0

Just learned about DPDA's on my Theory of computation class. Professor gave us a semester task to create a deterministic pushdown automaton state diagram that is able to accept all strings multiples of 3; (Binary notation multiples of 3 of the string of 1's and 0's given) on JFLAP software.

I tried to do it but im confused as if it is even possible, . I created this CFG but im not sure is the appropiate way to solve this issue.

S -> 0A | 1B A -> 0S | 1C B -> 0C | 1S C -> 0B | 1A

Any help is appreciated, thanks in regards.

Improve this question

1 Answer 1

Reset to default
1

It is possible to design a DPDA for this language. The important fact about this language is that, it is in fact a regular language, which means that the power of a DPDA is not needed to recognize it. The language can also be recognized by a weaker device, i.e., a DFA or an NFA. You need three states. Each state corresponds to the remainder of dividing a number (in its binary form) by three (0, 1, or 2). Because the multiples of three are supposed to be accepted, the state that corresponds to 0 (which is also the initial state) should be assigned as the final state.

Now, if there is a requirement that you must use a DPDA to describe this language, and not a DFA, just attach a stack to your DFA, but don't use it at all. That is, don't push anything onto the stack, and don't pop anything from it. In this case, you will have a DPDA for this language. I drew this DPDA in JFLAP. As you can see, the stack is not used at all.

enter image description here

Improve this answer
Sign up to request clarification or add additional context in comments.

Comments

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.