A SAT Solver and Computer Algebra Attack on the Minimum Kochen-Specker Problem

One of the foundational results in quantum mechanics is the Kochen-Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as revealing a pre-existing value. The theorem hinges on the existence of a mathematical object called a KS vector system. While many KS vector systems are known to exist, the problem of finding the minimum KS vector system has remained stubbornly open for over 55 years, despite significant attempts by leading scientists and mathematicians. In this paper, we present a new method based on a combination of a SAT solver and a computer algebra system (CAS) to address this problem. Our approach improves the lower bound on the minimum number of vectors in a KS system from 22 to 24, and is about 35,000 times more efficient compared to the previous best computational methods. The increase in efficiency derives from the fact we are able to exploit the powerful combinatorial search-with-learning capabilities of a SAT solver together with the isomorph-free exhaustive generation methods of a CAS. The quest for the minimum KS vector system is motivated by myriad applications such as simplifying experimental tests of contextuality, zero-error classical communication, dimension witnessing, and the security of certain quantum cryptographic protocols. To the best of our knowledge, this is the first application of a novel SAT+CAS system to a problem in the realm of quantum foundations

Automated Formal Analysis of Internet Routing Configurations

Today\u27s Internet interdomain routing protocol, the Border Gateway Protocol (BGP), is increasingly complicated and fragile due to policy misconfigurations by individual autonomous systems (ASes). To create provably correct networks, the past twenty years have witnessed, among many other efforts, advances in formal network modeling, system verification and testing, and point solutions for network management by formal reasoning. On the conceptual side, the formal models usually abstract away low-level details, specifying what are the correct functionalities but not how to achieve them. On the practical side, system verification of existing networked systems is generally hard, and system testing or simulation provide limited formal guarantees. This is known as a long standing challenge in network practice --- formal reasoning is decoupled from actual implementation. This thesis seeks to bridge formal reasoning and actual network implementation in the setting of the Border Gateway Protocol (BGP), by developing the Formally Verifiable Routing (FVR) toolkit that combines formal methods and programming language techniques. Starting from the formal model, FVR automates verification of routing models and the synthesis of faithful implementations that carries the correctness property. Conversely, starting from large real-world BGP systems with arbitrary policy configurations, automates the analysis of Internet routing configurations, and also includes a novel network reduction technique that scales up existing techniques for automated analysis. By developing the above formal theories and tools, this thesis aims to help network operators to create and manage BGP systems with correctness guarantee

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

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

CRAFT: A library for easier application-level Checkpoint/Restart and Automatic Fault Tolerance

In order to efficiently use the future generations of supercomputers, fault tolerance and power consumption are two of the prime challenges anticipated by the High Performance Computing (HPC) community. Checkpoint/Restart (CR) has been and still is the most widely used technique to deal with hard failures. Application-level CR is the most effective CR technique in terms of overhead efficiency but it takes a lot of implementation effort. This work presents the implementation of our C++ based library CRAFT (Checkpoint-Restart and Automatic Fault Tolerance), which serves two purposes. First, it provides an extendable library that significantly eases the implementation of application-level checkpointing. The most basic and frequently used checkpoint data types are already part of CRAFT and can be directly used out of the box. The library can be easily extended to add more data types. As means of overhead reduction, the library offers a build-in asynchronous checkpointing mechanism and also supports the Scalable Checkpoint/Restart (SCR) library for node level checkpointing. Second, CRAFT provides an easier interface for User-Level Failure Mitigation (ULFM) based dynamic process recovery, which significantly reduces the complexity and effort of failure detection and communication recovery mechanism. By utilizing both functionalities together, applications can write application-level checkpoints and recover dynamically from process failures with very limited programming effort. This work presents the design and use of our library in detail. The associated overheads are thoroughly analyzed using several benchmarks

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers