The language L accepted by Non-deterministic finite automata (NFA) with ε, denoted by M= (Q, Σ, 𝛿, q0, F) and can be defined as follows −Let M= (Q, Σ, 𝛿, q0, F) be a NFA with εWhere, Q is a set of statesΣ is input setδ is a transition function ... Read More

ProblemConvert the given finite automata (FA) into regular expression (RE).SolutionThere are two popular methods for converting a DFA to its regular expression −Arden’s MethodState elimination methodLet’s consider the state elimination method to convert FA to RE.RulesThe rules for state elimination method are as follows −Rule 1The initial state of DFA ... Read More

ProblemDerive a derivation tree for the string aabbabba for the given context free grammar (CFG) −S->aB|bA A->a|aS|bAA B->b|bS|aBBSolutionDerivation is a sequence of production rules, which is used to get input strings.Derivation treeIt is a graphical representation for derivation of given production rules for a given CFG. It is also called ... Read More

Finite automata (FA) is an abstract computing device. It can be represented in the following −Graphical (Transition diagrams)Tabular (Transition table)Mathematical (Transition function)The formal definition of FA is that it is a five tuples.M=(Q, Σ, δ, q0, F)Where, Q: Finite set called statesΣ: Finite set called alphabetsδ: Q × Σ → ... Read More

ProblemLet’s consider a grammar to derive “abb” string using LMD and RMD   S->AB/ ε   A-> aB   B-> SbSolutionWe have to use context free grammar.Derivation is a sequence of production rules, which is used to get input strings.During parsing, we have to take two decisions, which are as follows −We have ... Read More

ProblemGenerate the language for the given context free grammar.S->0S, S-> λS-> A0, A->1A, A-> λS->000S, S-> λSolutionContext free grammar (CFG) is a formal grammar that is used to generate all the possible patterns of strings in a given formal language.CFG is defined by four tuplesG=(V, T, P, S)Where, T: Set ... Read More

We extend the class of NFAs by allowing instantaneous ε transitions −The automaton may be allowed to change its state without reading the input symbol 2.In diagrams, such transitions are depicted by labeling the appropriate arcs with ε.Note that this does not mean that E has become an input symbol. ... Read More

ProblemConvert the following Non-Deterministic Finite Automata (NFA) to Deterministic Finite Automata (DFA).SolutionThe transition diagram is as follows −The transition table of NFA is as follows −Stateab->q0q0q0, q1q1-*q2*q2--The DFA table cannot have multiple states. So, make q0q1 as a single state.Let’s convert the given NFA to DFA by considering two states ... Read More

In Non-Deterministic Finite Automata, for any current state and input symbol, there exists more than one next output state.Any string is accepted if and only if there exists at least one transition path which is starting at initial state and ending at final state.The following steps are followed to convert ... Read More

ProblemDesign a Moore machine for a binary input sequence such that if it has a substring 101, the machine outputs A, if the input has substring 110, it outputs B otherwise it outputs C.SolutionFor designing such a machine, we will check two conditions, and those are 101 and 110. If ... Read More