Simple algorithm to construct deterministic finite automata from non-deterministic finite automata using initial state transitions successor

Abstract

Theory of Computational Science (TCS) is a mathematical-based subject. We sensible had known that several Computer Science and Engineering learners face trouble in designing and understanding Finite Automata (FA). It is always being disquiet for the learners to understand the examples due to there are no universal steps to solving examples. The steps depend on the examples. FA includes Deterministic Finite Automata (DFA), Non-deterministic Finite Automata (NFA). Sometimes it is not possible to design DFA directly but, it is possible to design NFA, and then it is possible to convert it into DFA. The one input symbol has zero more than zero transitions in NFA while DFA has exactly one transition for each input symbol from each state. Every NFA has an equivalent DFA. The construction of DFA from NFA requires combinations of states which is in respect to the power of states. If there are ‘n’ states, then the combinations for conversion into DFA require a power set of ‘n’ states i.e. 2n states. If the number of states in NFA is more then it becomes complex to combine the states to convert into DFA and Also, it requires DFA minimization for avoiding repetition of states. Overcome the problem of a combination of states and DFA minimization. The algorithm uses initial state transitions successor for conversion into DFA. Initial transition states are considered as new states and take transition for all input symbols. This process is continued up to state transitions does not contain any new state. The Java Formal Languages and Automata Package (JFLAP) tool is used to implement the algorithm for the conversion of any kind of NFA to DFA. Conversion of NFA to DFA is a time-intensive procedure and it also handles the validations for acceptance or rejection of user-given input string. The algorithm is implemented step by step for a better understanding of learners which includes the design of the transition table, transition graph, and definition of DFA using tuple format. Also, it illustrates the acceptance or rejection of any constraint given by learners using Regular Expression(RE). The algorithm construction precise and optimum DFA for the NFA.