Abstract The TLA $$^+$$ + language has been widely used, both in academia and industry, to specify and reason about distributed systems. This paper presents Apalache , an efficient and flexible symbolic model checker for TLA $$^+$$ + . Apalache ’s engine is based on bounded model checking, with symbolic transitions being extracted from TLA $$^+$$ + specifications and verification conditions suitable for satisfiability modulo theories (SMT) solvers being generated from them. Reasoning can be done in terms of safety and liveness properties, with liveness checking realised via a liveness-to-safety reduction. Apalache ’s flexibility lies in its three complementary functionalities: bounded exhaustive verification, for bounded guarantees, randomised symbolic execution, for prototyping and bug detection, and inductiveness checking, for unbounded guarantees. The paper describes Apalache ’s architecture and features, including its support for PlusCal and Quint, two languages that share the same semantic foundation as TLA $$^+$$ + . Industrial usage of Apalache is also presented, together with a case study which illustrates how Apalache can be used to verify the agreement property of a consensus protocol.

Abstract The need to provide formal guarantees about the behaviour of the algorithms underpinning modern distributed systems became evident in recent years. This interest made apparent the complexities involved in applying verification techniques in a distributed setting, with significant effort being made in both academia and industry to aid in this endeavour. Many formalisms have been proposed to tackle the difficulties faced by practitioners, with one that has seen widespread use in industry being TLA $$^+$$ + , adopted, for instance, by Amazon Web Services. TLA $$^+$$ + provides engineers with a way of specifying both systems and desired properties, and is supported by a number of verification tools. Despite their extensive use, such tools suffer considerably from lack of scalability. To solve this, we propose a novel encoding of TLA $$^+$$ + into SMT constraints to improve symbolic model checking efficiency. Our insight is the need to provide the SMT solver with structural information about the TLA $$^+$$ + specification encoded, i.e., how data structures and their component elements interact, which we do by relying on the SMT theory of arrays. We implemented our approach by modifying the SMT-based model checker Apalache and evaluated it against comparable tools. Our results show that our approach outperforms existing ones on a number of benchmarks, with an order of magnitude improvement in checking time.

Cloud services provide the ability to provision virtual networked infrastructure on demand over the Internet. The rapid growth of these virtually provisioned cloud networks has increased the demand for automated reasoning tools capable of identifying misconfigurations or security vulnerabilities. This type of automation gives customers the assurance they need to deploy sensitive workloads. It can also reduce the cost and time-to-market for regulated customers looking to establish compliance certification for cloud-based applications. In this industrial case-study, we describe a new network reachability reasoning tool, called Tiros, that uses off-the-shelf automated theorem proving tools to fill this need. Tiros is the foundation of a recently introduced network security analysis feature in the Amazon Inspector service now available to millions of customers building applications in the cloud. Tiros is also used within Amazon Web Services (AWS) to automate the checking of compliance certification and adherence to security invariants for many AWS services that build on existing AWS networking features.

TLA+ is a language for formal specification of all kinds of computer systems. System designers use this language to specify concurrent, distributed, and fault-tolerant protocols, which are traditionally presented in pseudo-code. TLA+ is extremely concise yet expressive: The language primitives include Booleans, integers, functions, tuples, records, sequences, and sets thereof, which can be also nested. This is probably why the only model checker for TLA+ (called TLC) relies on explicit enumeration of values and states. In this paper, we present APALACHE -- a first symbolic model checker for TLA+. Like TLC, it assumes that all specification parameters are fixed and all states are finite structures. Unlike TLC, APALACHE translates the underlying transition relation into quantifier-free SMT constraints, which allows us to exploit the power of SMT solvers. Designing this translation is the central challenge that we address in this paper. Our experiments show that APALACHE outperforms TLC on examples with large state spaces.

Threshold automata, and the counter systems they define, were introduced as a framework for parameterized model checking of fault-tolerant distributed algorithms. This application domain suggested natural constraints on the automata structure, and a specific form of acceleration, called single-rule acceleration: consecutive occurrences of the same automaton rule are executed as a single transition in the counter system. These accelerated systems have bounded diameter, and can be verified in a complete manner with bounded model checking. We go beyond the original domain, and investigate extensions of threshold automata: non-linear guards, increments and decrements of shared variables, increments of shared variables within loops, etc., and show that the bounded diameter property holds for several extensions. Finally, we put single-rule acceleration in the scope of flat counter automata: although increments in loops may break the bounded diameter property, the corresponding counter automaton is flattable, and reachability can be verified using more permissive forms of acceleration.