International Journal of Advanced Engineering Research and Science (IJAERS) [Vol-6, Issue-7, Jul- 2019] https://dx.doi.org/10.22161/ijaers.6726 ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Page | 218 Analysis of Genetic Algorithm for synthesis digital systems modeled in finite state machine Mateus Ferreira da Silva, Warley Gramacho da Silva, Rafael Lima de Carvalho, Edeilson Milhomem da Silva, Tiago da Silva Almeida Department of Computer Science, Universidade Federal do Tocantins, Palmas/TO, Brazil Abstract —To achieve smaller digital systems, like microprocessors, controller, etc., it is require design them with a small area and the treats the power dissipation. These issues are important because can prolong the time of use of the equipment and reduce the manufacturing costs. To do so, digital circuits can be modeled as finite state machines with a large amount of states for most practical problems. To achieve a minimum result, you need to optimize a state assignment. Find a solution that meets these characteristics, i.e., find the optimal state assignments is a complex task, because it is an NP-Complete problem. Thus, this research analyzed the Genetic Algorithm to obtain an optimization in the state assignment in a reasonable time. The experiments showed good results, however, the adjusts of the parameters of GA must be investigated to find better results. Keywords—Digital Systems, Finite State Machine, Genetic Algorithm, Metaheuristic, Synthesis of Circuits. I. INTRODUCTION Nowadays, transistor fabrication technology has reached such a scale of miniaturization that physical limitations can become an obstacle to continuous evolution proposed in Moore's law [1]. The production scale of the transistors is currently very small, about 10 nm, reducing more than this is challenge, because as the transistors get smaller, they are subject to more imperfections during the manufacturing process. Which makes it increasingly difficult maintain the integrity of the electrical signals. Therefore, it is necessary to plan more efficient logical structures, able to reduce the area in silicon. Hence the importance of the work in revisiting the area of Finite State Machine (FSM) optimization with the goal of designing efficient logic circuits. Minor digital circuits occupy a small area and additionally have low power dissipation. These characteristics can be obtained with the optimization of the state assignment in FSM. FSM is a sequential circuit design technology widely adopted at the system level [2],FSMs are composed of inputs, outputs and states. A state is a record of the main information of a system, each state must receive a specific binary code (which is named assignment state). According to [3], FSM is a generic sequential circuit consisting of a section made of combinational logic and a section of memory (usually flip-flops). An FSM called X can be defined as the mathematical model  = (,,,,) , where I, O and S are finite and non-empty sets of inputs, outputs and states, respectively.:  ×  →  is the next state function, :× → is the output function for Mealy Model and : →  is the output function for Moore Model. Note that minimal FSMs are desirable because they consume less resources, that is, transistors, which in turn will consume less power, occupy less area on the viable surface of the silicon chip, dissipate less heat and can work in higher frequencies. To optimize the combinational circuit of FSMs a very important factor is the assignment of states. Optimizing the state assignment is a complex task, since all possible arrangements must be tested to obtain the optimal assignment, the total number of possible single assignment for an FSM is given by.  ( , ) = ( 2  −1 ) ! (! ( 2  − ) !) (1) wheren is the number of states and b is the number of bits needed to represent each state, therefore, it is an NP- Complete problem. The general objective of this work is to evaluate the results of the application of metaheuristic (Genetic Algorithm - GA) algorithms in the search for an optimization in the assignment of states in polynomial time. II. RELATED WORK Algorithms specializing in heuristic searches are becoming popular for solving complex optimization problems, which are in the class of NP-Complete