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In-memory processing offers a promising solution for enhancing the performance of data-intensive applications. While analog in-memory computing demonstrates remarkable efficiency, its limited precision is suitable only for approximate computing tasks. In contrast, digital in-memory computing delivers the deterministic precision necessary to accelerate high-assurance applications. Current digital in-memory computing methods typically involve manually breaking down arithmetic operations into in-memory compute kernels. In contrast, traditional digital circuits are synthesized through intricate and automated design workflows. In this article, we introduce a logic synthesis framework called LOGIC, which facilitates the translation of high-level applications into digital in-memory compute kernels that can be executed using non-volatile memory. We propose techniques for decomposing element-wise arithmetic operations into in-memory kernels while minimizing the number of in-memory operations. Additionally, we optimize the sequence of in-memory operations to reduce non-volatile memory utilization. To address the NP-hard execution sequencing optimization problem, we have developed twolook-aheadalgorithms that offer practical solutions. Additionally, we leverage data layout reorganization to efficiently accelerate applications that heavily rely on sparse matrix-vector multiplication operations. Our experimental evaluations demonstrate that our proposed synthesis approach improves the area and latency of fixed-point multiplication by 84% and 20% compared to the state-of-the-art, respectively. Moreover, when applied to scientific computing applications sourced from the SuiteSparse Matrix Collection, our design achieves remarkable improvements in area, latency, and energy efficiency by factors of 4.8×, 2.6×, and 11×, respectively.