BU CS 332 – Theory of Computation Lecture 19: • More on P • Nondeterministic time, NP Mark Bun April 8, 2020 Reading: Sipser Ch 7.2-7.3 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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CS 332: Theory of Computation Professor Mark Bun Boston University April 6, 2020 Homework 7 – Due Monday, April 13, 2020 before 2:00PM Reminder Collaboration is permitted, but you must write the solutions by yourself without assistance, and be ready to explain them orally to the course staff if asked. You must also identify your
BU CS 332 – Theory of Computation Lecture 21: • NP‐Completeness • Cook‐Levin Theorem • Reductions Reading: Sipser Ch 7.3‐7.5 Mark Bun April 15, 2020 Last time: Two equivalent definitions of 1) is the class of languages decidable in polynomial time on a nondeterministic TM 2) A polynomial‐time verifier for a language is
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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 4/29/2020 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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BU CS 332 – Theory of Computation Lecture 18: • Time Complexity • Complexity Class P Reading: Sipser Ch 7.1-7.2 Mark Bun April 6, 2020 Where we are in CS 332 Automata & Formal Languages Computability Complexity Previous unit: Computability theory What kinds of problems can / can’t computers solve? Final unit: Complexity theory What
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BU CS 332 – Theory of Computation Lecture 20: • More on NP Reading: Sipser Ch 7.3-7.5 Mark Bun April 13, 2020 Goals of complexity theory Ultimate goal: Classify problems according to their feasibility and inherent computational difficulty P ≈ Decision problems which can be solved efficiently Can we exhibit general classes of problems which
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BU CS 332 – Theory of Computation Lecture 8: • Equivalence between PDAs and CFGs • Closure Properties Mark Bun February 18, 2020 Reading: Sipser Ch 2.2 Pushdown Automaton (the idea) • Nondeterministic finite automaton + stack • Stack has unlimited size, but machine can only manipulate (push, pop, read) symbol at the top Input
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Prof. Mark Bun CAS CS 591 B: Communication Complexity Lecture Notes 8: Disjointness Lower Bound Fall 2019 Reading. • Rao-Yehudayoff Chapter 6 The lower bound of Ω(n) on the randomized communication complexity of Disjointness is perhaps the most impactful result in the entire area. It has consequences in circuit complexity, property testing, algorithmic game theory,
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BU CS 332 – Theory of Computation Lecture 20: • More on NP Reading: Sipser Ch 7.3‐7.5 • P vs. NP Mark Bun April 13, 2020 Goals of complexity theory Ultimate goal: Classify problems according to their feasibility and inherent computational difficulty Decision problems which can be solved efficiently Can we exhibit general classes of
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CS 332: Theory of Computation Professor Mark Bun Boston University February 13, 2020 Homework 3 – Due Tuesday, February 18, 2020 before 2:00PM Reminder Collaboration is permitted, but you must write the solutions by yourself without assistance, and be ready to explain them orally to the course staff if asked. You must also identify your