Due: Friday, Sep 13th by 11:59 PM

Update 9/10 - Clarification: don't use multiple input symbols on transitions.

Your task is to create finite automata for the regular languages described below.

For each of the following finite automata problems, use JFLAP to construct the automaton, saving it in a JFLAP file (which will have a .jff file extension). Please use the filenames prob1.jff, prob2.jff, etc.

The JFLAP jar file is here:

JFLAP.jar

You can either double click on it, or start it from a terminal window with the command

```java -jar JFLAP.jar
```

If the problem asks for a deterministic finite automaton, make sure that your automaton does not have any nondeterministic states. (In JFLAP, use the Test->Highlight Nondeterminism menu option.)

Important: For all of your finite automata, make sure that each transition is labeled with either a single input symbol, or lambda (λ), which is how JFLAP denotes an epsilon transition (a transition that does not consume a symbol from the input string.) JFLAP allows transitions to consume multiple input symbols, but please do not use this feature.

### Problem 1

Construct a deterministic finite automaton that recognizes the language over the alphabet {a, b} containing all strings with an odd number of b's.

For example, the following strings are members of the language:

b
ab
aba
bbabaa

The following strings are not members of the language:

ε
abb
bababb

### Problem 2

Construct a deterministic finite automaton that recognizes the language over the alphabet {a, b} containing all strings with an even number of a's and an odd number of b's.

For example, the following strings should be accepted by the automaton:

b
aab
aba
baa
bbabaaa

The following strings should be rejected by the automaton:

ε
ab
aabb
abab

### Problem 3

Construct a finite automaton (deterministic or nondeterministic) that recognizes the language over the alphabet {a, b} generated by the regular expression:

(a|ab|abb|abbb)*

For example, the following strings should be accepted by the automaton:

ε
a
aa
aab
abba
abbabbab

The following strings should be rejected by the automaton:

ba
abbbb

### Problem 4

Construct a finite automaton (deterministic or nondeterministic) that recognizes the language over the alphabet {a, b, c} of all strings not containing the substring ba.

For example, the following strings are members of the language:

ε
a
ab
bb
bc
cbc
abbb

The following strings are not members of the language:

ba
baba
aba
ccaabac

### Problem 5

Construct a deterministic finite automaton that recognizes the language over the alphabet {a, b} of all strings where the number of a's in the string is a multiple of 3.

For example, the following strings should be accepted by the automaton:

ε
bb
ababa
aaba
aaababaa

The following strings should be rejected by the automaton:

a
aba
baaabaa

## Submitting

Create a zip file that has the JFLAP (.jff) files containing your automata for problems 1-5.

Submit the zip file to Marmoset as assign02. The Marmoset URL is

https://cs.ycp.edu/marmoset