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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 noted that an unsolvable problem might be partially solvable by an algorithm that makes a complete search for a solution. In such case the solution is eventually found whenever it is defined, but the search might continue forever whenever the solution is undefined. Similarly, an undecidable problem might also be partially decidable by an algorithm that makes an exhaustive search.
The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carrie
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One of the first issues to resolve, when exploring any mechanism for defining languages is the question of how to go about constructing instances of the mechanism which define part
The path function δ : Q × Σ* → P(Q) is the extension of δ to strings: This just says that the path labeled ε from any given state q goes only to q itself (or rather never l
Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be
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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
The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo
We developed the idea of FSA by generalizing LTk transition graphs. Not surprisingly, then, every LTk transition graph is also the transition graph of a FSA (in fact a DFA)-the one
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