| Summary: | The model called Finite State Machine with Input Multiplexing (FSMIM) was proposed as a mechanism for implementing Finite State Machines (FSMs) using ROM memory. This paper presents a novel approach for achieving more efficient FSMIM implementations in Field Programmable Gate Array (FPGA) devices. The aim of the proposed approach is to obtain further reductions in the use of Embedded Memory Blocks (EMBs). Unlike previous works, the proposed approach reduces the depth of the ROM by grouping states before simplifying the input selectors of the FSMIM. For this purpose, a new strategy for grouping states is proposed, and its optimality is proven. In addition, a new variant of the Minimum Maximal <i>k</i>-Partial Matching (MMKPM) problem and its corresponding Integer Linear Programming (ILP) formulation are proposed for simplifying input selectors. The proposed approach requires a significantly smaller number of EMBs than the approaches proposed previously.
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