International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 04 | Apr 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 4960 Partition Method for DFA Minimization Abhishek Singh 1 , Dr. Satwinder Singh 2 1 M. Tech (Computer Science and Technology), Central University of Punjab, Bathinda. 2 Assistant Professor, Dept. of Computer Science and Technology, Central University of Punjab, Bathinda. ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - It is usually perceived that there are many DFAs which have those states which are not necessary for the machine. Removal of those states cannot do any harm to machine. In this paper, our priority is to merge those states who are equal in terms of transition. A method is proposed through which it can be done. Key Words: DFA, Minimization. 1. INTRODUCTION DFA is a mathematical conception, due to which strings are operated by taking an input and after processing they give some output in the form of string. The language accepted or recognized by DFA is Regular Language. There are finite number of states in DFA, in which, there is at-most on outgoing edge/transition from one state to another. It has only one initial state but consists of a finite number of final states, means final state can be more than one. DFA minimization is a process in which DFA is converted to an equivalent another DFA in which number of states are particularly less. All states are compared through an algorithm and states those have same transitions are merged as they give equivalent output for an equivalent input. The main advantages for a minimal DFA is as follows: 1. A minimal DFA executes faster in terms of time. 2. As number of states go less, the cost for designing a machine also go less. 3. Having less number of states helps in designing the less complex structure of a machine. There are three types of non-productive states which can be merged or removed when minimization algorithm is applied on a given DFA. Two of them don’t change the structure of DFA but one of them changed it, however, language recognized by the DFA will be the same after minimization. The explanation of these non-productive states is: 1. Unreachable State: It is a state which cannot be reached directly or indirectly from initial state. If it is removed then, no changes are done in the language of machine as well as structure of machine. 2. Dead State: It is a state from which we cannot come back to any state and it will go to itself number of times as it will trap in itself. If it is removed, then no changes are done in the language of machine but there is a change in structure of machine. The DFA will be converted into NFA after removing dead state. 3. Equal State: Two states are said to be equal when both of states go to the final or non-final state for the same input transition. If both are go to the final or non-final state, then they can be merged as give same output for the same input. If they are merged, there is no change in language of machine as well as structure of machine. There is numerous minimization algorithm present to convert a DFA into minimal DFA. In this paper, we proposed a partition algorithm from which one can minimize the DFA. 2. PROPOSED WORK In our proposed algorithm, we take partition of states for minimization in a particular pattern. After applying the method, equivalent states are merged and the process is continued till all the states are compared for minimization and we get a minimized DFA.