Checking Presence Reachability Properties on Parameterized Shared-Memory Systems

We consider the verification of distributed systems composed of an arbitrary number of asynchronous processes. Processes are identical finite-state machines that communicate by reading from and writing to a shared memory. Beyond the standard model with finitely many registers, we tackle round-based shared-memory systems with fresh registers at each round. In the latter model, both the number of processes and the number of registers are unbounded, making verification particularly challenging. The properties studied are generic presence reachability objectives, which subsume classical questions such as safety or synchronization by expressing the presence or absence of processes in some states. In the more general round-based setting, we establish that the parameterized verification of presence reachability properties is PSPACE-complete. Moreover, for the roundless model with finitely many registers, we prove that the complexity drops down to NP-complete and we provide several natural restrictions that make the problem solvable in polynomial time

Checking Presence Reachability Properties on Parameterized Shared-Memory Systems

We consider the verification of distributed systems composed of an arbitrary number of asynchronous processes. Processes are identical finite-state machines that communicate by reading from and writing to a shared memory. Beyond the standard model with finitely many registers, we tackle round-based shared-memory systems with fresh registers at each round. In the latter model, both the number of processes and the number of registers are unbounded, making verification particularly challenging. The properties studied are generic presence reachability objectives, which subsume classical questions such as safety or synchronization by expressing the presence or absence of processes in some states. In the more general round-based setting, we establish that the parameterized verification of presence reachability properties is PSPACE-complete. Moreover, for the roundless model with finitely many registers, we prove that the complexity drops down to NP-complete and we provide several natural restrictions that make the problem solvable in polynomial time.Comment: 27 pages, 6 figure

Parameterized Broadcast Networks with Registers: from NP to the Frontiers of Decidability

We consider the parameterized verification of arbitrarily large networks of agents which communicate by broadcasting and receiving messages. In our model, the broadcast topology is reconfigurable so that a sent message can be received by any set of agents. In addition, agents have local registers which are initially distinct and may therefore be thought of as identifiers. When an agent broadcasts a message, it appends to the message the value stored in one of its registers. Upon reception, an agent can store the received value or test this value for equality with one of its own registers. We consider the coverability problem, where one asks whether a given state of the system may be reached by at least one agent. We establish that this problem is decidable; however, it is as hard as coverability in lossy channel systems, which is non-primitive recursive. This model lies at the frontier of decidability as other classical problems on this model are undecidable; this is in particular true for the target problem where all processes must synchronize on a given state. By contrast, we show that the coverability problem is NP-complete when each agent has only one register

Parameterized safety verification of round-based shared-memory systems

International audienceWe consider the parameterized verification problem for distributed algorithms where the goal is to develop techniques to prove the correctness of a given algorithm regardless of the number of participating processes. Motivated by an asynchronous binary consensus algorithm [3], we consider round-based distributed algorithms communicating with shared memory. A particular challenge in these systems is that 1) the number of processes is unbounded, and, more importantly, 2) there is a fresh set of registers at each round. A verification algorithm thus needs to manage both sources of infinity. In this setting, we prove that the safety verification problem, which consists in deciding whether all possible executions avoid a given error state, is PSPACE-complete. For negative instances of the safety verification problem, we also provide exponential lower and upper bounds on the minimal number of processes needed for an error execution and on the minimal round on which the error state can be covered

Parameterized Broadcast Networks with Registers: from NP to the Frontiers of Decidability

Long version of a paper published at FoSSaCS 2024International audienceWe consider the parameterized verification of arbitrarily large networks of agents which communicate by broadcasting and receiving messages. In our model, the broadcast topology is reconfigurable so that a sent message can be received by any set of agents. In addition, agents have local registers which are initially distinct and may therefore be thought of as identifiers. When an agent broadcasts a message, it appends to the message the value stored in one of its registers. Upon reception, an agent can store the received value or test this value for equality with one of its own registers. We consider the coverability problem, where one asks whether a given state of the system may be reached by at least one agent. We establish that this problem is decidable; however, it is as hard as coverability in lossy channel systems, which is non-primitive recursive. This model lies at the frontier of decidability as other classical problems on this model are undecidable; this is in particular true for the target problem where all processes must synchronize on a given state. By contrast, we show that the coverability problem is NP-complete when each agent has only one register

STIM1 Juxtaposes ER to Phagosomes, Generating Ca(2+) Hotspots that Boost Phagocytosis

BACKGROUND: Endoplasmic reticulum (ER) membranes are recruited to phagosomes, but the mechanism and functional significance of this ER recruitment is not known. Here, we show that the ER Ca(2+) sensor stromal interaction molecule 1 (STIM1) sustains high-efficiency phagocytosis by recruiting thin ER cisternae that interact productively but do not fuse with phagosomes. RESULTS: Endogenous STIM1 was recruited to phagosomes upon ER Ca(2+) depletion in mouse neutrophils, and exogenous YFP-STIM1 puncta coincided with localized Ca(2+) elevations around phagosomes in fibroblasts expressing phagocytic receptors. STIM1 ablation decreased phagocytosis, ER-phagosome contacts, and periphagosomal Ca(2+) elevations in both neutrophils and fibroblasts, whereas STIM1 re-expression in Stim1(-/-) fibroblasts rescued these defects, promoted the formation and elongation of tight ER-phagosome contacts upon ER Ca(2+) depletion and increased the shedding of periphagosomal actin rings. Re-expression of a signaling-deficient STIM1 mutant unable to open Ca(2+) channels recruited ER cisternae to the vicinity of phagosomes but failed to rescue phagocytosis, actin shedding, and periphagosomal Ca(2+) elevations. The periphagosomal Ca(2+) hotspots were decreased by extracellular Ca(2+) chelation and by Ca(2+) channels inhibitors, revealing that the Ca(2+) ions originate at least in part from phagosomes. CONCLUSIONS: Our findings indicate that STIM1 recruits ER cisternae near phagosomes for signaling purposes and that the opening of phagosomal Ca(2+) channels generates localized Ca(2+) elevations that promote high-efficiency phagocytosis