Among Nontrusting Applications\" OR id:(Beadle et al., 2 Sep 2025)","max_results":5,"sort_by":"submittedDate","sort_order":"descending"} Intermittent bounded bypass is a liveness property for mutual exclusion protocols that weakens bounded bypass while remaining stronger than starvation-freedom. In its formal sense, it permits a process to ignore overtakes that occur during the execution of a bounded number of designated write operations to shared registers, called interrupting assignments, and counts only the remaining competitions before entry to the critical section. The notion was introduced to repair deficiencies in older formulations of bounded bypass and to capture fairness guarantees that remain achievable in weaker shared-memory models, especially with safe and regular registers. Outside mutual exclusion, the phrase has no standardized cross-domain meaning; related literatures instead use it only by analogy for bounded intermittent postponement, temporary detours, or bounded execution bursts under interruptions (&&&^^^^2query2^^^^&&&).

^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^. Origins and conceptual motivation

The classical motivation for bounded bypass is that starvation-freedom guarantees only eventual entry, not a uniform numeric bound on how many times other processes may enter first. The literature had long treated bounded bypass, or bounded waiting, as a strengthening of starvation-freedom, but the 2^^^^2query22^^^^6 formulation argues that earlier definitions were unsatisfactory as standalone liveness properties. In particular, Raynal’s wording—there exists a function PRESERVED_PLACEHOLDER_^^^^2query2^^^^ such that each invocation of lock loses at most PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^ competitions—does not imply eventual entry. The counterexample given is a protocol in which each lock is simply await false: no competition is ever lost, so the old definition is vacuously satisfied, yet the protocol is neither deadlock-free nor starvation-free (&&&^^^^2query2^^^^&&&).

A second difficulty concerns when counting should start. If bypasses are counted immediately from invocation of lock, then a process may be charged for overtakes occurring before it has performed even its first shared-memory action. The corrected bounded-bypass notion therefore starts counting only after the first instruction of lock completes. Intermittent bounded bypass retains this concern but weakens the fairness requirement in a different direction: it allows a bounded number of exceptional write intervals later in the execution during which bypasses are ignored. This isolates precisely those intervals in which weak-register anomalies can destroy any ordinary bypass bound.

2. Formal meaning

The paper defines a competition loss in the standard overlap sense: process $i$ running lock loses a competition with process $j$ if $j$’s lock overlaps in time with $i$’s and terminates earlier. Since terminating lock means entering the critical section, this is the bypass event being counted (&&&^^^^2query2^^^^&&&).

The repaired bounded-bypass notion is: every process that invokes lock enters the critical section, and this happens after losing at most $f(n)$ competitions from the moment in which it completes the execution of the first instruction of the lock. Intermittent bounded bypass weakens this by introducing interrupting assignments.

Formally, a MUTEX protocol satisfies an intermittent bounded-bypass of $f(n)$ within $h(n)$ interrupting assignments if a set $S$ of assignments to shared registers can be defined such that each time a process PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2query2^^^^ starts its lock, it reaches its critical section after a period PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^ satisfying two conditions: PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\22^^^^ and

PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^3

The writes in PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^4 are the interrupting assignments. Thus the property ignores bypasses during the execution intervals of certain selected writes, but only finitely many of them, and only up to the bound PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^5. Outside those intervals, the number of overtakes remains uniformly bounded. The notion is therefore quantitatively stronger than starvation-freedom, even though it is weaker than ordinary bounded bypass.

A subtle but important definitional distinction remains. For intermittent bounded bypass, lock is said to start when its first instruction starts, precisely so that the time before the first instruction is not automatically absorbed into an ignored interval. This differs from corrected bounded bypass, where counting begins only after completion of the first instruction.

3. Position in the liveness hierarchy

The paper places intermittent bounded bypass in a strict implication hierarchy together with bounded bypass, post-doorway bounded bypass, starvation-freedom, and deadlock-freedom. The established implications are

PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^6

and also

PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^7

Intermittent bounded bypass and post-doorway bounded bypass are incomparable (&&&^^^^2query2^^^^&&&).

The separating examples are central to the meaning of the notion. Dekker’s algorithm is starvation-free but not bounded, not intermittent bounded-bypass, and not post-doorway bounded-bypass: after both processes begin trying, one process can temporarily withdraw its flag and sleep, allowing the other to enter arbitrarily many times. Anderson’s algorithm satisfies post-doorway bounded bypass but not bounded bypass and not intermittent bounded bypass, because if counting begins too early one process may be bypassed unboundedly before advancing beyond the first doorway instruction. The Bar-David transformation with safe registers satisfies intermittent bounded bypass but not full bounded bypass, which shows that the weakening is not merely terminological but captures behavior genuinely obtainable in weaker memory models.

The conceptual difference between intermittent and post-doorway variants is orthogonal. Post-doorway bounded bypass ignores all bypasses during one initial bounded prefix of lock, called the doorway, and that prefix may include reads, writes, and the time between them. Intermittent bounded bypass ignores bypasses only during the execution of certain selected write actions, possibly later and non-contiguously during lock.

4. Achievability and exact bounds under different register models

The main constructive result studies Yoah Bar-David’s ^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^998 transformation, which wraps any deadlock-free MUTEX protocol with a FLAG/TURN discipline. In the transformed lock(i), process PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^8 performs FLAG[i] ← ^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^, repeatedly reads TURN, proceeds if tmp = i or FLAG[tmp] = ^^^^2query2^^^^, and then executes the underlying deadlock-free lock(i). In unlock(i), it writes FLAG[i] ← ^^^^2query2^^^^, reads TURN, possibly advances TURN to PRESERVED_PLACEHOLDER_^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^9, and then executes the underlying unlock(i). The paper labels the shared-memory actions W^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^, W2, W3 and R^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^–R4, and these labels are used throughout the proofs (&&&^^^^2query2^^^^&&&).

The transformation yields different guarantees depending on the register semantics.

Register model	Property obtained	Bound
Atomic registers	Bounded bypass	$i$^^^^2query2^^^^
Safe or regular registers	Intermittent bounded bypass	$i$^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^ within $i$2 interrupting assignments

In the atomic-register setting, once a process completes W^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^, it enters the critical section after losing at most

$i$3

competitions, and the bound is stated to be tight. The proof decomposes the waiting time into the phase before TURN reaches the process and the phase after it does. Before TURN reaches $i$4, each increment of TURN can cost at most $i$5 losses, across at most $i$6 values, giving $i$7. After TURN reaches $i$8, at most $i$9 further losses remain, for a total of

$j$^^^^2query2^^^^

In the safe-register setting, full bounded bypass is impossible for this transformation. The key counterexample uses three processes: if TURN = ^^^^2query2^^^^ and $j$^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^ remains inside W^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^ for a long time, then one process may repeatedly read FLAG[^^^^2query2^^^^] = ^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^ and stay blocked while another repeatedly reads FLAG[^^^^2query2^^^^] = ^^^^2query2^^^^, enters, and exits, causing unbounded ordinary bypasses. The same scenario applies to regular registers. Nevertheless, by ignoring bypasses during a bounded number of selected W^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^ intervals, the paper proves an intermittent bounded bypass of

$j$2

and states that the bound is tight for $j$3. The interrupting assignments are $j$4’s own W^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^ together with certain W^^^^2id:([2606.19003](/papers/2606.19003)) OR title:\2^^^^ writes by the current TURN process that overlap the relevant waiting period in the precise sense given in the theorem.

5. Logical formalization and mechanized verification

The paper does not stop at proof sketches. It formalizes bounded bypass, post-doorway bounded bypass, and intermittent bounded bypass in the modal $j$5-calculus and checks the claims with mCRL2. The transition system uses actions such as lock_p, crit_p, wstart_p, and wfinish_p, where crit_q actions are the finishing events that count as bypasses by process $j$6 (&&&^^^^2query2^^^^&&&).

For intermittent bounded bypass, the formalization tracks three resources simultaneously: remaining bypass budget $j$7, remaining interrupt budget $j$8, and the set of currently active writes. A bypass decrements $j$9 only when no chosen interrupting write is active. This directly encodes the definition’s requirement that overtakes are ignored only during selected write intervals and only up to a bounded number of them.

Model checking had substantive theoretical impact. It exposed an earlier non-tight atomic bound of $j$^^^^2query2^^^^, leading to the corrected tight bound $j$^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^. It also showed that, in the safe-register proof, interrupting writes must be identified by conditions holding during the write rather than merely at its end. The verified examples match the proof structure: Dekker violates the bounded variants checked, Anderson satisfies post-doorway bounded bypass with the specified doorway but not stronger variants, and the Bar-David transformation matches the atomic and safe/regular bounds above.

6. Broader technical analogues and non-equivalent usages

Outside shared-memory mutual exclusion, intermittent bounded bypass is not a standardized term. Several other literatures study mechanisms that resemble it structurally—bounded postponement, bounded temporary detours, or bounded bursts of privileged execution under interruption—but these are analogues rather than the same liveness property.

In synchronous broadcast over intermittent channels, the closest analogue is parity-constrained delayed forwarding. The extension of amnesiac flooding in “Synchronous Concurrent Broadcasts for Intermittent Channels with Bounded Capacities” permits postponement only to the next available round of the same parity. This restores termination under finite intermittent unavailability and extends to bounded-capacity concurrent broadcast, with delivery in at most

$j$2

rounds and termination in at most

$j$3

when $j$4 node-round send opportunities are unavailable (&&&^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^&&&). This is a bounded intermittent postponement discipline, but it is not a competition-counting fairness property.

In protected-library kernel-bypass I/O, “Safe Sharing of Fast Kernel-Bypass I/O Among Nontrusting Applications” studies a different pattern: every protected-library invocation must complete in modest bounded time, so unbounded waiting is moved outside the protected library via futex wrappers. Threads therefore alternate between short bounded protected execution and external waiting, then re-enter for the next bounded step (Beadle et al., 2 Sep 2025). This strongly resembles intermittent bounded bypass as an execution pattern, but it concerns time-bounded kernel-bypass service sharing rather than overtake bounds in MUTEX.

In congestion control, PABO temporarily bounces packets to upstream switches when output queues are congested, with bounce probability depending on queue utilization and prior bounce count. The mechanism is intermittent because it activates only above a threshold and softly bounded because repeat bouncing becomes less likely as bounce count increases (&&&^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^&&&). Again, the resemblance is architectural rather than definitional.

Related analogues also appear in consensus under intermittent communication and input saturation, where trajectories are certified to remain inside computable bounded enclosing regions despite switching communication graphs (&&&^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\22^^^^&&&), and in fault-tolerant computation under isolated bounded bursts of faults, where recovery proceeds locally on bounded intervals provided bursts are separated by $j$5 (&&&^^^^2id:(Glabbeek et al., 17 Jun 2026) OR title:\2^^^^3&&&). These works share the motif of bounded operation under intermittent disruption, but they do not define intermittent bounded bypass in the mutual-exclusion sense.

Within its literal technical usage, intermittent bounded bypass remains a MUTEX liveness notion: every lock succeeds, and except for a bounded number of designated write intervals, the number of overtakes is uniformly bounded. Its significance lies in showing that quantitative fairness need not collapse entirely when the memory model is too weak for ordinary bounded bypass.