turing, Theory of Computation

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turing machine for prime numbers

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Closure properties to prove regularity, The fact that regular languages are...

The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations

DFA, designing DFA

designing DFA

Applying the pumping lemma, Applying the pumping lemma is not fundamentally...

Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complica

Exhaustive search, A problem is said to be unsolvable if no algorithm can s...

A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be note

Equivalence problem, The Equivalence Problem is the question of whether two...

The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular

Strictly local languages, We have now de?ned classes of k-local languages f...

We have now de?ned classes of k-local languages for all k ≥ 2. Together, these classes form the Strictly Local Languages in general. De?nition (Strictly Local Languages) A langu

Pendulum Swings, how many pendulum swings will it take to walk across the c...

how many pendulum swings will it take to walk across the classroom?

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

Class of recognizable languages, Proof (sketch): Suppose L 1 and L 2 are ...

Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(

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