Technology Category
Constraint Satisfaction and Optimization: Distributed CSP/OptimizationKnowledge Representation and Reasoning: Computational Complexity of ReasoningMultiagent Systems: Distributed Problem Solving
Undecidability of the Emptiness Problem for Weak Models of Distributed Computing
🤖 AI Summary
This paper investigates the emptiness problem for weak asynchronous distributed automata—i.e., networked finite-state machines: given such an automaton, does there exist any input graph it accepts? Within the Esparza–Reiter framework, this problem encompasses seven equivalence classes of weakly distributed models. Using computability-theoretic analysis and distributed automata theory, the authors establish, for the first time, that emptiness is undecidable for six of these seven classes, exposing a fundamental limitation in the verification of weak distributed systems; for the seventh class, emptiness is trivially decidable. This result fully characterizes the decidability boundary of emptiness checking within the Esparza–Reiter framework, providing a foundational theoretical benchmark for formal verification of distributed systems.
Technology Category
Application Category
📝 Abstract
Esparza and Reiter have recently conducted a systematic comparative study of weak asynchronous models of distributed computing, in which a network of identical finite-state machines acts cooperatively to decide properties of the network's graph. They introduced a distributed automata framework encompassing many different models, and proved that w.r.t. their expressive power (the graph properties they can decide) distributed automata collapse into seven equivalence classes. In this contribution, we turn our attention to the formal verification problem: Given a distributed automaton, does it decide a given graph property? We consider a fundamental instance of this question - the emptiness problem: Given a distributed automaton, does it accept any graph at all? Our main result is negative: the emptiness problem is undecidable for six of the seven equivalence classes, and trivially decidable for the remaining class.
Problem
Research questions and friction points this paper is trying to address.
Study undecidability of emptiness in weak distributed models
Analyze distributed automata's graph property verification problem
Determine emptiness problem decidability across seven model classes
Innovation
Methods, ideas, or system contributions that make the work stand out.
Distributed automata framework for weak models
Emptiness problem undecidable for six classes
Comparative study of asynchronous distributed computing
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