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By F. D. Lewis

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What about the inputs: #bbb, #b011, and #11b10? 2. Examine the following Turing machine: I1 0 1 b # 1 0 b # right right left right same same next same I2 0 1 # 1 0 # halt left halt same What does it do when presented with the inputs #1011, #1111, and #0000? In general, what does this machine accomplish? 3. Design a Turing machine that subtracts 1 from its input. 4. Design a Turing machine that recognizes inputs that read the same forwards and backwards. ) 5. How many instructions does the machine of the previous exercise execute on inputs which are n symbols in length?

Since n-track machines can do everything that 1-track machines can do, we know immediately that every computable function can be computed by an n-track Turing machine. We must now show that for every n-track machine there is an equivalent 1-track machine. We shall demonstrate the result for a specific number of tracks since concrete examples are always easier to formulate and understand than the general case. So, rather than show this result for all values of n at once, we shall validate it for 2-track machines and claim that extending the result to any number of tracks is an fairly simple expansion of our construction.

1967. Finite and Infinite Machines. Prentice-Hall, The papers by Church, Kleene, Post, and Turing cited above have been reprinted in the collection: M. , The Undecidable. Y. 1965. PROBLEMS L The NICE Programming Language 1. Define a model of computation that does not depend on computers or programming. 2. We used floating point numbers instead of real numbers in our programming language. Why? 3. Add the data types character and string to the NICE language. Describe the operations that are needed to manipulate them.

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