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Unformatted text preview: Turing Machines Chapter 3.1 1 Plan Turing Machines(TMs) Alan Turing ChurchTuring Thesis Definitions Computation Configuration Recognizable vs. Decidable Examples Simulator 2 Alan Turing Alan Turing was one of the founding fathers of CS. His computer model the Turing Machine (1936) was the inspiration for the electronic computer that came two decades later Was instrumental in cracking the Nazi Enigma cryptosystem in WWII Invented the Turing Test used in AI The Turing Award. Preeminent award in Theoretical CS (called the Nobel Prize of CS) 3 ChurchTuring Thesis Thesis Every effectively calculable function is a computable function Everything that is computable is computable by a Turing machine The thesis remains a hypothesis Despite the fact that it cannot be formally proven the ChurchTuring thesis now has nearuniversal acceptance. 4 Turing Machine Most powerful machine so far Similar to a finite automata 1. Uses infinite tape as memory 2. Can both read from and write to the tape 3. Read/write head can move left/right 4. Accept/reject take affect immediately Cannot solve all problems Comparison with Previous Models 6 Device Separate Input? Read/Write Data Structure Deterministic by default? FA Yes None Yes PDA Yes LIFO Stack No TM No 1way infinite tape. 1 cell access per step. Yes Formal Definition of a TM 7 Successor Program Sample Rules: 1. If read 1, write 0, go right, repeat....
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 Spring '08
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