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Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks

Results show that the novel, scalable, and efficient technique presented can successfully prove properties of networks that are an order of magnitude larger than the largest networks verified using existing methods.
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Satisfiability Modulo Theories

This chapter provides a brief overview of SMT together with references to the relevant literature for a deeper study and an alternative approach in which a SAT solver is integrated with a separate decision procedure for conjunctions of literals in the background theory.
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The SMT-LIB Standard Version 2.0

This paper introduces Version 2 of the SMT-LIB Standard, a major upgrade of the previous Version 1.2 which, in addition to simplifying and extending the languages of that version, includes a new command language for interfacing with SMT solvers.

Handbook of Satisfiability

The number of particles in the solution is likely to increase, but the amount of particles bound to cover the solution will not increase as much as previously thought.
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The Marabou Framework for Verification and Analysis of Deep Neural Networks

Marabou is an SMT-based tool that can answer queries about a network’s properties by transforming these queries into constraint satisfaction problems, and it performs high-level reasoning on the network that can curtail the search space and improve performance.
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A DPLL(T) Theory Solver for a Theory of Strings and Regular Expressions

A set of algebraic techniques for solving constraints over the theory of unbounded strings natively, without reduction to other problems are presented and implemented in the SMT solver cvc4 to expand its already large set of built-in theories to a theory of strings with concatenation, length, and membership in regular languages.
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CVC Lite: A New Implementation of the Cooperating Validity Checker Category B

We describe a tool called CVC Lite (CVCL), an automated theorem prover for formulas in a union of first-order theories. CVCL supports a set of theories which are useful in verification, including…
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CVC: A Cooperating Validity Checker

The CVC ("Cooperating Validity Checker") decision procedure is described, which implements a framework for combining subsidiary decision procedures for certain logical theories into a decision procedure for the theories' union.
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Algorithms for Verifying Deep Neural Networks

This article surveys methods that have emerged recently for soundly verifying whether a particular network satisfies certain input-output properties and provides pedagogical implementations of existing methods and compare them on a set of benchmark problems.
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Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT

This paper describes an alternative but similar approach to using SAT in conjunction with a more expressive fragment of first-order logic, however, rather than translating the entire formula up front, the formula is incrementally translated during a search for the solution.
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