For each state, there is exactly one transition corresponding to each symbol of the respective alphabet. This is termed as the Deterministic Finite Automaton (DFA)Nondeterministic Finite Automaton (NFA)For each state there can be zero, one, two, or more transitions corresponding to a particular symbol.If NFA gets to a state with ... Read More

Finite automata is an abstract computing device. It is a mathematical model of a system with discrete inputs, outputs, states and a set of transitions from state to state that occurs on input symbols from the alphabet Σ.Formal definition of Finite AutomataFinite automata is defined as a 5-tuplesM=(Q, ∑, δ, ... Read More

ProblemGenerate the push down automata (PDA) that recognizes the language E={aibj| i is not equal to j and I is not equal to 2j}.SolutionConsider the two languages as given below −L1={aibj|i, j>=0 and i>2j}L2={aibj|i, j>=0 and iaA   A->aaAb|aA|epsilonIn L2, the number of a's are less than double the number of ... Read More

All grammars are not always optimized, which means the grammar may consist of some extra symbols (non-terminals) which increase the length of grammar.So, we have to reduce the grammar by removing the useless symbols.PropertiesThe properties to reduce grammar are explained below −Each non-terminal and terminal of G appears in the ... Read More

A Deterministic Finite automata (DFA) is a five tuplesM=(Q, ∑, δ, q0, F)Where, Q − Finite set called states.∑ − Finite set called alphabets.δ − Q × ∑ → Q is the transition function.q0 ∈ Q is the start or initial state.F − Final or accept state.Let’s see the worst ... Read More

ProblemDefine the language, E={aibj|i not equal to j and i not equal to 2j} and design an unambiguous context free grammar (CFG) in Chomsky normal form (CNF) that generates E.SolutionThe unambiguous CFG for the given language is as follows −S->AC|CBA->aA|aB->Bb|bC->aCb|aaCb|epsilonNow, convert this CFG into CNF. You can follow the below ... Read More

Context Free Grammars (CFG) are definitely recognized by Non-deterministic push down automata (NPDA), but Programming languages are translated to binary (Machine Code) via Deterministic PDA.This is because it has the following below mentioned impacts −If Programming languages were supposed to be translated via NPDA then for one given program instance ... Read More

The instantaneous description (ID) of a push down automata (PDA) is represented by a triple (q, w, s)Where, q is the state.w is unconsumed input.s is the stack contents.ID is an informal notation of how a PDA compares an input string and makes a decision that string is accepted or ... Read More

All grammars are not always optimized, which means the grammar may consist of some extra symbols (non-terminals) which increase the length of grammar.So, we have to reduce the grammar by removing the useless symbols.PropertiesThe properties to reduce grammar are explained below −Each non-terminal and terminal of G appears in the ... Read More

Let us understand the concept of recursive language before learning about the recursively enumerable language in the theory of computation (TOC).Recursive LanguageA language L is recursive (decidable) if L is the set of strings accepted by some Turing Machine (TM) that halts on every input.ExampleWhen a Turing machine reaches a ... Read More