CSE 30151 Spring 2014
Homework 2
Due on February 18, 2014
1. NFAs. Give state diagrams of NFAs recognizing each of the following languages:
(a) 1 = 1cfw_01'0'01
(b) 2 = cfw_x E cfw_O,1'
Ix
contains an even number of Osor contains exactly two 1s
(c) 3 = cf
Solution to Homework 4, CSE 30151 Spring 2014
1. (58 points total; case (a) is 10 points, other cases are 12 points each) Different possibilities
exist.
(a) 5 -+ aTa I bTb I a I b
T -+ aT I bT I E
(b) Here 5, corresponds to the case i = j and 52 to the ca
Solution to Homework 1, CSE 30151 Spring 2014
1. (28 points total; 4 points for (a)-(e) and 8 points for (f)
(a) an odd number of b's; bbbbb and b are in L1, while bbbb and
(b) any binary string with III as a substring;
0
are not.
0111 and 11111 are in L2
1
CSE 30151 Spring 2014
Homework 1
Due on January 28, 2014
1.
Languages. For each case, describe in English the language giving as concise description as
possible, Show two strings that are in L and two that are not (if there are fewer than two
strings in
CSE 30151 Spring 2014
Homework 4
Due at 2:00pm on March 18, 2014
1.
(
Context-free grammars.
cases, i,j,k ~ O.
Give CFGs generating each of the following languages. In all
(a) cfw_x E cfw_a, b*1x starts and ends with the same symbol
(b) cfw_aicfw_)ck Ii =
Solution to Homework 6, CSE 30151 Spring 2014
1. (45 points, 15 points each)
(a) The input is assumed to be in the form 0*1+. The TM below erases one 0 in the
beginning and replaces one 1 with x.
q (~eet C)
i rYLfC'CJt
(b) The TM below marks the first cha
/
Finite state transducers for CSE 30151
Regular finite state machines are used as language recognizers. But it is a simple matter to augment the
model to allow for output at each step of a machine's operation. In such situations often we may no longer
ca
/
State minimization for CSE 30151
A OFA can be very useful as a component of a larger system or a stand-alone possibly widely deployed
device, in which case we want it to be efficient with a minimal number of states. Also, conversions (NFA
to OFA, regula
Additional
examples
of proofs
that
a language
is non-regular
for CSE 30151
cfw_u E a, b* I the number of occurrences of substring aba in u is equal to the number of
occurrences of substring bab in u (the substrings can be overlapping)
1. L =
By contradict
Deterministic
push-down automata for CSE 30151
When we talk about deterministic push-down automata (DPDA), our definition will be different
from that of finite automata, but the idea remains the same: at any point of execution we shouldn't
have more than