BU CS 332 – Theory of Computation Lecture 24: • Final review Reading: Sipser Ch 7.1‐8.3, 9.1 Mark Bun April 29, 2020 Final Topics 5/5/2020 CS332 ‐ Theory of Computation 2 Everything from Midterms 1 and 2 • Midterm 1 topics: DFAs, NFAs, regular expressions, pumping lemma, context‐free grammars, pushdown automata, pumping lemma for CFLs […]
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CS 591 B1: Communication Complexity, Fall 2019 Problem Set 2 Due: 5:00PM, Friday, October 25, 2019. Homework Policies: • Submit your completed assignment by email to mbun[at]bu[dot]edu. Please include the string “CS591PS2” somewhere in your subject line. • Solutions must be typeset, e.g., using LATEX or Microsoft Word. • To help your instructor calibrate the
BU CS 332 – Theory of Computation Lecture 12: • TM Variants Reading: Sipser Ch 3.2, 4.1 • Decidable Languages Mark Bun March 4, 2020 Recognizers vs. Deciders • • in state OR • • halts on in state in state the set of all strings which accepts is Turing‐recognizable if
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BU CS 332 – Theory of Computation Lecture 16: • Mapping Reducibility Reading: Sipser Ch 5.3 Mark Bun March 25, 2020 Problems in language theory 𝑨𝑨𝐃𝐃𝐃𝐃𝐃𝐃 𝑨𝑨𝐂𝐂𝐃𝐃𝐂𝐂 𝑨𝑨𝐓𝐓𝐓𝐓 undecidable 𝑬𝑬𝑬𝑬𝑬𝑬 decidable decidable 𝐃𝐃𝐃𝐃𝐃𝐃 𝐂𝐂𝐃𝐃𝐂𝐂 𝐓𝐓𝐓𝐓 𝑬𝑬𝑬𝑬 𝑬𝑬𝑬𝑬 𝑬𝑬𝑬𝑬 𝐃𝐃𝐃𝐃𝐃𝐃 𝐂𝐂𝐃𝐃𝐂𝐂 decidable decidable undecidable 𝐓𝐓𝐓𝐓 3/24/2020 decidable ? ? CS332 – Theory of Computation 2 Reductions
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Prof. Mark Bun CAS CS 591 B: Communication Complexity Lecture Notes 2: Fooling Sets, Rank, and Covers Fall 2019 Reading. • Rao-Yehudayoff Chapter 1 (Fooling Sets and Rectangle Covers), Chapter 2 (through pg. 58) 1 Fooling Sets The method of fooling sets refines arguments based on rectangle size. Intuitively, a fooling set is a set
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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 9: • Midterm I review Reading: Sipser Ch 0‐2.3 Mark Bun February 19, 2020 Midterm I Topics 2/19/2020 CS332 ‐ Theory of Computation 2 Deterministic FAs (1.1) • Given an English or formal description of a language , draw the state diagram of a DFA recognizing (and
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Prof. Mark Bun CAS CS 591 B: Communication Complexity Lecture Notes 15: Introduction to Lifting Fall 2019 Reading. • Rao-Yehudayo, Chapter 8 Today we’ll begin our discussion of lifting theorems. Sometimes you will see these referred to as simulation theorems or hardness escalation theorems. Lifting is a quite general technique which takes lower bounds against
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BU CS 332 – Theory of Computation Lecture 19: • More on P Reading: Sipser Ch 7.2‐7.3 • Nondeterministic time, NP Mark Bun April 8, 2020 First topic: Time complexity Last time: Answering the basic questions 1. How do we measure complexity? (as in CS 330) 2. Asymptotic notation (as in CS 330) 3. How
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THE SIGN-RANK OF AC0 ∗ ALEXANDER A. RAZBOROV† AND ALEXANDER A. SHERSTOV‡ Abstract. The sign-rank of a matrix A = [Aij] with ±1 entries is the least rank of a real matrix B = [Bij] with AijBij > 0 for all i,j. We obtain the first exponential lower bound on the sign-rank of a function
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