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# 600.271: Automata and Computation Theory

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❶Uncountability of the number of languages that can be formed from a simple alphabet. Parse trees as capturing all derivation sequences.

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Scan the tape to see if there is any unmarked 0 found. This machine is identical to 3. If no unmarked 0 is found, accept. If no such unmarked 0 is found, accept.

Obviously, be an ordinary Turing machine. If recognizes the class of Turing- can simulate of can without problems. How simulates of is described as follows. We assume the following during the shifting for Step 3: We use states to remember the symbol to be shifted right. The first symbol of the tape after the shift is a symbol not used by the original M.

If the current symbol is c and the next symbol is the marked b, after the shifting, c becomes marked but b is not marked. The shifting stops when we see a blank symbol.

Let and be two decidable languages and and be the corresponding TMs. The aim is to construct a TM based on and such that the concatenation is also decidable. Since a given input concatenation of strings and has finite possible partitions, a nondeterministic TM is chosen to simplifies the description. Nondeterministically split into and 2. Besides, iff there exists a split of eventually halts because and is decidable since there exists an NTM Therefore, such that accepts are both deciders.

Let be a decidable language and be the corresponding TM. The aim is to construct a TM based on such that is also decidable. Since a given input has finite possible combinations of strings where and , a nondeterministic TM is chosen to simplify the description. Besides, eventually halts because is a decider. Therefore, is decidable since there exists an NTM which decides. Let be a decidable language and based on such that is described as follows.

TM be the corresponding TM. The aim is to construct a TM , the complement of , is also decidable. Besides, eventually halts because is decidable since there exists a TM which decides. The Let aim is to construct a TM based on and such that the intersection is is described as follows. Besides, is decidable 3. The aim is to construct a TM based on and such that the concatenation is also Turing-recognizable. Since a given input concatenation of strings and has finite possible partitions, a nondeterministic TM is chosen to simplify the description.

However, are not deciders. Therefore, which recognizes iff there exists a partition of such that may loop forever on some input because is Turing-recognizable since there exists an NTM. The aim is to is also Turing-recognizable. Since a given input has finite possible combinations of strings where nondeterministic TM is chosen to simplify the description. However, , where is not empty. The aim is to construct a TM based on and such that the intersection is also Turing-recognizable.

The resulting TM is described as follows. Convert G to an equivalent grammar in Chomsky normal form. Let which is a CFL from Problem 2. If TM accepts, produces no strings of lengths at least string of length at least p. If not, produces a 4. The goal is that is decidable iff the emptiness of is also decidable. Since is a CFL from in theorem 4. Let be the CFG of Problem 2. Suppose that every decider is in A. Since A is Turingrecognizable, A is also enumerable.

Let be the ith decider in A. We may construct the following decider as follows: Then can be derived by applying the diagonalization method as illustrated by the following table. The table below demonstrates an example. Obviously, reject accept accept Theory of Computation Homework 5 Solution.

Homework 3 Solution Set. Introduction to the Theory of Computation Homework 2 Solutions. Math Foundations of Mathematics Homework 8 Sample solution. Turing machine is the example of model of computation. Beside this, other models of computation given below: Our Theory of Computation Assignment help tutors help with topics like grammars and machines, Chomsky hierarchy, decidability;Models of computation such as Turing machines, RAM machines, Markov algorithms, Post systems, recursive functions, lambda-calculus; Computability: Some of the Theory of Computation assignments help topics include: We help with topics like properties of r.

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