Finite State Machines with Input Multiplexing (FSMIMs) were proposed in previous work as a technique for efficient mapping Finite State Machines (FSMs) into ROM memory. In this paper, we present new contributions to the optimization process involved in the implementation of FSMIMs in Field Programmable Gate Array (FPGA) devices. This process consists of two stages: (1) the simplification of the bank of input selectors of the FSMIM, and (2) the reduction of the depth of the ROM. This has a significant impact both on the number of used Look-Up Tables (LUTs) and on the number of the Embedded Memory Blocks (EMBs) required by the ROM. For the first stage, we present two approaches to optimize FSMIM implementations based on the Minimum Maximal k-Partial Matching (MMKPM) problem: one of them applies the greedy algorithm for the MMKPM problem, and the other based on a new multiobjetive variant of the MMKPM and its corresponding Integer Linear Programing formulation. We also propose a modification of the second stage, in which the characteristics of EMBs are taken into account to improve implementation results. The new optimization process significantly reduces the number of used FPGA resources with respect to the previous one. In addition, the proposed approaches achieve an adequate trade-off between the usage of EMBs and LUTs with respect to conventional FSM implementations based on ROM and to those based on LUT.

在以前的工作中提出了具有输入多路复用的有限状态机 (FSMIM) 作为一种将有限状态机 (FSM) 有效映射到 ROM 存储器的技术。在本文中，我们提出了对在现场可编程门阵列 (FPGA) 设备中实施 FSMIM 所涉及的优化过程的新贡献。这个过程包括两个阶段：（1）简化 FSMIM 的输入选择器组，以及（2）减小 ROM 的深度。这对使用的查找表 (LUT) 的数量和 ROM 所需的嵌入式存储器块 (EMB) 的数量都有重大影响。对于第一阶段，我们提出了两种基于最小最大k优化 FSMIM 实现的方法- 部分匹配（MMKPM）问题：其中一个应用贪心算法解决 MMKPM 问题，另一个基于 MMKPM 的新多目标变体及其相应的整数线性规划公式。我们还提出了对第二阶段的修改，其中考虑了 EMB 的特性以改善实施结果。与之前的优化过程相比，新的优化过程显着减少了使用的 FPGA 资源数量。此外，相对于基于 ROM 的传统 FSM 实现和基于 LUT 的实现，所提出的方法在 EMB 和 LUT 的使用之间实现了充分的权衡。