You own one share of a non dividend-paying stock. Because you worry that its price may drop over the next year, you decide to employ a rolling insurance strategy, which entails obtaining one 3-month European put option on the stock every three months, with the first one being bought immediately. You are given: (i) The continuously compounded risk-free interest rate is 8%. (ii) The stock's volatility is 30%. (iii) The current stock price is 45. (iv) The strike price for each option is 90% of the then-current stock price. Your broker will sell you the four options but will charge you for their total cost now. Under the Black-Scholes framework, how much do you now pay your broker?

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(a) What is the von Neumann bottleneck and why can it limit performance on today's RISC machines? (b) What computer architecture techniques are used to mitigate the effects of the von Neumann bottleneck on RISC machines as compared to early computers like EDSAC? (e change the memory hierarchy? Justify your answer. (a) Consider a multicore processor running the MSI cache coherence protocol in each core's private caches. The caches are connected to each other and memory via a snoopy bus. (i) What is a cache coherence protocol and in what systems is it needed? [4 marks] (ii) What events would lead a cache to issue a bus transaction if it holds a block of data in state S? [4 marks] (iii) When and why does data need to be flushed back to memory in this protocol? [4 marks] (b) (i) What are the semantics of load linked and store conditional instructions?

Evil Robot has been kidnapped by experimental psychologists, who are forcing him to solve problems involving the stacking of blocks. For example, given the start state on the left, he is asked to re-arrange the blocks into the state shown on the right. = B D D C B A C A You are to help him solve these problems by designing a system using planning graphs. A block can only be moved if it does not have another block on top of it. Only one block can be placed directly on top of another, although stacks of multiple blocks are allowed. (a) Explain how this problem can be represented as a planning problem, such that it can be analyzed using a planning graph. Describe how state should be represented, and how actions should be represented, giving a specific example relevant to the stated problem in each case. [5 marks] (b) Using the start state in the diagram above, draw the initial planning graph for the problem, including the initial state level, the first action level, and the state level resulting from the first action level. Do not add any mutex links at this stage. [4 marks] (c) Define an inconsistent effects mutex and an interfering actions mutex. Add to your diagram for Part (b) a single example of each, or explain why this is not possible. [4 marks] (d) Define a competing for preconditions mutex. By adding a small number of actions to the second action level of your planning graph, give a single example of such a mutex, or explain why this is not possible. [2 marks] (e) How many more action levels would you expect to need before a valid plan could be extracted to solve the problem stated? Explain your answer. [2 marks] (f ) Give two examples of the difficulties that might arise if we also wish to include long blocks as follows: B E B D D A C A = E C In each case explain why it might be difficult to address such an extension using planning graphs. [3 marks] 2 CST1.2019.6.3 2 Artificial Intelligence (a) Describe the state-variable representation for planning by discussing the following, giving specific examples of each concept: (i) Rigid relations and state variables. [2 marks] (ii) Actions. [2 marks] (iii) The representation of state. [2 marks] (iv) Goals and solutions. [2 marks] (b) Your boss has suggested using heuristic search to solve a planning problem expressed in the state-variable representation. Explain how this might be achieved. You do not need to suggest a specific heuristic at this stage. [3 marks] (c) Comment on whether or not heuristic search is a good approach to solving planning problems in the state-variable representation, compared with the alternative of using a constraint satisfaction solver. [5 marks] (d) Suggest an admissible heuristic that could be used when applying A? search to solving a planning problem in the state-variable representation. Show that it is admissible. [4 marks] 3 (TURN OVER) CST1.2019.6.4 3 Complexity Theory A Boolean formula is said to be satisfiable if there is an assignment : V {true, false} of values to the variables of that makes it true. A quantified Boolean formula is an expression that is (i) either a Boolean formula; or (ii) X where is a quantified Boolean formula and X is variable; or (iii) X where is a quantified Boolean formula and X is variable. We say that a quantified Boolean formula is satisfied by an assignment : V {true, false} if either is a Boolean formula that is made true by ; or is X and either [X/true] or [X/false] make true; or is X and both [X/true] and [X/false] make true. Here, [X/v] denotes the assignment that is the same as for all variables apart from X, and it maps X to the truth value v. We write QBF for the decision problem of determining whether a given quantified Boolean formula is satisfiable. In answering the questions below, you may assume the NP-completeness of any standard problem, as long as you state your assumptions clearly. (a) Show that QBF is

(a) In the above network, use Dijkstra's shortest-path algorithm to compute the shortest path from E to all network nodes. Show your working in a table: each column indicating a destination node, each row indicating an iteration of the algorithm. [10 marks] (b) In 2008 an ISP was reported to have hijacked traffic for YouTube causing traffic for YouTube to be diverted into the ISP's network. At the time, YouTube used only three IP addresses; 208.65.153.238, 208.65.153.251 and 208.65.153.253, announced as a single prefix 208.65.152.0/22. Despite YouTube using only three addresses, each browser's YouTube URL requests are ultimately routed to the closest of over a dozen data-centres Google operates world-wide. (i) Describe two concepts from the course that make this possible. [2 marks] (ii) State the smallest advertised netblock that would identify all YouTube addresses. [1 mark] (iii) In an attempt to resolve the problem, YouTube advertised the netblock 208.65.153.0/24, but this was the same netblock as advertised by the rogue ISP. Why would this not solve the problem? [2 marks] (iv) YouTube advertised two smaller netblocks, each one half of 208.65.153.0/24. Why should this now work? [2 marks] (v) BGP networks may optionally filter netblocks that are below a given size. This filtering affected the YouTube fix in (b)(iv), but not that in (b)(iii). Estimate the size of the netblock filter. [1 mark] (vi) Why does BGP implement such filtering? [2 marks] 7 (TURN OVER) CST.2015.5.8 6 Computer Networking (a) An older home-network router has an upload bandwidth of 1Mbit/s to the Internet, and a 100kbyte first-in first-out (FIFO) buffer for packets awaiting transmission. Packets have a maximum transmission unit (MTU) of 1500 bytes. (i) If the buffer is completely full, how long does it take the router to transmit all of the bytes in the buffer? [2 marks] (ii) Suppose the router supports two FIFO queues, one high-priority for interactive applications (like Voice over IP) and the other lower-priority for all remaining traffic. If a VoIP packet arrives when the queue for interactive applications is empty, what is the maximum time before the router starts transmitting the VoIP packet? (Assume that the router does not preempt any ongoing packet transmission.)

(a) (i) Name the four necessary conditions for deadlock. [2 marks] (ii) Which of these conditions is frequently precluded in operating-system kernel designs in order to prevent deadlocks and why? [2 marks] (b) Deadlocks are not limited to locks; cycles of waiting on condition variables can also lead to the "deadly embrace". (i) Explain why it might be more difficult to debug deadlocks involving condition variables than those simply involving locks. [2 marks] (ii) Briefly describe a condition-variable API change that might allow this problem to be solved in some cases; explain why it cannot always help. [2 marks] (c) FreeBSD's WITNESS feature checks statically defined and dynamically discovered lock orders. Each time a lock is acquired, any previously undiscovered graph edges involving lock types currently held by the thread and the newly acquired lock type will be added to the graph. Cycle detection is performed, and debug information is printed if a previously unreported cycle is discovered. (i) Describe a common code structure in which programmers are likely to be able to define a static order between two lock types. [2 marks] (ii) Describe a common case in which programmers are likely to rely instead on dynamic discovery of an order between two lock types. [2 marks] (iii) Unlike the deadlock-detection algorithm presented in lecture, the WITNESS algorithm does not remove edges when locks are released. Explain why WITNESS's behaviour might be more useful in practice. [2 marks] (iv) WITNESS is subject to false positives: warnings can be emitted due to legitimate cycles even though, by design, the cycle could never trigger an actual deadlock. Describe a situation in which this might arise, and explain why deadlock could never occur. [3 marks] (v) WITNESS, as written, is intended to be used with mutexes and other lock types providing mutual exclusion. A developer might navely extend WITNESS to support reader-writer locks (rwlock) by introducing graph edges for both read and write acquires as it does for mutex acquires. Explain why this might not always lead to the desired result. [3 marks] 9 (TURN OVER) CST.2015.5.10 8 Concurrent and Distributed Systems (a) (i) Define the term capability. [2 marks] (ii) What two fields must RBAC-based ACL entries always contain? [2 marks] (b) Network-Attached Secure Disks (NASD) utilise file managers and block servers. File-manager RPCs exchange an authorised user ID, password, and object ID for a keyed cryptographic capability granting block access: f(k, ObjID, rights). (i) Describe the consequences of a user learning the value of key k. [2 marks] (ii) Alice obtains a capability for object Oi . Bob then issues an RPC to the file manager revoking Alice's access to Oi . Describe what occurs when Alice performs her next block-server read on Oi . [2 marks] (iii) Explain why it might be desirable, from a security perspective, to add a timeout field t, protected by the keyed hash, to the capability. [2 marks] (iv) Developers extend NASD to support Quorum-replicated block servers. What new failure mode may arise during a Quorum block write, relative to unmodified NASD capabilities, in adding capability timeouts? (c) The Andrew File System (AFS) is authenticated and encrypted using Kerberos; ACLs expressing positive and negative rights for users and groups. Multiuser AFS clients (e.g., UNIX servers) build a secure RPC connection for each local user, authenticated with their Kerberos ticket, and issue RPCs (e.g., file read) on their behalf only via their own connection. If no suitable Kerberos ticket is available (e.g., the ticket has expired, the user has destroyed their ticket, or a job is running unattended), then an insecure connection is used instead. (i) The group system:anyuser holds the union of unauthenticated (anonymous) users and all authenticated users. Explain why an ACL granting read access to system:anyuser via a positive entry, but denying read access to user rnw via an overriding negative entry, might prove problematic. [2 marks] (ii) Describe the consequences to AFS authentication and authorisation of a malicious local user gaining root access on a multiuser client. [2 marks] (iii) An AFS client uses the unauthenticated Network Time Protocol (NTP) to synchronise its clock with the AFS server. Attacker Mallory is able to inspect, drop, and insert packets between the AFS client and server (e.g., by controlling a network switch). Describe an attack that allows Mallory to inject malicious content into the client's AFS cache, but that does not allow Mallory to write content directly to the AFS server.