So how do you compute if a binary number is divisible by 3? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. To subscribe to this RSS feed, copy and paste this URL into your RSS reader.
Creating new Help Center documents for Review queues: Project overview, Algorithms computing if a number is a multiple of 3, Simplification of regular expression and conversion into finite automata, Finite State Automata for recognising consecutive characters, The number of different regular languages, Deciding if a finite automata accepts strings of any length, Deterministic finite automata that accepts the only the string “aabb”, timed automata - advance only in certain states.
Find minimal DFA: Remove all the unwanted stated from DFA. The initial state is the one containing e, also in our case. The usual way of making a DFA that computes something like this is to first make an NFA (since NFAs are must easier to compose vis union/intersection/etc), and then convert the NFA to a DFA. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. We’ve got you covered. it
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To subscribe to this RSS feed, copy and paste this URL into your RSS reader. I dabble in C/C++, Java too. To make the discussion simpler, we define a "three token" as follows: A three-token is a substring of the input which represents a number evenly divisible by three in binary notation.
How do we use sed to replace specific line with a string variable? For big endian, you instead add an additional start state that transitions to 0 and 1 on a single 0 or 1 bit. MathJax reference.
(COA) Computer Organization & Architecture. My solution is shorter because it also accepts strings starting with $0$. Asking for help, clarification, or responding to other answers. To learn more, see our tips on writing great answers.
Your name can also be listed here. Remove all the unwanted stated from DFA.
Adjective agreement-seems not to follow normal rules. Save my name, email, and website in this browser for the next time I comment. We can look at this now and rationalize the rules mathematically. We can use the Myhill Nerode theorem to guide us toward a minimal DFA for this language directly. So how do you compute if a binary number is divisible by 3?
Combine both the above automata to construct DFA that accepts all the strings with the total number of ‘a’ is an odd & total number of b’s is not divisible by 3.
To get minimal DFA, remove any dead/unwanted/unreachable/duplicate state from the DFA. Why does separation of variable gives the general solution to a PDE, Author has published a graph but won't share their results table. My boss makes me using cracked software.
Thanks for contributing an answer to Computer Science Stack Exchange! To solve this kind of questions use divide and conquer strategy.
What numbers are divisible by 3?
Or browse a list of nearly 700 numbers divisible by 3. A finite automaton accepts a language, i.e. Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. If you'd rather make such strings not part of your language, then 0 is distinct from e. We will let it be indistinguishable. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. There is no change in the transition state for the occurrence of b. I have found in a book the example of how to make a FA that accepts those numbers that are divisible by 3, that means that n mod 3=0. Suppose if we read same string in same order but first placing numbers sequentially in power of 2 if we read 1 it be first bit and 0 2nd bit so we will read as 001 for above DFA we read the string oppositely ....so what is DFA for this by placing bits from left to right.
If we are constructing a new three-token, reading the next symbol s multiplies our current value v by 2 and then adds s; that is, v' = 2v + s. The only way v' can be divisible by 3 is if v is 1 (mod 3) and s is 1. In the example the author used the binary representation of the number to be evaluated. Quick way to move an object some distance from one external vertex to another external vertex? The empty string, e, can be followed by any string in L to get a string in L. Call this . We'll get to that in a bit. Combine both the above automata to construct DFA that accepts all the strings with the total number of ‘a’ is an odd & total number of b’s is not divisible by 3. Given a binary number you can generate base 2k digits by simply taking them in groups. The string 1 is distinguishable since not all strings in L can follow it and produce a string in L. Indeed, a moment's reflection will show that no string in L can follow 1 and lead to another string in L. Call this <1>.
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And the transitions couldn't be easier to figure out: if x = ys, then the state corresponding to y's class leads to the state corresponding to x's class on symbol s. Naturally, the accepting states are the ones which contain strings in L; only fits the bill here. Why does a blocking 1/1 creature with double strike kill a 3/2 creature?
Strings are distinguishable if they are followed by different sets of strings to get strings in the target language.
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The string 100 is, perhaps surprisingly, indistinguishable from the string 1: anything we can add to 1 to get a string in L leads to a string in L if added to 100 as well.
Given a string, imagine placing a token on the initial state, then for each character of the string, left to right, move the token along the transition labelled $0$ or $1$, according to which character you read. How is it possible that a