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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.
How useful is production function in production planning?
S-->AAA|B A-->aA|B B-->epsilon
Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff ≡L partitions Σ* into ?nitely many Nerode equivalence classes. Proof: For the "only if" direction (that every recogn
how to convert a grammar into GNF
You are required to design a system that controls the speed of a fan's rotation. The speed at which the fan rotates is determined by the ambient temperature, i.e. as the temperatur
Automata and Compiler (1) [25 marks] Let N be the last two digits of your student number. Design a finite automaton that accepts the language of strings that end with the last f
Describe the architecture of interface agency
This was one of the ?rst substantial theorems of Formal Language Theory. It's maybe not too surprising to us, as we have already seen a similar equivalence between LTO and SF. But
Paths leading to regions B, C and E are paths which have not yet seen aa. Those leading to region B and E end in a, with those leading to E having seen ba and those leading to B no
Exercise Show, using Suffix Substitution Closure, that L 3 . L 3 ∈ SL 2 . Explain how it can be the case that L 3 . L 3 ∈ SL 2 , while L 3 . L 3 ⊆ L + 3 and L + 3 ∈ SL
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