Construct a recognizer, Let L1 and L2 be CGF. We show that L1 ∩ L2 is CFG t...

Let L1 and L2 be CGF. We show that L1 ∩ L2 is CFG too. Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the sec

Binary form and chomsky normal form, Normal forms are important because the...

Normal forms are important because they give us a 'standard' way of rewriting and allow us to compare two apparently different grammars G1  and G2. The two grammars can be shown to

Push down automata, Construct a PDA that accepts { x#y | x, y in {a, b}* su...

Construct a PDA that accepts { x#y | x, y in {a, b}* such that x ? y and xi = yi for some i, 1 = i = min(|x|, |y|) }. For your PDA to work correctly it will need to be non-determin

Context free grammar, A context free grammar G = (N, Σ, P, S)  is in binary...

A context free grammar G = (N, Σ, P, S)  is in binary form if for all productions A we have |α| ≤ 2. In addition we say that G is in Chomsky Normaml Form (CNF) if it is in bi

Notes, write short notes on decidable and solvable problem

write short notes on decidable and solvable problem

Create a general algorithm from a checking algorithm, Claim Under the assum...

Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about

Boolean operations - class of recognizable languages, Theorem The class of ...

Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give

Strictly local generation automaton, Another way of interpreting a strictly...

Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh

Arden''s theorem,

How to solve the checking problem, The objective of the remainder of this a...

The objective of the remainder of this assignment is to get you thinking about the problem of recognizing strings given various restrictions to your model of computation. We will w