Exploring formal verification methodology for FPGA-based digital systems.

Abstract Not Provide

Verification of a Rust Implementation of Knuth's Dancing Links using ACL2

Dancing Links connotes an optimization to a circular doubly-linked list data structure implementation which provides for fast list element removal and restoration. The Dancing Links optimization is used primarily in fast algorithms to find exact covers, and has been popularized by Knuth in Volume 4B of his seminal series The Art of Computer Programming. We describe an implementation of the Dancing Links optimization in the Rust programming language, as well as its formal verification using the ACL2 theorem prover. Rust has garnered significant endorsement in the past few years as a modern, memory-safe successor to C/C++ at companies such as Amazon, Google, and Microsoft, and is being integrated into both the Linux and Windows operating system kernels. Our interest in Rust stems from its potential as a hardware/software co-assurance language, with application to critical systems. We have crafted a Rust subset, inspired by Russinoff's Restricted Algorithmic C (RAC), which we have imaginatively named Restricted Algorithmic Rust, or RAR. In previous work, we described our initial implementation of a RAR toolchain, wherein we simply transpile the RAR source into RAC. By so doing, we leverage a number of existing hardware/software co-assurance tools with a minimum investment of time and effort. In this paper, we describe the RAR Rust subset, describe our improved prototype RAR toolchain, and detail the design and verification of a circular doubly-linked list data structure employing the Dancing Links optimization in RAR, with full proofs of functional correctness accomplished using the ACL2 theorem prover.Comment: In Proceedings ACL2-2023, arXiv:2311.08373. arXiv admin note: substantial text overlap with arXiv:2205.1170

Lessons from Formally Verified Deployed Software Systems (Extended version)

The technology of formal software verification has made spectacular advances, but how much does it actually benefit the development of practical software? Considerable disagreement remains about the practicality of building systems with mechanically-checked proofs of correctness. Is this prospect confined to a few expensive, life-critical projects, or can the idea be applied to a wide segment of the software industry? To help answer this question, the present survey examines a range of projects, in various application areas, that have produced formally verified systems and deployed them for actual use. It considers the technologies used, the form of verification applied, the results obtained, and the lessons that can be drawn for the software industry at large and its ability to benefit from formal verification techniques and tools. Note: a short version of this paper is also available, covering in detail only a subset of the considered systems. The present version is intended for full reference.Comment: arXiv admin note: text overlap with arXiv:1211.6186 by other author

Functional pearl: a SQL to C compiler in 500 lines of code

We present the design and implementation of a SQL query processor that outperforms existing database systems and is written in just about 500 lines of Scala code - a convincing case study that high-level functional programming can handily beat C for systems-level programming where the last drop of performance matters. The key enabler is a shift in perspective towards generative programming. The core of the query engine is an interpreter for relational algebra operations, written in Scala. Using the open-source LMS Framework (Lightweight Modular Staging), we turn this interpreter into a query compiler with very low effort. To do so, we capitalize on an old and widely known result from partial evaluation known as Futamura projections, which state that a program that can specialize an interpreter to any given input program is equivalent to a compiler. In this pearl, we discuss LMS programming patterns such as mixed-stage data structures (e.g. data records with static schema and dynamic field components) and techniques to generate low-level C code, including specialized data structures and data loading primitives

Synchronous Digital Circuits as Functional Programs

Functional programming techniques have been used to describe synchronous digital circuits since the early 1980s and have proven successful at describing certain types of designs. Here we survey the systems and formal underpinnings that constitute this tradition. We situate these techniques with respect to other formal methods for hardware design and discuss the work yet to be done

A functional approach to heterogeneous computing in embedded systems

Developing programs for embedded systems presents quite a challenge; not only should programs be resource efficient, as they operate under memory and timing constraints, but they should also take full advantage of the hardware to achieve maximum performance. Since performance is such a significant factor in the design of embedded systems, modern systems typically incorporate more than one kind of processing element to benefit from specialized processing capabilities. For such heterogeneous systems the challenge in developing programs is even greater.In this thesis we explore a functional approach to heterogeneous system development as a means to address many of the modularity problems that are typically found in the application of low-level imperative programming for embedded systems. In particular, we explore a staged hardware software co-design language that we name Co-Feldspar and embed in Haskell. The staged approach enables designers to build their applications from reusable components and skeletons while retaining control over much of the generated source code. Furthermore, by embedding the language in Haskell we can exploit its type classes to write not only hardware and software programs, but also generic programs with overloaded instructions and expressions. We demonstrate the usefulness of the functional approach for co-design on a cryptographic example and signal processing filters, and benchmark software and mixed hardware-software implementations. Co-Feldspar currently adopts a monadic interface, which provides an imperative functional programming style that is suitable for explicit memory management and algorithms that rely on a certain evaluation order. For algorithms that are better defined as pure functions operating on immutable values, we provide a signal and array library that extends a monadic language, like Co-Feldspar. These extensions permit a functional style of programming by composing high-level combinators. Our compiler transforms such high-level code into efficient programs with mutating code. In particular, we show how to execute an FFT safely in-place, and how to describe a FIR and IIR filter efficiently as streams. Co-Feldspar’s monadic interface is however quite invasive; not only is the burden of explicit memory management quite heavy on the user, it is also quite easy to shoot on eself in the foot. It is for these reasons that we also explore a dynamic memory management discipline that is based on regions but predictable enough to be of use for embedded systems. Specifically, this thesis introduces a program analysis which annotates values with dynamically allocated memory regions. By limiting our efforts to functional languages that target embedded software, we manage to define a region inference algorithm that is considerably simpler than traditional approaches

Preimage Attack on MD4 Hash Function as a Problem of Parallel Sat-Based Cryptanalysis

In this paper we study the inversion problem of MD4 cryptographic hash function developed by R. Rivest in 1990. By MD4-k we denote a truncated variant of MD4 hash function in which k represents a number of steps used to calculate a hash value (the full version of MD4 function corresponds to MD4-48). H. Dobbertin has showed that MD4-32 hash function is not one-way, namely, it can be inverted for the given image of a random input. He suggested to add special conditions to the equations that describe the computation of concrete steps (chaining variables) of the considered hash function. These additional conditions allowed to solve the inversion problem of MD4-32 within a reasonable time by solving corresponding system of equations. The main result of the present paper is an automatic derivation of “Dobbertin’s conditions” using parallel SAT solving algorithms. We also managed to solve several inversion problems of functions of the kind MD4-k (for k from 31 up to 39 inclusive). Our method significantly outperforms previously existing approaches to solving these problems