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1. Simulate a TM with infinite tape on both ends using a two-track TM with finite storage
2. Prove the following language is non-Turing recognizable using the diagnolization principle { (M, w) | TM M, starts with input w, does not halt}
3. Construct a TM for L = {w| w contains equal number of 0's and 1's} over {0,1} a) provide an algorithmic description b) draw the transition diagram
4. Consider a language L = {0m10n10max(m,n)| m, n>= 0}. Construct a TM that decides the language. Describe the algorithm and draw the transition diagram of the TM.
5. Given the following TM M, does M a) accept or b) reject on inputs w1 = 000 and w2=0000? Show the content of the input tape and positions of the head step-by-step.
The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea
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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
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We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al
The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan
First model: Computer has a ?xed number of bits of storage. You will model this by limiting your program to a single ?xed-precision unsigned integer variable, e.g., a single one-by
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