ACL2 Proofs of Nonlinear Inequalities with Imandra

We present a proof-producing integration of ACL2 and Imandra for proving nonlinear inequalities. This leverages a new Imandra interface exposing its nonlinear decision procedures. The reasoning takes place over the reals, but the proofs produced are valid over the rationals and may be run in both ACL2 and ACL2(r). The ACL2 proofs Imandra constructs are extracted from Positivstellensatz refutations, a real algebraic analogue of the Nullstellensatz, and are found using convex optimization.Comment: In Proceedings ACL2-2023, arXiv:2311.0837

Neural Networks in Imandra: Matrix Representation as a Verification Choice

The demand for formal verification tools for neural networks has increased as neural networks have been deployed in a growing number of safety-critical applications. Matrices are a data structure essential to formalising neural networks. Functional programming languages encourage diverse approaches to matrix definitions. This feature has already been successfully exploited in different applications. The question we ask is whether, and how, these ideas can be applied in neural network verification. A functional programming language Imandra combines the syntax of a functional programming language and the power of an automated theorem prover. Using these two key features of Imandra, we explore how different implementations of matrices can influence automation of neural network verification.Comment: FOMLAS'22, The 5th Workshop on Formal Methods for ML-Enabled Autonomous System

Template-Based Conjecturing for Automated Induction in Isabelle/HOL

Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We automate this laborious process with template-based conjecturing, a novel approach to generate auxiliary lemmas and use them to prove final goals. Our evaluation shows that our working prototype, TBC, achieved 40 percentage point improvement of success rates for problems at intermediate difficulty level.Comment: To appear at Fundamentals of Software engineering 2023 (http://fsen.ir/2023/

Early Verification of Legal Compliance via Bounded Satisfiability Checking

Legal properties involve reasoning about data values and time. Metric first-order temporal logic (MFOTL) provides a rich formalism for specifying legal properties. While MFOTL has been successfully used for verifying legal properties over operational systems via runtime monitoring, no solution exists for MFOTL-based verification in early-stage system development captured by requirements. Given a legal property and system requirements, both formalized in MFOTL, the compliance of the property can be verified on the requirements via satisfiability checking. In this paper, we propose a practical, sound, and complete (within a given bound) satisfiability checking approach for MFOTL. The approach, based on satisfiability modulo theories (SMT), employs a counterexample-guided strategy to incrementally search for a satisfying solution. We implemented our approach using the Z3 SMT solver and evaluated it on five case studies spanning the healthcare, business administration, banking and aviation domains. Our results indicate that our approach can efficiently determine whether legal properties of interest are met, or generate counterexamples that lead to compliance violations

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

The Design and Regulation of Exchanges: A Formal Approach

We use formal methods to specify, design, and monitor continuous double auctions, which are widely used to match buyers and sellers at exchanges of foreign currencies, stocks, and commodities. We identify three natural properties of such auctions and formally prove that these properties completely determine the input-output relationship. We then formally verify that a natural algorithm satisfies these properties. All definitions, theorems, and proofs are formalized in an interactive theorem prover. We extract a verified program of our algorithm to build an automated checker that is guaranteed to detect errors in the trade logs of exchanges if they generate transactions that violate any of the natural properties

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing