Fault-Tolerant Algorithms for Tick-Generation in Asynchronous Logic: Robust Pulse Generation

Abstract

Today's hardware technology presents a new challenge in designing robust systems. Deep submicron VLSI technology introduced transient and permanent faults that were never considered in low-level system designs in the past. Still, robustness of that part of the system is crucial and needs to be guaranteed for any successful product. Distributed systems, on the other hand, have been dealing with similar issues for decades. However, neither the basic abstractions nor the complexity of contemporary fault-tolerant distributed algorithms match the peculiarities of hardware implementations.This paper is intended to be part of an attempt striving to overcome this gap between theory and practice for the clock synchronization problem. Solving this task sufficiently well will allow to build a very robust high-precision clocking system for hardware designs like systems-on-chips in critical applications. As our first building block, we describe and prove correct a novel Byzantine fault-tolerant self-stabilizing pulse synchronization protocol, which can be implemented using standard asynchronous digital logic. Despite the strict limitations introduced by hardware designs, it offers optimal resilience and smaller complexity than all existing protocols.

Unfaithful Glitch Propagation in Existing Binary Circuit Models

“…They use pure delay channels and assume the existence of SPF modules to circumvent glitch propagation induced by faults. The same modeling and analysis framework is also used in the self-stabilizing Byzantine fault-tolerant FATAL protocol for distributed clock generation in SoCs [14].…”

Efficient Construction of Global Time in SoCs Despite Arbitrary Faults

“…Moreover, to establish clocks (instead of anonymous pulses), it relies on consensus, implying that again (i) applies. These issues are avoided by the algorithms described in [19], [20], which, however, exhibit a stabilization time that is exponential in the number of clock bits; they are thus suitable for providing small-sized clocks only.…”

“…Note carefully, though, that it is outside the scope of this work (in fact, irrelevant) how the short clocks are implemented. Ideally, one would use a self-stabilizing pulse generation algorithm (like, e.g., in [19]) for this purpose.…”

Unfaithful Glitch Propagation in Existing Binary Circuit Models

“…Analyzing the propagation of such pulses along a pipeline is thus important in order to assess the achievable resilience against such threats [11]. The situation is even worse in case of self-stabilizing algorithms [9], which must be able to recover from an arbitrary initial/error state: Neither handshaking nor any bounded delay condition can be resorted to during stabilization in an algorithm like the one presented by Dolev et al [8]. Consequently, glitches and the possibility of metastability cannot be avoided.…”