Abstract The Vampire automated theorem prover is extended to output proofs in such a way that each inference is represented by a quantifier-free SMT instance. If every instance is unsatisfiable, the proof can be considered verified by an external SMT solver. This pragmatic form of proof checking places only a very light burden on the SMT solver, and can easily handle inferences that other systems may find difficult, such as theory inferences or extensive ground reasoning. The method is considerably easier to implement than proof formats based on small kernels and covers a greater variety of modern-day inferences.

We propose a compositional approach to combine and scale automated reasoning in the static analysis of decentralized system security, such as blockchains. Our focus lies in the game-theoretic security analysis of such systems, allowing us to examine economic incentives behind user actions. In this context, it is particularly important to certify that deviating from the intended, honest behavior of the decentralized protocol is not beneficial: as long as users follow the protocol, they cannot be financially harmed, regardless of how others behave. Such an economic analysis of blockchain protocols can be encoded as an automated reasoning problem in the first-order theory of real arithmetic, reducing game-theoretic reasoning to satisfiability modulo theories (SMT). However, analyzing an entire game-theoretic model (called a game) as a single SMT instance does not scale to protocols with millions of interactions. We address this challenge and propose a divide-and-conquer security analysis based on compositional reasoning over games. Our compositional analysis is incremental: we divide games into subgames such that changes to one subgame do not necessitate re-analyzing the entire game, but only the ancestor nodes. Our approach is sound, complete, and effective: combining the security properties of subgames yields security of the entire game. Experimental results show that compositional reasoning discovers intra-game properties and errors while scaling to games with millions of nodes, enabling security analysis of large protocols.

We present the CheckMate tool for automated verification of game-theoretic secu- rity properties, with application to blockchain protocols. CheckMate applies automated reasoning techniques to determine whether a game-theoretic protocol model is game- theoretically secure, that is, Byzantine fault tolerant and incentive compatible. We describe CheckMate’s input format and its various components, modes, and output. CheckMate is evaluated on 15 benchmarks, including models of decentralized protocols, board games, and game-theoretic examples.

We present the CheckMate framework for full automation of game-theoretic security analysis, with particular focus on blockchain technologies. CheckMate analyzes protocols modeled as games for their game-theoretic security - that is, for incentive compatibility and Byzantine fault-tolerance. The framework either proves the protocols secure by providing defense strategies or yields all possible attack vectors. For protocols that are not secure, CheckMate can also provide weakest preconditions under which the protocol becomes secure, if they exist. CheckMate implements a sound and complete encoding of game-theoretic security in first-order linear real arithmetic, thereby reducing security analysis to satisfiability solving. CheckMate further automates efficient handling of case splitting on arithmetic terms. Experiments show CheckMate scales, analyzing games with trillions of strategies that model phases of Bitcoin's Lightning Network.

We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on computation rules, where both kinds of rules are defined using the type-theoretic concept of object-invertible rules. We also give sufficient syntactic criteria for recognizing such rules, as well as a simple pattern-matching algorithm for applying them. A third component of the algorithm is a suitable notion of principal arguments, which determines a notion of normal form. By varying these, we obtain known notions, such as weak head-normal and strong normal forms. We prove that our algorithm is sound. We implemented it in the Andromeda 2 proof assistant, which supports user-definable type theories. The user need only provide the equality rules they wish to use, which the algorithm automatically classifies as computation or extensionality rules, and select appropriate principal arguments.