Lecture 1 : Course Overview and Turing machine complexity
نویسنده
چکیده
1. Basic properties of Turing Machines (TMs), Circuits & Complexity 2. P, NP, NP-completeness, Cook-Levin Theorem. 3. Hierarchy theorems, Circuit lower bounds. 4. Space complexity: PSPACE, PSPACE-completeness, L, NL, Closure properties 5. Polynomial-time hierarchy 6. #P and counting problems 7. Randomized complexity 8. Circuit lower bounds 9. Interactive proofs & PCP Theorem Hardness of approximation 10. Communication complexity (?) 11. Strong Exponential Time Hypothesis (SETH). COnnecting the complexity of SAT and polynomialtime problems.
منابع مشابه
Algebra and Computation Course Instructor : V . Arvind Lecture 22 : Simon ’ s Problem and towards Shor
Last lecture we saw a toy problem that showed that the quantum model could be more efficient than the turing machine model, query complexity in the last example. In this lecture, we shall inspect one more problem, which in a way is a true separation from the classical and quantum model since it beats even randomized algorithms on classical turing machines. The techniques used here will be essen...
متن کاملLecture 11 : Randomization and Complexity
Definition 1.1. A probabilistic Turing machine (PTM) M is a TM with two transition functions in place of the usual one: δ0 : Q × Γ → Q × (Γ × L, S,R) and δ1 : Q × Γ → Q× (Γ× L, S,R). At each time step, independently, the algorithm chooses b from {0, 1} with equal probability 1/2 and makes its move using transition function δb. The running time of M is the maximum number of steps before M halts ...
متن کاملITCS : CCT 09 : Computational Complexity Theory Mar 18 , 2009 Lecture 7
In the previous lectures, we have introduced the concept of deterministic oracle Turing machines. The concept of non-deterministic oracle Turing machines is just a direct extension of that to the non-deterministic case. To be precise, a non-deterministic oracle Turing machine (sometimes abbreviated to “oracle NTM”) is just like a deterministic oracle TM, but with a non-deterministic transition ...
متن کاملEe291e Lecture 21: Controller Synthesis: Formulation
1 Overview A control problem involves: 1. A plant 2. A speciication 3. A controller Controller synthesis involves coming up with a methodology for designing controllers that meet the speciica-tion. The discussion in this lecture is based on 1].
متن کاملBasic Complexity
This paper summarizes a series of three lectures the first author was invited to present at the NZMRI summer 2000 workshop, held in Kaikoura, New Zealand. Lecture 1 presents the goals of computational complexity theory. We discuss (a) what complexity provably can never deliver, (b) what it hopes to deliver but thus far has not, and finally (c) where it has been extremely successful in providing...
متن کامل