CIS 625: Mid Term Exam
 
Mo, May 3, 1999, 50 minutes
Open Notes, Open Books
The exam consists of problems
Answers not appearing in designated spaces WILL NOT be graded

• Problem #1 (10 points) Give a grammar that produces the following language.

  {x#y|x and y are over {a, b} and (the number of a’s in x)>(the number of a’s in y) }

• Problem #2 (10 points) Write a program that on a given input outputs a value v which appears at location i from the end of the input, where i v.

  Example On input “4, 5, 3, 1” we can have “5” or “3” as output values, but not “4” or “1”..

• Problem #3 (10 points) Give the transition diagram of a finite state transducer that computes the following relation.

  {(x, y)|x and y are in {a, b}^*, and there is an i such that x and y agree on their i’th characters}

  Example The outputs “aa” and “bbba” are allowed for input “aba”, but “ba” is not allowed.

• Problem #4 (10 points) Transform the following finite state automaton into a deterministic fine state automaton.

  

grades