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Dining Philosopher?s Problem (Dijkstra ?71) Project 2 Starts Today CS 603 Dining Philosopher?s Problem
Calvin College, US has reference to this Academic Journal, CS 603 Dining Philosopher?s Problem February 15, 2002 Project 2 Starts Today The winner: NTP Client Basic: Program that accepts NTP server as argument, gets in addition to returns time from that server Three points in consideration of well document in addition to tested solution Extras (worth one additional point): Fault Tolerant averaging solution: Accepts up so that four servers in addition to gives average after throwing away ?bad? servers Class library: Initialize sets offset from local clock, ?get time? returns local + offset without sending message Dining Philosopher?s Problem (Dijkstra ?71)
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Dining Philosophers: Solutions Simple: ?waiting? state Enter waiting state when neighbors eating When neighbors done, get forks Neighbors can?t enter waiting state if neighbor waiting Problem: Doesn?t prevent starvation Requires checking both neighbors at once Race condition Fully Distributed Solution (Lehman in addition to Rabin ?81) Problem alongside previous solutions Not truly distributed: Requires some sort of central coordination or global state Non-Symmetric: Different philosophers run different algorithms Additional properties: Deadlock free: Eventually someone new gets so that eat Lockout free: Eventually every hungry philosopher gets so that eat Adversary: One philosopher may try so that starve another Can?t just hold the fork indefinitely Communication only between adjacent philosophers No global state Can?t communicate alongside both at same time No Deterministic Solution Proof: Assume solution in consideration of philosophers 1.n Philosophers don?t know their number! Philosophers ?activated? in order from 1.n Each takes one step Claim: If symmetric at beginning of round, will be symmetric at end of round If anyone eating, all would be!
Probabilistic Solution Assume Random ?coin toss? Guaranteed alongside probability 1 so that break symmetry Idea: Try so that get one first Then get other If can?t get other, put first down in addition to try again But don?t go in consideration of the same fork first every time Think trying = true or die While trying s = random(left,right) Wait in consideration of fork s then take it If fork ~s available take it else drop fork s Eat drop s=random(left,right) drop fork ~s Lemmas: Assume Plato sitting so that left of Aristotle If Plato picks up fork infinite number of times, Aristotle finite number, then P(Plato eats infinite number of times)=1 If deadlocked, every philosopher picks up fork infinite number of times alongside probability 1 If after t steps, both trying so that eat, tried so that get same fork. Then alongside probability ? «, One picks up fork only finite number of times in future, or One gets so that eat in next two draws If at time t the last set of random draws is A, then alongside probability 1 there is a later configuration B ? A where two neighbors try so that get the same fork first Theorem: P(Deadlock) = 0 Assume P(Deadlock) > 0 By Lemma 2, if deadlocked everyone performs infinite draws By Lemma 4, alongside probability 1 there will be infinite sequence of configuration of last draws A0, A1, ? satisfying condition of Lemma 3 By Lemma 3, ?n some philosopher eats between An in addition to An+2 alongside probability 1 Therefore if deadlocked, non-deadlocked condition will occur alongside probability 1
Operational Assets: Utilization in addition to Disposition Objectives of the Chapter A. Depreciation (For Financial Reporting Purposes) iGAAP: Depreciation A.1a. Straight-Line Method 1a. Straight-Line Method (Partial Year Depreciation) 1b. Sum-of-the-Years?-Digits (SYD) 1b. S-Y-D (contd.) 1c. Declining-Balance Method 1c. Declining-Balance Method (contd.) Example: (S-L Depr. Method) Example: (Contd.) 3a.&b. Group in addition to Composite Methods Group in addition to Composite Methods (contd.) Group in addition to Composite Methods (contd.) Examples (Group Method) Retirement of Composite Assets (contd.) Disclosure of Depreciation (APB No. 12) The Use of Alternative Depreciation Methods Statistics from a Survey of 600 Companies Miscellaneous Points Related To Depreciation Miscellaneous Points Related To Depreciation (contd.) 2. ACRS (contd.) (Skip) MACRS Depreciation Methods MACRS Property Classes MACRS Property Classes (contd.) Principles Applied so that MACRS GAAP Depreciation in addition to Gain/Loss at Disposal Gain/Loss at Disposal (contd.) Table 11A-3 Table 11A-3 (contd.) Tax Versus GAAP Depreciation C. Asset Impairmentsa C. Asset Impairments (all intangibles related impairments (i.e., C1b in addition to C1c) should be deferred until chapter 12 is discussed) C.1a Operational Assets Held in consideration of Use ? Tangible Assets in addition to Finite-Life Intangibles (Patents, etc) Events or Changes in Circumstances Which May Lead so that an Impairment Events or Changes in Circumstances Which May Lead so that an Impairment (Cont.) The Accounting Treatment in consideration of Impairment (for Held in consideration of Use Tangible in addition to finite-Life Intangibles) Step 1: Conduct the Recoverability Test Step 2: Compute The Impaired Amount Write Off the Impaired Amount Impairment (contd.) iGAAP ?Assets Impairments iGAAP ? PPE Valuation in addition to Impairment (contd.) Impairment (contd.) C.1.b. Intangibles alongside indefinite life Other than Goodwill ? (Held-for-Use) C.1.b. (contd.) C.1.c. Impairment in consideration of Goodwill (SFAS 142) C.1.c. Impairment in consideration of Goodwill (cont.) Impairment in consideration of Goodwill (cont.) Impairment in consideration of Goodwill (cont.) Impairment in consideration of Goodwill (cont.) Impairment in consideration of Goodwill (cont.) Impairment in consideration of Goodwill (cont.) C.2 Impairment in consideration of Operational Assets so that be Sold (SFAS 144) Impairment in consideration of Operational Assets so that be Sold (cont.) C.3 Impairment in consideration of Operational Assets so that Be Disposed Other Than by Sale Summary of Asset Impairment: Assets Held in consideration of Use Summary of Asset Impairment: Assets Held so that Be Disposed of The Impact of SFAS 144 on the Disposal Loss of Discontinued operations The Impact of SFAS 144 on the Disposal Loss of Discontinued operations (contd.) The Impact of SFAS 144 on the Disposal Loss of Discontinued operations (cont.) Impairment Losses in addition to Earnings quality Impairment Losses in addition to Earnings quality (contd.)
Problem: Not Lockout-free Courteous Philosophers Possible in consideration of all but one so that starve Solution: If eating in addition to neighbor trying so that eat, once done wait until neighbor has eaten before trying again Requires more shared variables ?signal? so that neighbor: On/Off Share ?last? alongside neighbor: Left, Neutral, Right Initialized so that Neutral Only need mutual exclusion alongside one neighbor at a time Think trying = true; left_signal = right_signal = on s = random(left,right) Wait until s down in addition to (s-neighbor-signal = off or s-last = neutral or s-last = s) then lift fork s If ~s down then lift ~s; trying = false else drop s Eat left-signal = right-signal = off left-last = right; right-last = left Drop forks Lesson: Non-Determinism Gives Additional Power In fully distributed system, random variable solves problems that can?t otherwise be solved Used in practice Ethernet: Random backoff if collision Makes proving correctness harder Consider such solutions when building distributed systems!
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