Argue that if there is a polynomial-time approximation algorithm… Argue that if there is a polynomial-time approximation algorithm that ha
Argue that if there is a polynomial-time approximation algorithm… Argue that if there is a polynomial-time approximation algorithm that has a constant approximation ratio for finding a maximum clique, then there is a polynomial-time approximation scheme (PTAS) for the problem. Hint: Your PTAS should be based on applying the given approximation algorithm with constant approximation ratio to G(k) for a proper choice of k > 0. Then use the equivalence in part (ii) to analyse its approximation ratio. [4 marks] 2 CST2.2019.9.3 2 Bioinformatics (a) Describe, with one example, the complexity of using dynamic programming in multiple align When using a feed-forward neural network to solve a classification problem, one alternative is to interpret the network’s outputs as posterior probabilities of class membership, and then to use these posterior probabilities to make classification decisions. Alternatively, we can treat the network as a discriminant function which is used to make the classification decisions directly. Discuss the relative merits of these two approaches. [8 marks] (b) Explain the concept of a likelihood function, and the principle of maximum likelihood in model building and inference from data. [2 marks] (c) Explain the key ideas of a Hopfield neural network for content-addressable, associative memory. In explaining how memories are stored and retrieved, be sure to define the notions of: configuration space connectivity matrix stable attractor basin of attraction network capacity, and its dependence on the number of “neurones”) Suppose we have a representation of a computer system, either as a set of axioms ? specifying its behaviour or as a model M, along with a property ? which we expect to hold (but which may not hold due to programming errors). Give two reasons why we might prefer to model-check M |= ? rather than use logical inference to prove ? ` ?. [2 marks] (b) Assuming a given set AP of atomic properties, ranged over by p, give the syntax of LTL formulae ?. (It is not necessary to be encyclopaedicfull marks can be obtained by including four constructs not present in classical logic.) Explain how an LTL formula is interpreted as true or false in a model. It suffices to consider two temporal operators along with conjunction and an atomic property p. [7 marks] (c) Suppose p is an atomic property. Give informal explanations of the two properties G(F p) and F(G p). State, giving reasons, whether the properties are equivalent or whether one implies the other. (d) Consider a program consisting of the following two threads where WORK is an unspecified unit of work not involving variables A or B. The threads are executed on a scheduler which first sets A and B to zero and then repeatedly and non-deterministically chooses to execute a whole line of code from either the left or right thread. An AWAIT e statement can only be scheduled if its condition e evaluates to true. L: AWAIT A=0; A:=1; M: AWAIT B=0; B:=1; AWAIT B=0; B:=1; AWAIT A=0; A:=1; WORK; WORK; A:=0; B model for this program, and draw it as a finite-state automaton. You should label one or more states of the automaton as satisfying the atomic property of deadlock. [5 marks] (e) Give a temporal logic formula expressing that deadlock does not occur. For the program in Part (d), would a model checker prove this formula or produce a counterexample trace? [3 marksConsider a database with one binary relation B. (a)Write programs in stratified Datalog for the following queries:(i) Give the set of elements x for which there are fewer than three elements y such that B(x, y). [3 marks] (ii) Give the set of elements x such that there is no path (in the formed by B) from x back to itself. [3 marks] (iii) Give the set of elements x such that B(x, y) for every y. [3 marks] (b) Which of the queries defined in part (a) is: (i) safe? [3 marks] (ii) domain independent? [4 marks] (iii) monotone? [4 marks] In each case, justify your answer fully.(b) Briefly describe how to generate values which are distributed exponentially for use in the simulator. [3 marks] (c) State Little’s Law. Outline a proof of Little’s Law with the aid of a diagram. [7 marks] 4 VLSI chip: (a) single global clock (b) two-phase clockImage transcription textPart I Write an interface for a Bank application.Part. 11 Write an abstract class for theinterface written in Part I. Part. III … Show more… Show more Computer Science Engineering & Technology Java Programming MUSC 0650 Share QuestionEmailCopy link
