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ProblemGenerate RE for a given finite automata by using the state elimination method.SolutionThere are two methods for converting a Deterministic Finite Automata (DFA) to Regular expression (RE).Arden's Theorem Method.State Elimination Method.The given automata is as follows−Step 1Initial state is A that has an incoming edge.So, we have to create a new initial state qi as follows−Step 2Initial state is B that has an incoming edge.So, we have to create a new final state qf as given below−Step 3Now, try to eliminate all intermediate states one by one.First eliminate state AThere is a path from state qi to B via A.So, ... Read More
ProblemGiven a Finite Automata, we need to convert the Finite Automata into equivalent Regular Expression using the State Elimination Method.Step 1 − Initial state q1 has incoming edge. So, create a new initial state qi.Step 2 − Final state q2 has outgoing edge. So, create a new final state.Step 3 − Start eliminating intermediate states one after another.If there is path going to qi to q2 via q1So after eliminating q1 we can connect a direct path from qi to q2 having costε .c*.a=c*aThere is a loop on q2 using state qiSo after eliminating state q1 we can draw a ... Read More
There are two methods for converting a Deterministic Finite Automata (DFA) to Regular expression (RE). These methods are as follows −Arden's Theorem Method.State Elimination Method.Now, let us learn about the state elimination method used in TOC.State Elimination MethodStep 1Initial state of DFA does not have any incoming edge.If there exists any incoming edge to the initial state, then we need to create a new initial state which has no incoming edge to it.An example about the relation between incoming edge and initial state is given below−Step 2There must be only one final state in DFA.If there exist multiple final states ... Read More
ProblemConstruct a regular expression for the given finite automata.SolutionStep 1 − Let us write down the equation.q1=q1a+ εq1 is the start state and ε will be added as the input a which is coming to q1 from q1.Hence, we writeState=source state of input * input coming to itStep 2 − Similarly, q2=q1b+q2bq3=q2aStep 3 − Let us simplify q1 first.q1=q1a+ εwe can re-write it as follows−q1= ε +q1aWhich is similar to R=Q+RP which has a solution as follows−R=QP*Step 4 − Assuming R=q1, Q= ε, P=aWe get q1 = ε.a* since ε.R=Rq1=a*Step 5 − Substituting values of q1 in q2 we get, ... Read More
Heap Sort is the sorting technique based on binary heap data structure. In order to proceed with heap sort, you need to be familiar with binary tree and binary heap.What is a Complete binary tree?A complete binary tree is a tree data structure where all the levels except the last one are completely filled. The last level must be filled from the left side.What is a Binary heap?Binary heap is a special case of the binary tree. Binary heaps are of two types −Max Heap − The parent node at each level is greater than its child nodes.Min Heap − ... Read More
Python has many active implementations. We will be addressing its different implementations and know which is the fastest implementation.Different implementations of Python −IronPython − This is the Python implementation which runs on .NET framework. This implementation is written in C#. It uses .net virtual machine for running. IronPython can use the python libraries and .net framework libraries.Jython − Jython is the implementation of Python which runs on the Java Platform. The jython makes use of the java classes and libraries. The jythoncode is compiled into java byte code and it is run on Java Virtual Machine.PyPy − This is the implementation of Python ... Read More
What is unit testing?Unit testing is a type of software testing where each individual component of the system is tested. Unit testing is important practice for the developers. It ensures that every component of the software is functioning appropriately as expected. Unit testing is mainly performed by the developers during the coding phase of the software development.Unit testing makes it easy to fix the problems as the developers come to know which particular component of the system or software has the issues and the developers can fix that particular unit.Python Unit TestingThe python has an in-built package called unittest which is ... Read More
Insertion sort is the simple method of sorting an array. In this technique, the array is virtually split into the sorted and unsorted part. An element from unsorted part is picked and is placed at correct position in the sorted part.The array elements are traversed from 1 to n.If the array element at position i is greater than its predecessor, it does not need to be moved.If the array element at position i is less than its predecessor, it needs to be shifted towards left until we find a predecessor smaller than it or if we reach at the leftmost ... Read More
Most of the applications need to be integrated or connected with a database for performing certain relevant operations. The majority of projects require database connectivity to store certain data about the users. MySQL Database can be integrated with the Python applications.To connect MySQL database, we need to have it installed on our system. We need MySQL Connector to establish connection with the database. We can install MySql Connector using the following command.python –m pip install mysql-connector-pythonThis will install the MySQL Connector which is used to connect the python project or application to a database.Create a connectionFirst of all, it is ... Read More
There are two methods for converting a Deterministic Finite Automata (DFA) to Regular expression (RE). These methods are as follows −Arden's Theorem Method.State Elimination Method.Let us understand the Arden's Theorem method in detail.Arden's TheoremLet P and Q be the two regular expressions.If P does not contain null string, then the following equation in R, viz R = Q + RP, Which has a unique solution by R = QP*Here, The finite automata (FA) does not have epsilon moves.It must have only initial state q1.Its states are q1, q2, q3, ....qn. The final state may be some qi where iRead More