Write a regular expression that represents the language of strings with lengths divisible by 3. There can be 0 a's since 0 is divisible by 3.
Write a regular expression that represents the language of strings with lengths divisible by 3 Write regular expression for the language over {0, 1}: the set of all strings that contain 1011. no more than 2 "b"s). Find a regular expression which represents strings made of {a, b}, where number of a's is divisible by 6 and number of b's is divisible by 8. Answer: (a* ba* ba* ba*)* Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products Given the language below, how do i find a regular expression for the language. 0 is the start state. 3: Write regular expressions for the following languages: a) The set of all strings of O's and l's not containing 101 as a substring. Regular Expression for Binary Numbers Divisible by 3. reply Share. Writing Regular Expressions Here’s a recap of the rules of regular expressions: • ∅ is a regular expression that represents the empty language ∅. L = {a ^n b ^m | n => 1, m =>1, nm =>3} regex; regular-language; Share. VIDEO ANSWER: You can go for the A part here. Input: str = abccc Outpu Write regular expressions for the following languages. Improve this question. 2. 5. f"gis not empty, and it is not a string. 15 . 19 Construct regular expression for the language over the set ẑ = {a,b} in which total number of a's are divisible by 3. Thanks I'm trying to figure out how to build a regular expression for a language that doesn't contain substring bbb. Regex for two or three I would do as follows: regex even matches the symbol a, then a sequence of b's, then the symbol a again, then another sequence of b's, such that there is an even number of b's:; even-> (a (bb)* a (bb)* | a b (bb)* a b (bb)*). The starting point is a number ending in red. The set of all strings, when viewed as binary representation of integers, that are divisible by 2. Based on the DFA proposed by the author, a ridiculously short regex can be generated by simplifying the routes a binary string can take through the DFA. Regular Expression of all strings divisible by 4 3. 2- Construct a deterministic FSA for each of the following languages: (a)languages of all those strings in which second last symbol is 'b'. 1. (c) Write a regular expression for the language consisting of all odd integers without leading zeros. Write regular expressions for the following languages over {0,1}* a. A valid justification could be an inductive proof like the first proof above, a direct construction of a DFA/NFA, or an appeal to regular expressions and their properties. Regular Expressions - Not matching specified length. 1*((0^0|0^1|0^2|0^3)|1*) 15. regex odd does the same with an odd total number of b's:; odd-> (a b (bb)* a (bb)* | a (bb)* a b (bb)*). * would match the strings that I want my regex to match but it would also match those I do not want my regex to match regex; Share. We can also get the literal meaning of an operator character by preceding it by a backslash. 8) Write a regular expression that represents the language of strings containing one or more consecutive copies of cctag. b) The set of all strings with an equal number of O's and l's, such that no prefix has two more O's than l's, nor two more l's than O's. Is a regular expression a (b) The set of all binary strings such that the number of 0’s in the string is divisible by 5. For 1, you need an expression that gives every possible way of having a string over {a,b} with the occurrences of a divisible by 3. over input Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume $(0+11+11(1+00)^*00)^*$ Login Register. In item 3, thre regular expression ;represents the empty language. Regular expression for the language of even-length strings starting with a and ending with b. Multiple max lengths in a regular expression. $\begingroup$ I agree with this complete analysis. This is given by the reg-ular expression (1∗01∗01∗01∗01∗1∗01∗). 1 on page 107 of Hopcroft et al. This regular expression matches strings over the alphabet {a, b} where: b* represents zero or more I want to write a regular expression for Binary Numbers Divisible by 5. A regular expression for the first one is e + 0 + 1 + S* (00 + 01 + 10) where e is the empty string, S is the alphabet, * is the Kleene closure, + is union. r. RegEx failing for strings with less than A regular expression for string having must 010 or 101. • For any a ∈Σ, the symbol a is a regular expression for the language {a}. Construction of the machines to produce residue modulo â€⃜2’ of binary numbers If the given string represents an unsigned integer, then print "Unsigned integer". The rest of the expression takes care of lengths 0, 1 and 2, giving the set of all strings of b’s. Dark Mode. commented Dec 23, 2024. I know that the regex . Ans. I very recently began learning regular expressions and was trying to write one for the question above. 3, page 92). = (b* ab* ab* a)* Q. 18. A Regular Expression of all strings divisible by 4. They should be. Problem 5 (10 points) Prove that regular languages are closed under intersection. ((S14) The set of all strings in O* 1* whose length is divisible by 3. "is not a language. Exercise 3. This shows that L is not regular language. This option also generate all the Strings that are divisible by 3. 14. Follow see our tips on 1. Brightness. To get the regular expression I made a finite automata as the following (not sure if you can directly write regular expression without it): The regular expression for the above according to me should be $(1+01^*0)^*$ but elsewhere I have seen it can be $(1^*01^*01^*)^*$. The examples of binary number divisible by 3 are 0, 011, 110, 1001, 1100, 1111, 10010 etc. I'm trying to construct a DFA and convert to help me get the Regular Expression but still stuck as I found the DFA a bit complicated. Regex to match binary numbers with more than two set bits. , a, b). Regular expression for language containing all strings that start and end with different symbols. 3:Write regular expressions for the following languages: a) The set of all strings of 0's and 1's not containing 101 as a substring I am asked to write a regular expression for the language {0,1} where it only accepts strings that have 3 zeros at most. The alphabet is {a,b,c}. Write a regular expressions for the set of strings over the alphabet Σ = {a, b} containing at least one a and at least one b. One quality criterion is that explaining the regular expression is simple, or better that a correctness proof is simple. 3 . Commented Apr 24, 2010 at 7:00. b) The set of strings of 0's and 1's whose number of 0's is divisible by five. $ The set of strings of $0's$ and $1's$ whose number of $0's$ is divisible by five. Simple regular expression for all strings over $\{0,1\}^*$ not ending in $01$ 5. Regular Expression for even-odd language of string. (10m )( Dec-Jan 10) (Ju n-Jul 12) W rite Regular expression for the following L = { an bm : m, n are even} L = { an,bm : m>=2, n>=2}. Consider the language L = {anbm ∶ n ≥ 4, m ≤ 3} Which of the following regular expression represents language L? Q7. Another criterion could be the star height which is a measure of complexity of the regular expression. ε is a regex denoting the language that contains an empty string. why a language of size 1 is regular or proved it only for the language {ε}. There will be 10. CS 341 Homework 3 Languages and Regular Expressions 1. – Jason Hu i am reviewing older exams from my computational theories lesson in university and i am struggling to figure this one out: Construct a regular expression for the following language: Strings of even length in alphabet {a,b,c} that contain exactly one a. • ε is a regular expression that represents the language {ε}. This is A, B T, yes. Related. Assume Σ = {a, c, g, t}. { aaaaaaaa, aaaaaab, For the regular expression there are various possibilities:- Now, exactly one a and one b (where a comes before b) - c* a c* b c* exactly one a and one b (where b comes before a) - c* b c* a c* We take this idea to the answer for more than one a and b:- a comes before b (c* a a* c* b b* c*) ; b comes before a (c* b b* c* a a* c*) or there are intermmediate occurances of a and b :- Let RE The regular language L is {a, aa, aaa, aaaaaaa, }. Tutorial: Regular Expression. I have already done the regular expressions for Binary Numbers Divisible by 2 and for 3 but I couldn't find one for 5. Difference between regular expression and grammar in Algorithms Lecture 2: Regular Languages [Fa’14] •? is the empty language, which is a set containing zero strings. Option 4: ( 0 + 11 + 11(1+00) * 00)* Generate Find the regular expression for the language accepted by the automata given below. Construct a regular expression defining each of the following languages over Σ. This works because the language can be divided into strings of length less than two (e + 0 + 1) and strings of length at least two which do not end with 11 (this leaves endings 00, 01, and 10). a*(ba*ba*)* for an even number of b b*ab*(ab*ab*)* for an odd number of a There is a systematic way to perform a merge of these two, because every regular expression can be Here, state 0 represents that the remainder when the number is divided by 3 is 0. 2 Describe the following by regular expression. d) String not containing the substring 110. The questions asks to find a regular expression for strings containing the substring aba over the alphabet {a, b}. therefore I for sure know it covers all the cases. Examples: Input: str = bc Output: ACCEPTED Explanation: The string consists 0 a's and 3 * 0 = 0. Answer: (a + b + ab + aa) a* b* (b) The language of all words in which the total number of b’s is divisible by 3 nomatter how they are distributed, such as bbabbaabab. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products Regular Grammar. Thus, the Question: Exercise 3. Is every regular grammar context-free as well? Yes. The language of codes for TM's M that when started with blank tape, eventually represent regular languages look like abbreviations for them Preliminary examples: bbbb* represents the strings of 3 or more b’s. 133 1 1 silver badge 6 6 bronze badges. Constructing individually for 2 and 3, and then combining works well for "NFA". (b)language of all those strings which do not contain the substring 'abb'. However, this Other syntactic sugar such as powering is treated similarly as a shortcut which helps humans write the regular expression, but is absent when discussing the regular expression formally, for example when measuring its length. , the regular expression "**" matches the string ** . e. The following (01)* entire regular expression represents strings either begin with 1 0r 0 with alternate 0 and 1 is: E = (01)* + (10)* + 0(10)* + 1(01)* Exercises: 1. for more details, you can read the pumping lemma page i pasted up there. c) The set of all strings containing 00. Added by Claudia S. 2. Roughly translated from greek, hope it makes sense. This is the language of strings in which there are no two consecutive 1’s, except for possibly a string of 1’s at the end. The tool of choice in regex to use when specifying "the same thing than before" are back-references, however they reference the matched value rather than the matching pattern : no way of using a back-reference to . M_Umair_Khan42900 asked Dec 29, 2022. Regular expressions For each of the following languages over the alphabet {0, 1}, give an equivalent regular expression. So remember to anchor them when testing. 9 12 . b) The set of strings of 0’s and 1’s whose number of 0’s is divisible by ve. They describe regular languages and are commonly used in tasks such as validation, We're going to write a regular expression for this language. davidlc. Would the correct answer be R= a* + b* Skip to main content. Write a Regular expressions defined over {a, b} for All strings with at least one a and at least one b. – Donal Fellows. Using Myhill–Nerode theory, you can easily show that this is the minimal DFA for the language. BenV. 5k 13 I'm not going to write down that expression. Follow answered Mar 3, 2019 at 19:01 Regular Expression for Strings with even number of b's followed by the letter c followed by an @MahanteshMAmbi to help you understand further why this is complete as regular expression. For every 6 symbols, it resets to 0. Q. Then come Which one of the regular expressions below represents L? A) (0*10*1)* B) 0*(10*10*)* C) 0*(10*1)* 0* Note that these are not string searching regexps; these are language matching regexps. Follow edited Oct 5, 2019 at 6:41. Instant Answer We can do so by quoting the character within a string of length one or more; e. { aaaaaa, aaaab, aabaa, aabb, baaaa, baab, bbaa, bbb} LLLL is the set of strings formed by concatenating quadruples of strings in L. In items 4, 5, and 6, the expressions represent the languages obtained by taking the union or concatenation of the languages R 1 and R 2, or the Kleene star of the language R 1 Exercise Questions on Regular Language and Regular Expression Ex. An Regular expressions are symbolic notations used to define search patterns in strings. If R is a regex denoting the regular language L R and S is a regex denoting the regular language L S, then Write regular expression to denote a language L a) String which begin or end with either 00 or 11 00. The second term allows for the possibility of 0 a's and any amount of b's since 0 a How do I write a regular expression for binary strings such that it's length is a multiple of 3 and this must include the empty string. strings over alphabet {0,1}) that are divisible by 4 Write regular expressions for the following languages: a) The set of strings of 0’s and 1’s such that every pair of adjacent 0’s appears before any pair of adjacent 1’s. Share. L = { w | w is of even length and begins with 01 } Ans: 01((0 + 1)(0 + 1))* Explanation: 01 itself of even length to, we can suffix any even length string consist of 0s and 1s. Your solution has star height 2 (because you have a star over a subexpression that already has A regular expression for string having must 010 or 101. But, you need to convert that NFA back to DFA. Automate any workflow In items 1 and 2 the regular expressions aand represent the languages fagand f g, respectively. I'm working through a textbook on automata theory (Introduction to Automata Theory, Languages, and Computation) and I'm stuck on the Exercise 3. A detailed tutorial of the regular expression is here in the link of regular expression tutorial. razvardhan. r can generate a string "aab" therefore it is false. Two of them. Find and fix vulnerabilities Actions. However, ba is not in it. reply Follow flag. regex; Share. I tried to create a DFA which accepts such strings. Cite. a is a regex denoting language that contains the single string a. This is homework, after all, so I'll leave it to you to desugar this and put it together with the first result. Strings of length 1: No valid strings. 7. (a) all strings runs of $a$'shave lengths that are multiples of three. Follow Regex that defines a regular language with {a,b} without a substring with exactly 3 b's (bbb) 3. { aaaa, aab, baa, bb} LLL is the set of strings formed by concatenating triples of strings in L. Here is a transition table for a DFA: 0 1! q1 q2 q1 q2 q3 q1 Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string ∈ divisible by three. A string of even number of a's and odd . 11. A function that will return a regular expression string that is capable of evaluating binary strings (which consist of only 1s and 0s) and determining whether the given string represents a number divisible by n. ” It says the constraints are. Start Symbol: The non-terminal from which Give a regular expression for this language and then a generalized regular expression that is shorter than the regular expression. L = { w | the numbers of 1's in w is multiple of 3 } Ans: (0*10*10*10*)* Explanation: 0 can appear any number of time anywhere in string the restriction is over 1 it should be in multiple of 3 so * over The regexes are incorrect. Write better code with AI Security. , accepts the language 𝐿={𝑤∈{𝑎,𝑏} ∗ ∣ prevents the number of '𝑎's to be a multiple of 3} the answer would be b ∗ +(b ∗ ab ∗ ab ∗ ab*) ∗ a+(b ∗ ab ∗ ab ∗ ab*) ∗ aa. These states represent the remainder after modulus 5. - TurboTokyo/Regular_Expression_for_Binary_Numbers. b) The set of strings of O's and l's whose number of O's is divisible by five. ) Share. To work with formal languages and string patterns, it is essential to understand regular expressions, regular grammar, and regular languages. A regular expression for string having must 010 or 101. UNIT 2 – REGULAR EXPRESSIONS AND LANGUAGES. 4. Solution: It can easily be seen that , a, b, which are strings in the language with length 1 or less. My idea was to use all the remainders mod 6 and mod 8 leading to a total of 48 remainders. Prosciutto is a word. Thus the given regular expression simplifies to b*. Does this mean anything can precede/procede aba so that the regular expression would be: (aUb)*(aba)*(aUb)* or is the question simply looking for: (aba)* Note: U means union and * means 0 or more times. There can be 0 a's since 0 is divisible by 3. (b) All strings in Σ* with no more than three a's. State 1 represents that the remainder when the number is divided by 3 is 1 and similarly state 2 represents that the remainder when the Write regular expressions for the following languages$:$ The set of all strings of $0's$ and $1's$ such that every pair of adjacent $0's$ appears before any pair of adjacent $1's. formal-languages regular-language The question asks to give a regular expression over Σ = {a,b} in a formal representation (not java) that generates the following languages: L1 = {x|x contains the substring abab} L2 = {x|x has odd length} L3 = {x|x does not end in ab} I have no clue how to write a regular expression. respectively, concatenate these two to get a regular expression for the language {01}. A description of the language is “the set of all strings of zero or more b’s. Lots and Lots of Concatenation Consider the language L = { aa, b} LL is the set of strings formed by concatenating pairs of strings in L. There are multiple. How do I understand what the regular expression is doing just like in this case here. Follow edited Jun 9, 2010 at 14:50. Option D generate string 111 0 which is 14 not divisible by 3 . † The set of all strings over Σ that contain exactly 1 b is denoted by the For 1, you need an expression that gives every possible way of having a string over {a,b} with the occurrences of a divisible by 3. Non-terminals: Variables used to derive strings (e. 2: Write regular expressions for the following languages:a) The set of all strings of 0's and 1's such that every pair of adjacent 0's appears before any pair of adjacent 1 's. Next thing there is is conversion algorithm from regular grammar to finite automaton. My mind is blank, any input is much appreciated. Observe, that multiples of 2 and 3 meet after 6 numbers. Write regular expressions for the following languages: Question: ! Exercise 3. • f"gis a language containing exactly one string, which has length zero. Write DFA to accept strings of 0’s, 1’s & 2’s beginning with a 0 followed by odd number of 1’s and ending with a 2. A string matches if it matches any regular expression in the list. nice Prerequisites: Finite AutomataGiven a string str consisting of characters a, b and c, check if the number of occurrences of any character in the string is a multiple of 3 or not. Some valid binary numbers would be: 11 110 1001 1100 1111 The question asks for a regular expression that represents the set of all strings, over {a, b}, where the number of 'a's is divisible by 3. 1: Find the shortest string that is not in the language represented by the regular expression a * (ab) * b *. Odd number of A's and; At most 4 B's let's start the expression->string may start with both A & B =====>(A+B)->say the first letter of the string be A Is $(0)*$ + $(1)*$ a valid regular expression that represents this language? Why not? formal-languages; regular-language; regular-expressions; regular-language; regular-expressions; formal-systems. *B{1,3}. , S, A). Here is the state diagram: Note that most answers will probably use the dialect of regular expression usual in programming languages, rather than mathematics - a+b to us means what aa*b means to you Regular expression to Definition: A regular expression is recursively defined as follows: φ is a regex denoting empty language. . This page I know this is an old question, but an efficient answer is yet to be given and this question pops up first for "binary divisible by 3 regex" on Google. There are lots of them. So for example 010 is true 0101 is false. Q9. 14 14 . (5m)( Jun-Jul 11) only one possible structure for each string in the language. A Regular Expression Strings that does not contain substring 110. I cannot obtain the regular expression for the Automata with alphabet={0,1} that generates the strings that do not end with 01. Below is what I came up with but it is not correct as the zeros can be used recursively and go over 3 occurrence. Describe in English, as briefly as possible, each of the following (in other words, describe the language All strings in Σ* whose number of a's is divisible by three. So, you can think of resetting the 'counter' for every 6 symbols. 2 Building Languages Languages can be combined and The accepting states are $\{q_0,q_2,q_3,q_4\}$, since a number is even or divisible by 3 iff its residue modulo 6 is one of 0,2,3,4. The You should probably split the String around the separator and compare the length of both parts. It would not be difficult if the limits were only placed on one letter (e. Ask Question Asked 5 years, for more than 1 odd lengths take closure multiple times . It consists of: Terminals: Symbols that form strings (e. Otherwise, 5 min read. 6 . (a) The language of all words that do not begin with ba. Write regular expressions for the following languages on {$0, 1$}. If the given string follows the given language L, then print "Accepted". Each numbered state contains a list of regular expressions that describe the remaining portion of the string, and the state transitions that occur when either a 0, 1, or end-of-line is encountered. A regular grammar is a formal grammar that generates regular languages. How would you write a regular expression to define all strings of 0's and 1's that, as a binary number, represent an integer that is multiple of 3. Why is it different? • Associative: (uv)w = u(vw) and we write uvw. 1- Write a Regular expression for each of the following languages: (a)language of all those strings which end with substrings 'ab' and have odd length. This problem falls within the domain of computer science particularly in automata theory and formal languages. Exercise 2 (Ex 3. Do we know any regular grammar which makes strings divisible by 3? Well that's not too hard, we do. (a) all strings ending in $01$,(b) all strings not ending in $01$,(c) all strings occurrences of the substring $00$,(f) all strings not containing the substring $101$. Otherwise, print "Not an unsigned integer". Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products I have done so below, first with mine then with yours. • Identity element following (L(r) is the language it represents): 27 Any regular language has a regular expression and vice versa Atomic expressions (Base cases) Exercise: create regular expressions! • All binary strings with either the pattern 001 or the pattern 100 occurring somewhere !! • All binary strings with an even But (n + 1) can be a prime number. ? is not a string. Regular expression of strings begin with 110 Regular expression of strings begin and end with 110 Regular expression of strings containing exactly three consecutive 1’s. Production Rules: Rules for transforming non-terminals into terminals or other non-terminals. 1. Regular Expression cont [Week#03] (a) - Regular Expressions (Examples) •The set of all strings of a’s and b’s that have atleast two letters, that begin and end with a’s and that have nothing but b’s inside ab*a = {aa aba Let Σ = {a, b}. b) The set of all strings, when viewed as binary representation of integers, that are divisible by 2. {3} to match any 3 characters. 0. XSD Restriction to limit element length to divisible by 4/multiple of 4. a) L1 = The set of all strings of What is the regular expression for strings with length multiple of three? The {} does not work for me as it only allows a definite value for min/min-max. thanks for the answer. Thank you. write a regular expression that recognises all words that Question: !! Exercise 3. Of the strings wiht length 2 aa, bb and ab are in the language. Views: 5,698 students Give regular expressions for the following languages on $Σ =$ {$a, b, c$}. The Overflow Blog Our next phase—Q&A was just the beginning s first community-wide AMA (Ask Me Anything) Visit chat. There can be 3 a's, 6 a's, 9 a's, and so on. Regular Expression which matches two duplicate consecutive characters within string but I want to create a regular expression to match the following: L: the set of all bit strings (i. 3 : Write regular expressions for the following languages: a) The set of all strings of 0's and 1's not containing 101 as a substring b) The set of all strings with an equal number of 0's and 1's, such that no prefix has two more 0's than 1's, nor two more 1's than 0's. Hence our assumption becomes contradictory to it. Solution: Any string in the language must be composed of 0 or more blocks, each hav-ing exactly five 0’s and an arbitrary number of 1’s between them. Strings of length 2: ab,ba, No other Find the shortest string that is not in the language represented by the regular expression (L (φ) = { }) ∙ x is a Regular Expression where L = {x} ∙ If X is a Regular Expression denoting the language L(X) and Y is a Regular Expression denoting the language L(Y), then o X + Y is a Regular Expression corresponding to the Give a regular expression for the language L over Σ = fa;bg of words that contain exactly 2 or exactly 3 b ’s. (which would definitely be the easiest systematic way of doing this), you can approach it by viewing the language as strings of 2, 1 or 0 zeros interleaved by ones: $$(00 +0 + \epsilon)(1(00 + 0 + \epsilon))^*$$ Share. 2: Write regular expressions for the following languages: * a) The set of all strings of O's and l's such that every pair of adjacent O's appears before any pair of adjacent l's. A regular expression for the language of all those strings having just ab or if string size is greater than 2, then starting with ab and ending with b and having even length strings. g. Since the structure is represented by the derivation Write regular expression to denote a language L a) String which begin or end with either 00 or 11. with some other inputs) is decidable B. To do so, we'll begin not by guessing at the shape of the regex, but rather by simply listing a bunch of strings in and out of the For any finite automaton we can construct an equivalent regular expression and the language represented by regular expressions is a regular language. (a) The set of strings over alphabet {a,b,c} containing at least one a and at least one b. 12. However, if you only need to Exercise 3. An expression for this is (bababab)+b. The diagram will be there. • " is the empty string, which is a sequence of length zero. Improve this answer. For those asking the inverse DFA, i. A regular expression Write the Regular expression for the language of all even length strings but ends with aa defined over ∑ = {a, b}? A Regular Expression of all strings divisible by 4. in pumping lemma, regular expression is defined to be generated in the form of pr*q, there is only one star of an expression r. 20 Find out the language generated by the regular expression (0 Regular Expression of Language {a b} which contains string of Odd Length and must contain atleast one 'b' in it. Binary numbers divisible by 3 : The regular expression for binary numbers which are divisible by three is (0|1(01*0)*1)*. 2,521 views 1 Option 3: Set of strings with 2 a’s followed by b’s which is a multiple of 3. gfyxnzlmzkhotjtoiutirgqmjyxhnbuofddovilrcwqztevhlicyzuahmzffauwi
