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Motivated by distributed data processing applications, we introduce a class of labeled directed acyclic graphs constructed using sequential and parallel composition operations, and study automata and logics over them. We show that deterministic and non-deterministic acceptors over such graphs have the same expressive power, which can be equivalently characterized by Monadic Second-Order logic and the graded µ-calculus. We establish closure under composition operations and decision procedures for membership, emptiness, and inclusion. A key feature of our graphs, called synchronized series-parallel graphs (SSPG), is that parallel composition introduces a synchronization edge from the newly introduced source vertex to the sink. The transfer of information enabled by such edges is crucial to the determinization construction, which would not be possible for the traditional definition of series-parallel graphs. SSPGs allow both ordered ranked parallelism and unordered unranked parallelism. The latter feature means that in the corresponding automata, the transition function needs to account for an arbitrary number of predecessors by counting each type of state only up to a specified constant, thus leading to a notion of counting complexity that is distinct from the classical notion of state complexity. The determinization construction translates a nondeterministic automaton with n states and k counting complexity to a deterministic automaton with 2 n 2 states and kn counting complexity, and both these bounds are shown to be tight. Furthermore, for nondeterministic automata a bound of 2 on counting complexity suffices without loss of expressiveness. 

While serverless platforms substantially simplify the provisioning, configuration, and management of cloud applications, implementing correct services on top of these platforms can present significant challenges to programmers. For example, serverless infrastructures introduce a host of failure modes that are not present in traditional deployments. Individual serverless instances can fail while others continue to make progress, correct but slow instances can be killed by the cloud provider as part of resource management, and providers will often respond to such failures by re-executing requests. For functions with side-effects, these scenarios can create behaviors that are not observable in serverful deployments. In this paper, we propose mu2sls, a framework for implementing microservice applications on serverless using standard Python code with two extra primitives: transactions and asynchronous calls. Our framework orchestrates user-written services to address several challenges, such as failures and re-executions, and provides formal guarantees that the generated serverless implementations are correct. To that end, we present a novel service specification abstraction and formalization of serverless implementations that facilitate reasoning about the correctness of a given application’s serverless implementation. This formalization forms the basis of the mu2sls prototype, which we then use to develop a few real-world microservice applications and show that the performance of the generated serverless implementations achieves significant scalability (3-5× the throughput of a sequential implementation) while providing correctness guarantees in the context of faults, re-execution, and concurrency. 

This article addresses the problem of verifying the safety of autonomous systems with neural network (NN) controllers. We focus on NNs with sigmoid/tanh activations and use the fact that the sigmoid/tanh is the solution to a quadratic differential equation. This allows us to convert the NN into an equivalent hybrid system and cast the problem as a hybrid system verification problem, which can be solved by existing tools. Furthermore, we improve the scalability of the proposed method by approximating the sigmoid with a Taylor series with worst-case error bounds. Finally, we provide an evaluation over four benchmarks, including comparisons with alternative approaches based on mixed integer linear programming as well as on star sets.