A push down automata (PDA) can be formally described as seven tuples(Q, Σ, S, δ, q0, I, F)Where, Q is finite number of statesΣ is input alphabetS is stack symbolΔ is the transition function: QX(Σ∪{e})XSXQq0 is the initial state (q0 belongs to Q)I is the initial state top symbolF is ... Read More

Turing machines are more powerful than both finite automata (FA) and pushdown automata (PDA). They are as powerful as any computer we have ever built.The main improvements from PDAs in Turing machine are explained below −Infinite “all” accessible memory (in the form of a tape) – option to read and ... Read More

Similar to the finite automata (FA), push-down automata (PDA) can be either deterministic or non-deterministic.A deterministic push down automata (DPDA) never has a choice of the next step −It has the possible output for every combination of state, input character and stack character, as compared to the deterministic finite automata ... Read More

A pushdown automaton is used to implement a context-free grammar in the same way that we use a technique to design DFA for a regular grammar. A DFA work on a finite amount of information, where as a PDA works on an infinite amount of information.Generally, a pushdown automaton is ... Read More

A string is accepted by an Non-deterministic Push down Automata (NPDA), if there is some path (i.e., sequence of instructions) from the start state to a final state that consumes all the letters of the string. Otherwise, the string is rejected by the NPDA.The language of an NPDA is the ... Read More

A regular grammar is the one where each production takes one of the following restricted forms −B → ∧, B → w, B → A, B → wA.(Where A, B are non-terminals and w is a non-empty string of terminals.)Restrictions of regular grammarOnly one nonterminal can appear on the right-hand ... Read More

Construct deterministic finite automata that accepts at most 3 a’s over an alphabet ∑={a, b}.At most 3 a’s means, The string contains 0 to max 3 a’s and any number of b’s.L= {Є, a, aa, aaa, ab, abb, bab, bbabaa, bbabaabbb, …..}Construct DFALet’s construct DFA step by step −Step 1Valid ... Read More

CKY means Cocke-Kasami-Younger. It is one of the earliest recognition and parsing algorithms. The standard version of CKY can only recognize languages defined by context-free grammars in Chomsky Normal Form (CNF).It is also possible to extend the CKY algorithm to handle some grammars which are not in CNF (Hard to ... Read More

ProblemConstruct DFA which accepts a string that contains second symbol is zero and fourth symbol is 1 over an alphabet ∑={0, 1}.SolutionInput − 00110Output is accepted; because in the given string the second symbol is ‘0’ and the fourth symbol is ‘1’.Input − 11001Output − string is not accepted, because the second symbol is ... Read More

According to the theorem, If L and M are two regular languages, then L ∩ M is also regular language.ExampleConstruct A∩B where A and B is given as follows −The language A ={10, 100, 00, 001, 1010, …..}The language B ={01, 1010, 10, 101, …..}AA = (QA, Σ, δA, qa, ... Read More