1. Consider the Mealy model FSM described by the state transition diagram shown below. Notation: I/Z 1/1 0/0 В A 1/1 1/0, 1/1 0/0 D 0/1 0/0 Can this FSM be minimized, i.e., can any of the states be combined? If it can be reduced, develop an optimal state diagram for the reduced machine. Show your work.
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- In Simulated Annealing, if the current state’s evaluation function value is 15, the selected successor state’s value is 11, and the current temperature is T = 10, what is the probability of moving to the successor state? (Assume we are maximizing the evaluation function.) Please give your answer as either an expression or a number.Suppose that F is a finite state machine with 6 states labeled 1 through 6. Suppose that the starting state is Land 4 and 6 are accepting states. The transition. function is as follows: (3, a) > 5 3 (1, a) → 2 (1, b)→ 3 (2. a) → 4 (2, b) → 3 (4, b) (i) Draw the state diagram of the machine. (ii) Find the production defined by each of the following words and determine which are accepted by the machine: abbaabb, ababaa, ababab, bbbaaaa (3, b) (4, a) (5, a) 4 (5.b)→ 6 (6. a) →→ 5 (6.b) -> 3 4 3Let M be the PDA defined by: Q = {90, 91, 92, 93, q4}, Σ = {a, b}, [ = {a, S}, F = {q4} and transition function is defined as below: 8(q0, E, e) = (q1, S) 8(q1, a, e) (q1, a) = 8(q1, E, e) = (q3, ε) 8(q1, b, a) = (q2, ε) 8(q2, b, a) = (q2, ε) 8(q2, &, a) = (q3, &) 8(q3, &, a) = (q3, &) 8(q3, &, $) = (q4, &) 1) draw the state diagram of the PDA. 2) Describe the language accepted by M
- PDA defined: Q={p,q}, E={0,1}, T={X,Z}, qo=q, Zo=Z Transition function: 8(q,1,X)=(q,X) 8(p,&,X)=(p,£) 8(p,1,X)=(p,XZ) Find the equivalent CFG by (a) Production of start symbol S (b) For each action in the transition function, identify the case and find the resulting productions.(1) Draw a transition graph for the dfa M={ Q,E, 8.q..F), where Q={g,.g1-42}. E= {a, b}, F = {q1} and ô is defined as S(q0, a) = q1- 8(q0, b) = q0, 8(q1, b) = q1. 8(q1, a) = q2, 8(q2, b) = q2, ô(q2, a) = q2 (2) Give the language accepted by the above dfa.2. Let Σ = {0,1} and consider the following nondeterministic state transition diagram with ε-transitions: 1 E E 0 1 O 1 Using the systematic method described in class (and in the text), convert the transition dia- gram into an equivalent (non)deterministic transition diagram without ɛ-transitions. Do not modify or simplify the resulting diagram any further.
- Use the Subset construction, as defined in the lecture notes, to construct DFA from the NFA produced by Thompson's construction on the regular expression x* ( y | € ) ( € | y) How many x-transitions (edges labelled x) does the DFA have? Choose... v How many accepting states does the DFA have? Choose... v How many states does the DFA have? Choose... How many y-transitions (edges labelled y) does the DFA have? Choose... v How many e-transitions (edges labelled € does the DFA have? Choose... vProblem 1 (14 points)Show that the autocovariance function can be written asγ(s, t) = E[(xs − μs)(xt − μt)] = E(xsxt) − μsμtwhere E(xt) = μt and E(xs) = μswrite the answer in fraction form and in simplest form. A unity feedback system with a forward transfer function of K G(s) = s(s+1)(s+ 2)(s+5) Assuming K > 0: a. Find the range of K for stability. b. Find the range of K for unstability. c. Find the value of K for marginal stability.
- 3. Eg vs a: Make one graph (in Excel, Matlab, etc) ploting Eg vs lattice constant ao for three series of materials: [GaN, GaP, GaAs, GaSb], [AlN, GaN, InN], and [C, Si, Ge]. For the nitrides, which are hexagonal, use the basal plane constant a (as opposed to the hexagonal axis length c). What trend do you see in terms of Eg as function of lattice constant for each of these series?Compute the gradient with respect to all parameters of f(w0 + w1a1 + w2a2) when w0 = 3, w1 = −2, a1 = 2, w2 = −1, a2 = 4, and β = 0.25 using backpropagationYou are given three different Bayesian network structures (1, 2, 3), for three alarm system designs. Each system consists of 4 binary random variables (A, B, C, D). Each variable corresponds to an alarm condition in an assembly line in a factory, whose state can be either “ON” or “OFF”. Structures in image Using the chain rule of probability for Bayes Nets, factor P(A,B,C,D) according to the independencies specified in the three structures above. What is the minimum number of parameters required to fully specify the distribution (i.e. to calculate P(A,B,C,D))? Hint: The chain rule of probability P(A,B) = p(A|B) p(B) for three variables: P(A,B,C) = P(A| B,C) P(B,C) = P(A|B,C) P(B|C) P(C) and in general to n variables: P(A1, A2, ..., An) = P(A1| A2, ..., An) P(A2| A3, ..., An) P(An-1|An) P(An)