Verifying Livelock Freedom on Parameterized Rings and Chains

IIEEE Trans. Software Eng.

Klinkhamer

2021

Self Cite

This paper investigates the problem of synthesizing parameterized systems that are self-stabilizing by construction. To this end, we present several significant results. First, we show a counterintuitive result that despite the undecidability of verifying self-stabilization for parameterized unidirectional rings, synthesizing self-stabilizing unidirectional rings is decidable! This is surprising because it is known that, in general, the synthesis of distributed systems is harder than their verification. Second, we present a topology-specific synthesis method (derived from our proof of decidability) that generates the state transition system of template processes of parameterized self-stabilizing systems with elementary unidirectional topologies (e.g., rings, chains, trees). We also provide a software tool that implements our synthesis algorithms and generates interesting self-stabilizing parameterized unidirectional rings in less than 50 microseconds on a regular laptop. We validate the proposed synthesis algorithms for decidable cases in the context of several interesting distributed protocols. Third, we show that synthesis of self-stabilizing bidirectional rings remains undecidable.

“…Next, we represent some of our previous result (from [14,26]) that we shall use in this paper. Propagations and Collisions.…”

Section: Basic Conceptsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Topology-Specific Synthesis of Self-Stabilizing Parameterized Systems with Constant-Space Processes

IIEEE Trans. Software Eng.

Klinkhamer

2021

Self Cite

“…We have also shown that verifying livelock-freedom remains undecidable even for a special type of livelocks, where exactly one process is enabled in every state of the livelocked computation; i.e., deterministic livelocks [39].…”

Section: Preliminariesmentioning

confidence: 98%

“…Next, we represent some of our previous results regarding livelocks (from [25,39]) that we shall use in this paper. Propagations and Collisions.…”

Section: Preliminariesmentioning

confidence: 99%

Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties

2019 Formal Methods in Computer Aided Design (FMCAD)

2019

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This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties R Q on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic and constantspace processes under no fairness and interleaving semantics, where R and Q are global state predicates. First, we show that verifying R Q for parameterized protocols on symmetric uni-rings is undecidable, even for deterministic and constant-space processes, and conjunctive state predicates. Then, we show that surprisingly synthesizing symmetric uni-ring protocols that satisfy R Q is actually decidable. We identify necessary and sufficient conditions for the decidability of synthesis based on which we devise a sound and complete polynomial-time algorithm that takes the predicates R and Q, and automatically generates a parameterized protocol that satisfies R Q for unbounded (but finite) ring sizes. Moreover, we present some decidability results for cases where leadsto is required from multiple distinct R predicates to different Q predicates. To demonstrate the practicality of our synthesis method, we synthesize some parameterized protocols, including agreement and parity protocols.

Synthesizing Parameterized Self-stabilizing Rings with Constant-Space Processes

Klinkhamer

Fundamentals of Software Engineering

2017

Self Cite

This paper investigates the problem of synthesizing parameterized rings that are "self-stabilizing by construction". While it is known that the verification of self-stabilization for parameterized unidirectional rings is undecidable, we present a counterintuitive result that synthesizing such systems is decidable! This is surprising because it is known that, in general, the synthesis of distributed systems is harder than their verification. We also show that synthesizing self-stabilizing bidirectional rings is an undecidable problem. To prove the decidability of synthesis for unidirectional rings, we propose a sound and complete algorithm that performs the synthesis in the local state space of processes. We also generate strongly stabilizing rings where no fairness assumption is made. This is particularly noteworthy because most existing verification and synthesis methods for parameterized systems assume a fair scheduler.