(a) Prove that ECFG is co-recognizable Hint: define the complement of EQcFG, and make use of a decider for AcFG to show that it\'s recognizable

(b) Prove that EQcFG is not decidable. Hint: use a reduction from ALLcFor, defined on p. 225 of the textbook (where it\'s also proved to be undecidable)

(c) We have proved in class that EQRExis decidable (it\'s also in the textbook). Explain why an analogous proof of the decidability of EQcFG would not work

(d) Using (a) and (b), prove that EQcFG is not recogizable.

(e) We\'ve shown in class that the complement of ATMis not recognizable. Use this fact together with result (a) above to prove that there can be no mapping reduction fromATto EQCFG

Q40;

Neural Networks implementation of mini batch SGD in python?

def mini_batch_gradient(param, x_batch, y_batch, reg_lambda): \\\"\\\"\\\"implement the function to compute the mini batch gradient input: param -- parameters dictionary (w, b) x_batch -- a batch of x (size, 784) y_batch -- a batch of y (size,) reg_lambdba -- regularization parameter output: dw -- derivative for weight w db -- derivative for bias b batch_loss -- average loss on the mini-batch samples \\\"\\\"\\\" # Your code goes here

return dw, db, batch_loss