Comparative Study of Performance of Tabulation and Partition Method for Minimization of DFA

Abstract

Automata is a machine that executes a set of functions in compliance with a seeded set of instructions. An automata is said to be finite automata if at any point of time, the machine can be in exactly one state among a finite set of states. Finite automata are categorized into two types: DFA and NFA. Deterministic finite automata is a finite and restricted state machine, where for every inserted symbol, there exists one and only one unique and idiosyncratic transition from a given particular state. Non-deterministic finite automata are a finite and restricted state machine where for every inserted symbol or character, there exist zero or one or more transitions on a given input symbol. Minimization of DFA involves reducing the number of states in a DFA and reaches the solution in lesser number of states. Since DFA is a rudimentary element of any computation machine, minimizing the number of states can reduce the computational time and increase the efficiency. Two algorithms for minimization tabulation method and partition method are conferred in this paper. To evaluate the performance, both the methods were implemented in C and Java languages. The execution times of both algorithms are compared to evaluate the performances of the algorithms in these two languages. The initial and final transition diagrams are graphically generated using Graphviz software.