A method is proposed targeting implementation of FPGA-based Mealy finite state machines. The main goal of the method is a reduction for the number of look-up table (LUT) elements and their levels in FSM logic circuits. To do it, it is necessary to eliminate the direct dependence of input memory functions and FSM output functions on FSM inputs and state variables. The method is based on encoding of the terms corresponding to rows of direct structure tables. In such an approach, only terms depend on FSM inputs and state variables. Other functions depend on variables representing terms. The method belongs to the group of the methods of structural decomposition. The set of terms is divided by classes such that each class corresponds to a single-level LUT-based circuit. An embedded memory block (EMB) generates codes of both classes and terms as elements of these classes. The mutual using LUTs and EMB allows diminishing chip area occupied by FSM circuit (as compared to its LUT-based counterpart). The simple sequential algorithm is proposed for finding the partition of the set of terms by a determined number of classes. The method is based on representation of an FSM by a state transition table. However, it can be used for any known form of FSM specification. The example of synthesis is shown. The efficiency of the proposed method was investigated using a library of standard benchmarks. We compared the proposed with some other known design methods. The investigations show that the proposed method gives better results than other discussed methods. It allows the obtaining of FSM circuits with three levels of logic and regular interconnections.

A method is proposed for reducing chip area occupied by logic circuits of FPGA-based Mealy finite state machines (FSMs). The proposed method aims at optimization of FSM circuits implemented with look-up table (LUT) elements of FPGA chip. The proposed method combines positive features of such state assignment methods as extended (ESCs) and composite (CSCs) state codes. The method is based on finding a partition of the set of internal states by classes of compatible states. To reduce LUT count, we propose a special kind of states codes named mixed state codes. These codes include two parts. The first part includes the maximum binary codes of states as elements of some partition class. The second part consists of the code of corresponding partition class. Unlike CSCs, the proposed approach allows obtaining partial state codes having different lengths. Unlike ESCs, all partial state codes consist of the same variables. Using mixed state codes allows obtaining LUT-based FSM circuits with exactly two levels of logic. The first level generates partial Boolean functions. The second level combines them into FSM outputs and input memory functions. If some conditions hold, then both levels consist of single-LUT circuits. Example of FSM synthesis based on mixed state codes is shown. The conducted experiments prove that the proposed approach allows reducing hardware compared with FSMs based on JEDI, one-hot state codes, CSCs and ESCs. On average, the proposed method reduces the value of LUT count by 6.21% compared to CSC-based FSMs and 22.21% compared to ESC-based counterparts. The advantages of the proposed approach grow with the growth of FSM complexness. An additional positive effect of the proposed method is a slight increase in the operating frequency.

A method is proposed which aims at reducing the number of LUTs in the circuits of FPGA-based Mealy finite state machines (FSMs) with transformation of...

Very often, a digital system includes sequential blocks which can be represented using a model of the finite state machine (FSM). It is very important to improve such FSM characteristics as the number of used logic elements, operating frequency and consumed energy. The paper proposes a novel technology-dependant design method targeting LUT-based Mealy FSMs. It belongs to the group of structural decomposition methods. The method is based on encoding the product terms of Boolean functions representing the FSM circuit. To diminish the number of LUTs, a partition of the set of internal states is constructed. It leads to three-level logic circuits of Mealy FSMs. Each function from the first level requires only a single LUT to be implemented. The method of constructing the partition with the minimum amount of classes is proposed. There is given an example of FSM synthesis with the proposed method. The experiments with standard benchmarks were conducted. They show that the proposed method can improve such FSM characteristics as the number of used LUTs. This improvement is accompanied by a decrease in performance. A positive side effect of the proposed method is a reduction in power consumption compared with FSMs obtained with other design methods.

Background: Petri nets are a formal specification technique for modelling of control processes and modern flexible manufacturing systems. Interpreted Petri nets take into account input and output signals, allowing to apply them in any control system or even in control part of a cyber-physical system. Due to the fact that Petri nets are not used in the industrial practice, the students sometimes lack motivation to learn them. Contributions: In the paper we propose how to help students learn interpreted Petri nets with Minecraft (as a game-based learning). We show how interpreted Petri nets can be modelled in Minecraft and how they communicate with the surrounding environment via input and output signals to visualize control processes. The proposed approach has been validated experimentally among university students. Hypotheses: (1) Creating interpreted Petri net models with Minecraft helps to understand the basic principles; (2) Minecraft makes the course more attractive. Methodology: Students were divided into an experimental group (with game-based learning) and a control group (with traditional learning). The experimental group filled in a knowledge test twice (on the entry and on the exit) and a questionnaire. The control group filled in the same knowledge test at the end of the course. Findings: The observations confirm that the Minecraft-based teaching of interpreted Petri nets allows to gain better results in final tests, making at the same time the course more attractive and enjoyable.

The main purpose of the method proposed in this article is to reduce the number of look-up-table (LUT) elements in logic circuits of sequential devices. The devices are represented by models of Mealy finite state machines (FSMs). Thesee are so-called MPY FSMs based on two methods of structural decomposition (the replacement of inputs and encoding of output collections). The main idea is to use two types of state codes for implementing systems of partial Boolean functions. Some functions are based on maximum binary codes; other functions depend on extended state codes. The reduction in LUT counts is based on using the method of twofold state assignment. The proposed method makes it possible to obtain FPGA-based FSM circuits with four logic levels. Only one LUT is required to implement the circuit corresponding to any partial function. An example of FSM synthesis using the proposed method is shown. The results of the conducted experiments show that the proposed approach produces LUT-based FSM circuits with better area-temporal characteristics than for circuits produced using such methods as Auto and One-hot of Vivado, JEDI, and MPY FSMs. Compared to MPY FSMs, the values of LUT counts are improved. On average, this improvement is 8.98%, but the gain reaches 13.65% for fairly complex FSMs. The maximum operating frequency is slightly improved as compared with the circuits of MPY FSMs (up to 0.64%). For both LUT counts and frequency, the gain increases together with the growth for the numbers of FSM inputs, outputs and states.