Verified AIG Algorithms in ACL2

And-Inverter Graphs (AIGs) are a popular way to represent Boolean functions (like circuits). AIG simplification algorithms can dramatically reduce an AIG, and play an important role in modern hardware verification tools like equivalence checkers. In practice, these tricky algorithms are implemented with optimized C or C++ routines with no guarantee of correctness. Meanwhile, many interactive theorem provers can now employ SAT or SMT solvers to automatically solve finite goals, but no theorem prover makes use of these advanced, AIG-based approaches. We have developed two ways to represent AIGs within the ACL2 theorem prover. One representation, Hons-AIGs, is especially convenient to use and reason about. The other, Aignet, is the opposite; it is styled after modern AIG packages and allows for efficient algorithms. We have implemented functions for converting between these representations, random vector simulation, conversion to CNF, etc., and developed reasoning strategies for verifying these algorithms. Aside from these contributions towards verifying AIG algorithms, this work has an immediate, practical benefit for ACL2 users who are using GL to bit-blast finite ACL2 theorems: they can now optionally trust an off-the-shelf SAT solver to carry out the proof, instead of using the built-in BDD package. Looking to the future, it is a first step toward implementing verified AIG simplification algorithms that might further improve GL performance.Comment: In Proceedings ACL2 2013, arXiv:1304.712

Implementing and reasoning about hash-consed data structures in Coq

We report on four different approaches to implementing hash-consing in Coq programs. The use cases include execution inside Coq, or execution of the extracted OCaml code. We explore the different trade-offs between faithful use of pristine extracted code, and code that is fine-tuned to make use of OCaml programming constructs not available in Coq. We discuss the possible consequences in terms of performances and guarantees. We use the running example of binary decision diagrams and then demonstrate the generality of our solutions by applying them to other examples of hash-consed data structures

Enabling natural interaction for virtual reality

This research focuses on the exploration of software and methods to support natural interaction within a virtual environment. Natural interaction refers to the ability of the technology to support human interactions with computer generated simulations that most accurately reflect interactions with real objects. Over the years since the invention of computer-aided design tools, computers have become ubiquitous in the product design process. Increasingly, engineers and designers are using immersive virtual reality to evaluate virtual products throughout the entire design process. The goal of this research is to develop tools that support verisimilitude, or likeness to reality, particularly with respect to human interaction with virtual objects. Increasing the verisimilitude of the interactions and experiences in a virtual environment has the potential to increase the external validity of such data, resulting in more reliable decisions and better products. First, interface software is presented that extends the potential reach of virtual reality to include low-cost, consumer-grade motion sensing devices, thus enabling virtual reality on a broader scale. Second, a software platform, VR JuggLua, is developed to enable rapid and iterative creation of natural interactions in virtual environments, including by end-user programmers. Based on this software platform, the focus of the rest of the research is on supporting virtual assembly and decision making. The SPARTA software incorporates a powerful physically-based modeling simulation engine tuned for haptic interaction. The workspace of a haptic device is both virtually expanded, though an extension to the bubble technique, and physically expanded, through integration of a haptic device with a multi-directional mobile platform. Finally, a class of hybrid methods for haptic collision detection and response is characterized in terms of five independent tasks. One such novel hybrid method, which selectively restores degrees of freedom in haptic assembly, is developed and assessed with respect to low-clearance CAD assembly. It successfully maintains the high 1000 Hz update rate required for stable haptics unlike previous related approaches. Overall, this work forms a pattern of contributions towards enabling natural interaction for virtual reality and advances the ability to use an immersive environment in decision making during product design