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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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CS 21 Decidability and Tractability Winter 2024 Posted: February 28 Solution Set 6 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. First, observe that subgroup isomorphism is in NP, because if we are given a specification of the subgraph of G
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CS21 Decidability and Tractability • undecidable problems – computation histories – surprising contrasts between Copyright By PowCoder代写 加微信 powcoder decidable/undecidable • Rice’s Theorem • Post Correspondence Problem (skip) • Beyond RE and co-RE • Recursion Theorem February 5, 2024 CS21 Lecture 14 2 Dec. and undec. problems • two problems regarding Context-Free Grammars: – does
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