We introduce a variant of a formalism appearing in recent work geared towards modelling systems in which a distinguished entity (leader) orchestrates the operation of an arbitrary number of identical entities (followers). Our variant is better suited for the verification of system properties involving complex arithmetic conditions. Whereas the original formalism is translated into a tractable fragment of first-order temporal logic, aiming to utilize automated (first-order temporal logic) theorem provers for verification, our variant is translated into linear integer arithmetic, aiming to utilize satisfiability modulo theories (SMT) solvers for verification. In particular, for any given system specified in our formalism, we prove, for any natural number n , the existence of a linear integer arithmetic formula whose models are in one-to-one correspondence with certain counting abstractions (profiles) of executions of the system for n time steps. Thus, one is able to verify, for any natural number n , that all executions for n time steps of any such system have a given property by establishing that said formula logically entails the property. To highlight the practical utility of our approach, we specify and verify three consensus protocols, actively used in distributed database systems and low-power wireless networks.

中文翻译：

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通过算术约束对领导者/跟随者系统进行参数化验证


我们引入了最近工作中出现的形式主义的变体，该变体面向建模系统，其中一个杰出的实体（领导者）协调任意数量的相同实体（追随者）的操作。我们的变体更适合验证涉及复杂算术条件的系统属性。原始形式主义被转化为一阶时序逻辑的易处理片段，旨在利用自动化（一阶时序逻辑）定理证明器进行验证，而我们的变体被转化为线性整数算术，旨在利用可满足性模理论（SMT） ）求解器进行验证。特别是，对于我们形式主义中指定的任何给定系统，我们证明，对于任何自然数 n ，存在一个线性整数算术公式，其模型与执行的某些计数抽象（配置文件）一一对应。 n 个时间步的系统。因此，对于任何自然数 n ，通过建立所述公式在逻辑上蕴含该属性，可以验证任何此类系统的 n 个时间步长的所有执行都具有给定属性。为了突出我们方法的实用性，我们指定并验证了三种共识协议，这些协议积极用于分布式数据库系统和低功耗无线网络。