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## Decidability

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Recall that algorithms represent procedures that stop on all inputs, so they are formalized by Turing machines (TMs) that also halt on any input strings. In terms of these machines, we investigate the power of problem -deciding algorithms in this chapter. In fact, we restrict our attention only to the algorithmic decidability concerning problems related to the mathematical models discussed earlier in this book.

Chapter Contents:

• 10.1 Turing deciders
• 10.2 Decidable problems
• 10.2.1 Decidable problems for finite automata
• 10.2.2 Decidable problems for context-free grammars
• 10.3 Undecidability: diagonalization
• 10.4 Undecidability: reduction
• 10.5 Undecidability: a general approach to reduction
• 10.6 Computational complexity
• 10.6.1 Time complexity
• 10.6.2 Space complexity

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