Information Technology FIT3143 – LECTURE WEEK 10 SIMD AND DATA PARALLEL ARCHITECTURES Copyright By PowCoder代写 加微信 powcoder Topic Overview • Flynn’s Taxonomy • Definition of SIMD • Streaming SIMD Extensions (SSE) • SSE vs MMX • SSE, SSE2, SSE3, SSE4 & AVX Learning outcome(s) related to this topic • Explain the fundamental principles of parallel […]
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Microsoft PowerPoint – CS332-Lec24-ann BU CS 332 – Theory of Computation Lecture 24: • More NP‐completeness • Space complexity (?) Reading: Sipser Ch 7.4‐7.5, 8.1‐8.2 Mark Bun April 26, 2021 Polynomial‐time reducibility Definition: A function ∗ ∗ is polynomial‐time computable if there is a polynomial‐time TM which, given as input any ∗, halts with only on its tape. Definition: Language is polynomial‐time reducible to language , written if there is a polynomial‐time computable function ∗ ∗ such that for all strings ∗, we have 4/26/2021 CS332 ‐ Theory of Computation 2 NP‐completeness “The hardest languages in NP” Definition: A language is NP‐complete if 1) and
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PowerPoint Presentation BU CS 332 – Theory of Computation Lecture 23: • NP-completeness Reading: Sipser Ch 7.4-7.5 Mark Bun April 21, 2021 Last time: Two equivalent definitions of NP 1) NP is the class of languages decidable in polynomial time on a nondeterministic TM NP = ⋃𝑘𝑘=1 ∞ NTIME(𝑛𝑛𝑘𝑘) 2) A polynomial-time verifier for a
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Microsoft PowerPoint – CS332-Lec16-ann BU CS 332 – Theory of Computation Lecture 16: • Examples of Reductions • Test 2 Review Reading: Sipser Ch 5.1 Mark Bun March 15, 2021 Reductions A reduction from problem to problem is an algorithm for problem which uses an algorithm for problem as a subroutine If such a reduction exists, we say “ reduces to ” 3/17/2021 CS332 ‐ Theory of Computation 2 Positive uses: If reduces to and is decidable, then is also decidable Ex. is decidable is decidable Negative uses: If reduces to and is undecidable, then is also undecidable Ex. is undecidable is decidable Equality Testing for TMs Theorem: is undecidable Proof: Suppose for contradiction that there exists a decider for
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PowerPoint Presentation BU CS 332 – Theory of Computation Lecture 15: • Review mid-semester feedback • Reductions Reading: Sipser Ch 5.1 Mark Bun March 15, 2021 What helps you learn best? • Lectures in general (13) • In-class examples / walkthroughs (11) • Interaction in lecture, polls (7) • Discussion sections in general (7) •
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b’6d2b600c6835d497c21831b347468c5c4eac31′ blob 10007�#include #include #include #include #include #include #include “contextmanager.h” #include “crypto.h” #include “err.h” using namespace std; /// Load an RSA public key from the given filename /// /// @param filename The name of the file that has the public key in it /// /// @return An RSA context for encrypting with the provided public
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PowerPoint Presentation BU CS 332 – Theory of Computation Lecture 22: • Nondeterministic time, NP • NP-completeness Reading: Sipser Ch 7.3-7.4 Mark Bun April 14, 2021 Big-Oh, formally 𝑓 𝑛 = 𝑂(𝑔 𝑛 ) means: There exist constants 𝑐 > 0, 𝑛0 > 0 such that 𝑓 𝑛 ≤ 𝑐𝑔 𝑛 for every 𝑛 ≥
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Microsoft PowerPoint – CS332-Lec21-ann BU CS 332 – Theory of Computation Lecture 21: • Complexity Class P • Nondeterministic time, NP Reading: Sipser Ch 7.2, 7.3 Mark Bun April 12, 2021 Complexity class Definition: is the class of languages decidable in polynomial time on a basic single‐tape (deterministic) TM • Class doesn’t change if we substitute in another reasonable deterministic model (Extended Church‐Turing) • Cobham‐Edmonds Thesis: Roughly captures class of problems that are feasible to solve on computers 4/12/2021 CS332 ‐ Theory of Computation 2 Describing and analyzing polynomial‐time algorithms • Due to Extended Church‐Turing Thesis, we can still use high‐level descriptions on multi‐tape machines • Polynomial‐time is robust under composition: executions of ‐time subroutines run on ‐ size inputs gives an algorithm running in time. Can freely use algorithms we’ve seen before as subroutines if we’ve analyzed their runtime • Need to be careful about size of inputs! (Assume inputs represented in binary unless otherwise stated.) 4/12/2021 CS332 ‐ Theory of Computation 3 Examples of languages in
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b’589772f610dcdc20e6b95b7539ee6a941ac1df’ blob 983�#include #include #include #include #include #include “err.h” using namespace std; /// Run the AES symmetric encryption/decryption algorithm on a buffer of bytes. /// Note that this will do either encryption or decryption, depending on how the /// provided CTX has been configured. After calling, the CTX cannot be used /// again until it
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Microsoft PowerPoint – CS332-Lec13-ann BU CS 332 – Theory of Computation Lecture 13: • Decidable Languages • Universal TM • Countability and Diagonalization Reading: Sipser Ch 4.1, 4.2 Mark Bun March 8, 2021 A “universal” algorithm for recognizing regular languages Theorem: is decidable Proof: Define a 3‐tape TM on input 1. Check if is a valid encoding (reject if not) 2. Simulate on , i.e., • Tape 2: Maintain 𝑤 and head location of 𝐷 • Tape 3: Maintain state of 𝐷, update according to 𝛿 3. Accept if ends in an accept state, reject otherwise 3/8/2021 CS332 ‐ Theory of Computation 2 More Decidable Languages: Emptiness Testing Theorem: is decidable Proof: The following TM decides On input , where is a DFA with
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