The Not So Short Introduction to LATEX2ε Or LATEX2ε in 139 minutes by Tobias Oetiker Hubert Partl, Irene Hyna and Elisabeth Schlegl Version 6.3, March 26, 2018 ii Copyright ©1995-2016 Tobias Oetiker and Contributors. All rights reserved. This document is free; you can redistribute it and/or modify it under the terms of the GNU General […]
BU CS 332 – Theory of Computation Lecture 12: • TM Variants • Decidable Languages Mark Bun March 4, 2020 Reading: Sipser Ch 3.2, 4.1 Recognizers vs. Deciders 𝐿𝐿(𝑀𝑀) = the set of all strings 𝑤𝑤 which 𝑀𝑀 accepts 𝐴𝐴 is Turing-recognizable if 𝐴𝐴 = 𝐿𝐿(𝑀𝑀) for some TM 𝑀𝑀: •𝑤𝑤∈𝐴𝐴 ⟹ 𝑀𝑀haltson𝑤𝑤instate𝑞𝑞accept •𝑤𝑤∉𝐴𝐴 ⟹
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% % To use this as a template for turning in your solutions, change the flag % \inclsolns from 0 to 1. Make sure you include macros.tex in the directory % containing this file. Edit the “author” and “collaborators” fields as % appropriate. Write your solutions where indicated. % \def\inclsolns{0} \documentclass[12pt]{article} \usepackage{fullpage} \usepackage{graphicx} \usepackage{enumerate} \usepackage{comment}
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BU CS 332 – Theory of Computation Lecture 10: • Turing Machines Reading: Sipser Ch 3.1-3.2 • TM Variants Mark Bun February 26, 2020 Turing Machines – Motivation So far in this class we’ve seen several limited models of computation Finite Automata / Regular Expressions • Can do simple pattern matching (e.g., substrings), check parity,
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The Unbounded-Error Communication Complexity of Symmetric Functions∗ ALEXANDER A. SHERSTOV† Abstract We prove an essentially tight lower bound on the unbounded-error communication complexity of every symmetric function, i.e., f (x, y) = D(|x ∧ y|), where D: {0,1,…,n} → {0,1} is a given predicate and x, y range over {0, 1}n . Specifically, we show
BU CS 332 – Theory of Computation Lecture 11: • TM Variants • Closure Properties Mark Bun March 1, 2020 Reading: Sipser Ch 3.2 The Basic Turing Machine (TM) Tape 𝑎𝑎𝑏𝑏𝑎𝑎𝑎𝑎 Finite … Input control • Input is written on an infinitely long tape • Head can both read and write, and move in both
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BU CS 332 – Theory of Computation Lecture 15: • Undecidable and Unrecognizable Languages Reading: Sipser Ch 4.2, 5.1 • Reductions Mark Bun March 23, 2020 How can we compare sizes of infinite sets? Definition: Two sets have the same size if there is a correspondence (bijection) between them A set is countable if •
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Lower Bounds in Communication Complexity: A Survey Troy Lee Adi Shraibman Columbia University Weizmann Institute Abstract We survey lower bounds in communication complexity. Our focus is on lower bounds that work by first representing the communication complexity measure in Euclidean space. That is to say, the first step in these lower bound techniques is to
Beyond Set Disjointness: The Communication Complexity of Finding the Intersection Joshua Brody Amit Chakrabarti Ranganath Kondapally Swarthmore College Dartmouth College Dartmouth College brody@cs.swarthmore.edu ac@cs.dartmouth.edu rangak@cs.dartmouth.edu ABSTRACT David P. Woodruff IBM Almaden dpwoodru@us.ibm.com Grigory Yaroslavtsev Brown University, ICERM grigory@grigory.us 1. INTRODUCTION Communication complexity [Yao79] quantifies the com- munication necessary for two or more players to compute
CS 535: Complexity Theory, Fall 2020 Homework 8 Due: 2:00AM, Saturday, November 14, 2020. Reminder. Homework must be typeset with LATEX preferred. Make sure you understand the course collaboration and honesty policy before beginning this assignment. Collaboration is permitted, but you must write the solutions by yourself without assistance. You must also identify your collaborators.
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