Temporal logic specifications play an important role in a wide range of software analysis tasks, such as model checking, automated synthesis, program comprehension, and runtime monitoring. Given a set of positive and negative examples, specified as traces, LTL learning is the problem of synthesizing a specification, in linear temporal logic (LTL), that evaluates to true over the positive traces and false over the negative ones. In this paper, we propose a new type of LTL learning problem called constrained LTL learning, where the user, in addition to positive and negative examples, is given an option to specify one or more constraints over the properties of the LTL formula to be learned. We demonstrate that the ability to specify these additional constraints significantly increases the range of applications for LTL learning, and also allows efficient generation of LTL formulas that satisfy certain desirable properties (such as minimality). We propose an approach for solving the constrained LTL learning problem through an encoding in first-order relational logic and reduction to an instance of the maximal satisfiability (MaxSAT) problem. An experimental evaluation demonstrates that ATLAS, an implementation of our proposed approach, is able to solve new types of learning problems while performing better than or competitively with the state-of-the-art tools in LTL learning.

Abstract A safety verification task involves verifying a system against a desired safety property under certain assumptions about the environment. However, these environmental assumptions may occasionally be violated due to modeling errors or faults. Ideally, the system guarantees its critical properties even under some of these violations, i.e., the system is robust against environmental deviations. This paper proposes a notion of robustness as an explicit, first-class property of a transition system that captures how robust it is against possible deviations in the environment. We modeled deviations as a set of transitions that may be added to the original environment. Our robustness notion then describes the safety envelope of this system, i.e., it captures all sets of extra environment transitions for which the system still guarantees a desired property. We show that being able to explicitly reason about robustness enables new types of system analysis and design tasks beyond the common verification problem stated above. We demonstrate the application of our framework on case studies involving a radiation therapy interface, an electronic voting machine, a fare collection protocol, and a medical pump device.

We present a formal, machine checked TLA+ safety proof of MongoRaftReconfig, a distributed dynamic reconfiguration protocol. MongoRaftReconfig was designed for and implemented in MongoDB, a distributed database whose replication protocol is derived from the Raft consensus algorithm. We present an inductive invariant for MongoRaftReconfig that is formalized in TLA+ and formally proved using the TLA+ proof system (TLAPS). We also present a formal TLAPS proof of two key safety properties of MongoRaftReconfig, LeaderCompleteness and StateMachineSafety. To our knowledge, these are the first machine checked inductive invariant and safety proof of a dynamic reconfiguration protocol for a Raft based replication system.

Distributed replication systems based on the replicated state machine model have become ubiquitous as the foundation of modern database systems. To ensure availability in the presence of faults, these systems must be able to dynamically replace failed nodes with healthy ones via dynamic reconfiguration. MongoDB is a document oriented database with a distributed replication mechanism derived from the Raft protocol. In this paper, we present MongoRaftReconfig, a novel dynamic reconfiguration protocol for the MongoDB replication system. MongoRaftReconfig utilizes a logless approach to managing configuration state and decouples the processing of configuration changes from the main database operation log. The protocol's design was influenced by engineering constraints faced when attempting to redesign an unsafe, legacy reconfiguration mechanism that existed previously in MongoDB. We provide a safety proof of MongoRaftReconfig, along with a formal specification in TLA+. To our knowledge, this is the first published safety proof and formal specification of a reconfiguration protocol for a Raft-based system. We also present results from model checking its safety properties on finite protocol instances. Finally, we discuss the conceptual novelties of MongoRaftReconfig, how it can be understood as an optimized and generalized version of the single server reconfiguration algorithm of Raft, and present an experimental evaluation of how its optimizations can provide performance benefits for reconfigurations.