Equality saturation (eqsat) is a program optimization technique that uses syntax-based term rewriting to simultaneously explore many possible optimizations of a program, storing equivalent programs efficiently in a data structure called an e-graph. By exploring optimizations simultaneously, eqsat mitigates the phase ordering problem, where the order of optimizations significantly affects quality of results. Eqsat is especially promising for Electronics Design Automation (EDA), whose tools suffer from phase ordering. Previous eqsat-for-EDA efforts have focused on single tool stages; while they demonstrate significant benefits within a stage, they do not address phase ordering between stages. When we investigated the reason for their limited scope, we found that previous works struggle to implement an efficient hardware representation useful in both high-level (e.g. arithmetic optimization) and low-level (e.g. logic synthesis) tasks. The root issue is that such a representation must maintain equivalences between the high- and low-level portions of the language. While these equalities are conceptually simple—e.g., two high-level bitvectors are equal if they contain the same low-level bits—maintaining them using syntax-based rewrites alone proves inefficient in modern eqsat engines. In response, this paper makes two contributions. First, we introduce semantic e-graphs, an enhancement to e-graphs that improves performance of a narrow but highly useful class of semantics-based equalities. Second, we present Nextmap, a new eqsat-based hardware optimization engine whose representation uses semantic e-graphs to efficiently bridge high- and low-level hardware expressions. As a result, Nextmap simultaneously runs more EDA stages than previous eqsat-based works, more effectively mitigating phase ordering and reaching previously inaccessible optimizations. Compared with open-source and commercial tools, Nextmap provides competitive quality of results on a range of designs.

During chip development, engineers must target different technologies, such as simulation and various ASIC and FPGA technologies. Conventionally, they split parts of the code (e.g., memories) into separate technology-specialized blocks implementing the same high-level behavior. This leads to brittle code, with multiple but subtly different blocks describing the same semantic behavior, harming verification, agility, and extensibility. We propose fungible memories, an HDL-level "write once, map anywhere" memory abstraction with rich enough semantics to automatically target all relevant technologies using a single generic interface. We incorporate fungible memories into a compiler called Memo. For designs without a specific technology mapping, we also present a memory decompiler which lifts memories from an existing gate-level design to Memo, enabling automated technology re-targeting, which is a holy grail for digital designers. We present a structure-aware equality saturation technique which scales to netlists with millions of cells and identifies memories that the state of the art cannot. We demonstrate that Memo effectively targets backends across different technology platforms (simulation, ASIC, and FPGA) over a suite of representative designs, including a RISC-V multicore SoC.

Visualizations have become crucial in the contemporary data-driven world as they aid in exploring, verifying, and sharing insights obtained from data. In this paper, we propose a new paradigm of visualization synthesis based on refinement types. Besides input-output examples, users can optionally use refinement-type annotations to constrain the range of valid values in the example visualization or to express complex interactions between different visual components. Our system's outputs include both data transformation and visualization programs that are consistent with refinement-type specifications. To mitigate the scalability challenge during the synthesis process, we introduce a new visualization synthesis algorithm that uses lightweight bidirectional type checking to prune the search space. As we demonstrate experimentally, this new synthesis algorithm results in significant speed-up compared to prior work.

Large language models (LLMs) excel at implementing code from functionality descriptions but struggle with algorithmic problems that require not only implementation but also identification of the suitable algorithm. Moreover, LLM-generated programs lack guaranteed correctness and require human verification. To address these challenges, we propose ALGO, a framework that synthesizes Algorithmic programs with LLM-Generated Oracles to guide the generation and verify their correctness. ALGO first generates a reference oracle by prompting an LLM to exhaustively enumerate all the combinations of relevant variables. This oracle is then utilized to guide an arbitrary search strategy in exploring the algorithm space and to verify the synthesized algorithms. Our study shows that the LLM-generated oracles are correct for 88% of the cases. With the oracles as verifiers, ALGO can be integrated with any existing code generation model in a model-agnostic manner to enhance its performance. Experiments show that when equipped with ALGO, we achieve an 8× better one-submission pass rate over the Codex model and a 2.6× better one-submission pass rate over CodeT, the current state-of-the-art model on CodeContests. We can also get 1.3× better pass rate over the ChatGPT Code Interpreter on unseen problems. The problem set we used for testing, the prompts we used, the verifier and solution programs, and the test cases generated by ALGO are available at https://github.com/zkx06111/ALGO.

The generalizability of PBE solvers is the key to the empirical synthesis performance. Despite the importance of generalizability, related studies on PBE solvers are still limited. In theory, few existing solvers provide theoretical guarantees on generalizability, and in practice, there is a lack of PBE solvers with satisfactory generalizability on important domains such as conditional linear integer arithmetic (CLIA). In this paper, we adopt a concept from the computational learning theory, Occam learning, and perform a comprehensive study on the framework of synthesis through unification (STUN), a state-of-the-art framework for synthesizing programs with nested if-then-else operators. We prove that Eusolver, a state-of-the-art STUN solver, does not satisfy the condition of Occam learning, and then we design a novel STUN solver, PolyGen, of which the generalizability is theoretically guaranteed by Occam learning. We evaluate PolyGen on the domains of CLIA and demonstrate that PolyGen significantly outperforms two state-of-the-art PBE solvers on CLIA, Eusolver and Euphony, on both generalizability and efficiency.

In this paper, we present a method to reconstruct motion trajectories of the upper body using inertial measurement units (IMUs). We combine the use of complementary filters and biomechanical models to reconstruct upper body motions. At rst, we use complementary lters to combine information from low-frequency part of accelerometers and magnetometers, and high-frequency part of gyros to estimate sensor orientations and gyro bias. Then we use the estimated orientations of the upper arm and forearm to calculate trajectories of upper limb movements. Finally, we determine the set of parameters for complementary lters that minimized training errors. Experimental results indicate higher than 90% accuracy using accelerometers, gyros and magnetometers.