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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 binary form and if the only sorts of production have the form
A → a (where a is a terminal symbol)
or
A → BC (where B and C are non-terminals)
We will show that every CFG G is λ- equivalent to a grammar G' that is in CNF (i.e. the only difference between G and G' is that may or may not be included. Since we know how to test for the presence of in our languages we will be able to construct equivalent grammars.
As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′ 0 . Since they cannot be reached from Q′ 0 there is no path from Q′ 0 to a sta
unification algorithm
(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?
Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
draw pda for l={an,bm,an/m,n>=0} n is in superscript
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
automata of atm machine
#Your company has 25 licenses for a computer program, but you discover that it has been copied onto 80 computers. You informed your supervisor, but he/she is not willing to take an
We now add an additional degree of non-determinism and allow transitions that can be taken independent of the input-ε-transitions. Here whenever the automaton is in state 1
The path function δ : Q × Σ* → P(Q) is the extension of δ to strings: This just says that the path labeled ε from any given state q goes only to q itself (or rather never l
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