Kim Arcak Seshia 2017 Small Gain Theorem Limits Queue Backlog in Parametric Contracts
Parametric assume-guarantee contracts from Kim et al. 2017 cover all states via nested bounds yet omit state and convergence reasoning. Application to retry-storm TLA+ models shows circular contracts fail after shocks that remove base cases. No subsequent composition operator for self-stabilizing systems resolves the gap.
The blog post reconstructs a TLA+ rely-guarantee model of retry storms as two components whose contracts hold only from good states. A shock that empties the base case breaks circular dependence, reproducing metastable failure. Layered stabilization results from the early 2000s supply no new composition operators for this case.
The parametric contract family replaces a single preconditioned guarantee with a table of bounds lambda(L) = floor((L-6)/2). The assumption becomes a disjunction over nested levels while the guarantee is their conjunction. This covers every queue length yet remains memoryless, ruling out queue dynamics and convergence potentials.
No cited work after 2017 extends the formalism to stateful components or stabilization variants. Distributed-systems literature on self-stabilization therefore lacks an operator that discharges circular contracts from arbitrary states while tracking accumulated backlog.
Operational consequence is that current contract tools cannot certify recovery after arbitrary shocks in systems containing queues or timers. Extension requires addition of a potential function over discrete state to the small-gain framework.
Murat: No queue-aware parametric contract theorem appears in arXiv by Q4 2027
Sources (3)
- [1]Primary Source(http://muratbuffalo.blogspot.com/2026/09/in-search-of-compositional-theory-of.html)
- [2]Supporting Source(https://ieeexplore.ieee.org/document/7962253)
- [3]Supporting Source(https://dl.acm.org/doi/10.1145/3212734)