Abstract: In-memory computing shows great potential for data-intensive applications, with memristor-aided logic (MAGIC) being a key enabler. Efficient electronic design automation (EDA) tools are essential for implementing arbitrary Boolean functions in this paradigm. This paper presents a logic synthesis and verification framework for MAGIC-based in-memory computing, enabling the mapping of Boolean functions to memristor arrays, generation of micro-operations, and verification of results. To improve upon previous approaches, we introduce an area-aware mapping tool that optimizes the utilization of resistive random-access memory (RRAM). During logic synthesis, we propose a reinforcement learning (RL)-based tool for automatically generating optimized sequence flows, adapting to network characteristics for better mapping. To verify the mapping correctness, we introduce an equivalence verification tool that uses circuit structure for fast validation, also identifying bugs missed by previous methods. Experimental results show that our mapping tool reduces RRAM usage by 13% and 10% on average, with minimal increases of 1% and 2% in computation cycles, compared to state-of-the-art techniques. Additionally, the proposed synthesis recipe generation tool outperforms fixed flows and three heuristic algorithms (greedy, simulated annealing, and genetic algorithms), reducing the area-delay product by 21% and 6% for the ISCAS’85 and EPFL benchmarks, respectively.

Abstract: In this short note, we initiate the study of the Linear Isomorphism Testing Problem in the setting of communication complexity, a natural linear algebraic generalization of the classical Equality problem. Given Boolean functions $f, g : \mathbb{F}_2^n \to \{-1, +1\}$, Alice and Bob are tasked with determining whether $f$ and $g$ are equivalent up to a nonsingular linear transformation of the input variables, or far from being so. This problem has been extensively investigated in several models of computation, including standard algorithmic and property testing frameworks, owing to its fundamental connections with combinatorial circuit design, complexity theory, and cryptography. However, despite its broad relevance, it has remained unexplored in the context of communication complexity, a gap we address in this work. Our main results demonstrate that the approximate spectral norm of the input functions plays a central role in governing the communication complexity of this problem. We design a simple deterministic protocol whose communication cost is polynomial in the approximate spectral norm, and complement it with nearly matching lower bounds (up to a quadratic gap). In the randomised setting with private coins, we present an even more efficient protocol, though equally simple, that achieves a quadratically improved dependence on the approximate spectral norm compared to the deterministic case, and we prove that such a dependence is essentially unavoidable. These results identify the approximate spectral norm as a key complexity measure for testing linear invariance in the communication complexity framework. As a core technical ingredient, we establish new junta theorems for Boolean functions with small approximate spectral norm, which may be of independent interest in Fourier analysis and learning theory.