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CS 21 Decidability and Tractability Winter 2024 Posted: February 21 Solution Set 5 If you have not yet turned in the Problem Set, you should not consult these solutions. Copyright By PowCoder代写 加微信 powcoder 1. (a) We will reduce 2-COLORABLE to 2-SAT, which we showed to be in P. Given a graph G, our reduction […]
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CS21 Decidability and Tractability Lecture 2 January 5, 2024 Terminology • finite alphabet Σ : a set of symbols Copyright By PowCoder代写 加微信 powcoder • language L ⊆ Σ∗: subset of strings over Σ • a machine takes an input string and either – accepts, rejects, or – loops forever • a machine recognizes the
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CS21 Decidability and Tractability Lecture 16 February 9, 2024 Complexity • Complexity Theory = study of what is computationally feasible (or tractable) with Copyright By PowCoder代写 加微信 powcoder limited resources: – running time – storage space – number of random bits – degree of parallelism – rounds of interaction – others… February 9, 2024 CS21
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CS21 Decidability and Tractability Lecture 9 January 24, 2024 Deciding CFLs • Convert CFG into Chomsky Normal Form Copyright By PowCoder代写 加微信 powcoder • parse tree for string x generated by nonterminal A: January 24, 2024 IfA→k x (k>1)thentheremust be a way to split x: • A → BC is a production and •B→i yandC⇒j
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CS21 Decidability and Tractability Lecture 25 March 4, 2024 • Challenges to Extended Church-Turing – randomized computation – quantum computation Copyright By PowCoder代写 加微信 powcoder March 4, 2024 CS21 Lecture 25 2 Extended Church-Turing Thesis • the belief that TMs formalize our intuitive notion of an efficient algorithm is: • randomizedcomputationchallengesthisbelief March 4, 2024 CS21
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CS21 Decidability and Tractability Lecture 6 January 17, 2024 Context-free grammars and languages • languages recognized by a (N)FA are exactly the languages described by regular expressions, and they are called the regular languages Copyright By PowCoder代写 加微信 powcoder • languages recognized by a NPDA are exactly the languages described by context-free grammars, and they
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CS21 Decidability and Tractability Lecture 23 February 28, 2024 • language L is in coNP iff its complement (co-L) is in NP • it is believed that NP ≠ coNP Copyright By PowCoder代写 加微信 powcoder • note: P = NP implies NP = coNP – proving NP ≠ coNP would prove P ≠ NP –
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CS21 Decidability and Tractability Lecture 10 January 26, 2024 Turing Machine diagrams start state qreject Copyright By PowCoder代写 加微信 powcoder b → R transition label: (tape symbol read → (1 accept + 1 reject) tape symbol written, direction moved) – a → R means “read a, move right” – a → L means “read a,
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CS21 Decidability and Tractability Lecture 21 February 23, 2024 • NP-complete problems: independent set, vertex cover, clique… • NP-complete problems: Hamilton path and cycle,Traveling Salesperson Problem Copyright By PowCoder代写 加微信 powcoder • NP-complete problems: Subset Sum • NP-complete problems: NAE-3-SAT, max cut February 23, 2024 CS21 Lecture 21 2 “x1” “x2 ” February 23, 2024
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CS21 Decidability and Tractability Lecture 3 January 8, 2024 NFA diagrams (single) start state • At each step, several choices for next state – if possible to reach accept, then input accepted Copyright By PowCoder代写 加微信 powcoder January 8, 2024 CS21 Lecture 3 2 transitions: (several) accept states • may have several with a given
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