Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java, C#/. The subset construction algorithm is also applied to the resultant NFA, resulting in a language-equivalent deterministic finite-state automata (DFA). e-NFA->DFA에 대한 과정을 구현하면서 꽤나 애먹었다. To convert the DFA to Regular Expression (RE), we are going to use a method called converting DFA to regular expression by eliminating states. Here is an algorithm to do so. B-> aB | bA | e. Pick an internal state (not the start state or the final state) to “rip out”. Convert the DFA to a regular expression. The resultant regular expression is a(a+b)*+c which is a specification of the language recognized by the original DFA. Convert simple regular expressions to deterministic finite automaton. There is a good discussion on how to algorithmically convert a DFA to a regular expression in this reference post, and I used one of the algorithms presented there to do a quick-and-dirty Python program. A regular expression can easily check whether a user entered something that looks like a valid phone number. The subset construction algorithm is also applied to the resultant NFA, resulting in a language-equivalent deterministic finite-state automata (DFA). Empty set transitions can be omitted. The general idea is: You convert a regular expression to an NFA, which can be done quite straightforwardly ( * is a loop, | and character ranges are branch points). Here is an example explaining the process in detail NFA Consider the following NFA State Transition – start, final – final. I've figured the regular expression to be: A (A+B+C+D)*D I'm stuck on converting it over to a DFA. How can you convince yourself that this regular expression is equivalent to the original DFA? Answer: The steps of conversion actually constitute a proof. This utility only parses stuff in between /regex/. For fun, we. In the other hand, you may be interested in consider algorithms to converting DFA to Regular expression, so you can find a dynamic programing algorithm, and the full description of this approach is given in the book of Models of Computation, Chapter 4. Proof: Indeed, convert the DFA into a NFA N. There are 2 ways to create a RegExp object: a literal notation and a constructor. Convert simple regular expressions to minimum deterministic finite automaton. stock market tomorrow open predictions ewe fun ajegun awon agba convert image to svg javascript claimsmade policy vs occurrence examples 3d movies online hoa lawyers for homeowners. It is to accept any string starting with A and ending with D. This utility only parses stuff in between /regex/. Lets take an regular expresion example: 0*(1(0+1))* Now convert above example in to regular language. In a normal NFA or DFA, every character in the string causes a single transition in the machine, and each transition in the machine "consumes" one character. (Regex => NFA => DFA) Supported grammars r = (s) r = st r = s|t r = s* r = s+ r = s? r = ϵ (Copy this character to input if needed) Examples (a|b)* (a*|b*)* ( (ϵ|a)b*)* (a|b)*abb (a|b)*. "Regular exp>NFA>DFA conversion" is not an option because such a conversion takes a lot of time to convert a rather complex regular expression. Jan 13, 2009 · They also have a tutorial on how to Convert FA to regular expression. We have defined regular expressions, the two sub-types of FAs and we have seen how we can convert between the two, as well as expressing a regular expression as both an NFA and a DFA. But, to recognize a token, it can need a token Recognizer, which is nothing but a Finite Automata (NFA). ٢١ رجب ١٤٤٠ هـ. In this video you learn how to design NFA for the Regular Expression(0+1)* (00+11)(0+1)* and then covert it into DFA. CONVERSION OF RE TO DFA. Convert simple regular expressions to deterministic finite automaton. Definitely, you can construct a CFG that result in a given regular expression. Solution : Two regular expressions are equivalent if languages generated by them are same. Utility – To construct DFA from a given regular expression, we can first construct an NFA for the given expression and then convert this NFA . Step1: Ignore any trap state at time of find regular expression from DFA/NFA. The resulting DFA is- Step-02: Initial state A has an incoming edge (self loop). After eliminating q1, the FA looks like following −. 2 Deterministic Finite Automata Contents 2. Our task consists in converting the given DFA to a regular expression, which accepts the same language L. Refresh the page, check Medium ’s site status, or find something interesting to read. So, after eliminating q1 we put a direct loop to q2 having cost. First of all you must remember the definition of a regular expression and the theorem: for any regular expression e, there exists a regular grammar G recognising exactly the language described by e. The State elimination . Arden’s method (using Arden's Lemma); State elimination method. Introduction Convert simple regular expressions to deterministic finite automaton. This is how to convert regex (REGular EXpression) to DFA by creating and using syntax tree in Java language. And a tip for making your regexes more readable: introduce comments inside your regexes. B-> aB | bA | e. A (A+B+C+D)*D One of the properties of regex to NFA conversion is that of concatenation- when a regex describes a sequence, their states do as well. Answer (1 of 4): DFA for regular expression (a+b)*abb length of substring = 3 Minimum number of states required in DFA = 3+1 = 4 {abb, aabb, ababb, abbabb} Required DFA is:. Steps Rules for Conversion of Regular Expression to NFA. So, it can convert Regular Expression into NFA. If this were a more complex automaton, with multiple final. Reduce the number of states if possible. (12) a) First, convert the DFA to a GNFA. some helpful links: From here and through my profile you can find some more helpful answers on FA. JFLAP is a tool to experiment with formal languages, grammars and parsing, including finite state machines, pushdown automata, Turing machines, LL and LR parsing, but also with proofs such as converting an NFA to a DFA to a min-state DFA to a regular expression or regular grammar. conversions of regular expressions to NFA, and DFA to regular expressions. · Hover the generated regular expression to see more information. It is to accept any string starting with A and ending with D. 0 include several conversions from one representation to another. Important states of NFA correspond to . This utility only parses stuff in between /regex/. · The resultant regular expression is a(a+b)*+c which is a specification of the language recognized by the original DFA. (a|b)*; (a*|b*)*; ((ϵ|a)b*)*; (a|b)*abb(a|b)*. Underlying Theory. I am then using subset construction to create the DFA from the NFA, shown here. basic program in c to convert nfa to dfa, 2 3 converting a regular expression into a deterministic , c program to construct dfa from nfa sanfoundry , nfa to dfa conversion c. To convert the RE to FA, we are going to use a method called the subset method. js and browser. Supported grammars r = (s) r = st r = s|t r = s* r = s+ r = s? r = ϵ (Copy this character to input if needed) Examples (a|b)* (a*|b*)* ((ϵ|a)b*)* (a|b)*abb(a|b)* Input: Convert ×Invalid Grammar URL:. JFLAP creates a new state q 0 by grouping the equivalent. A new, free-to-use website provides a regular expression generator that aims to take the headache out of forming and using regular expressions. Actually, different CFG grammars can produce the same language. A (A+B+C+D)*D One of the properties of regex to NFA conversion is that of concatenation- when a regex describes a sequence, their states do as well. Here is an algorithm to do so. It is to accept any string starting with A and ending with D. In the expression tree, you'd get a node for the star operator, and an a node for the symbol the operator acts upon. 4 Case Study: The Up: 2 Lexical Analysis Previous: 2. This automaton replaces the transition function with the one that allows the empty string ∈ as a possible input. Finite State Machine simulator for Deterministic Finite Automata, Non-Deterministic Finite Automata, and Push-Down Automata. Enter a FSM below and the application will convert and show the equivalent regular expression. Now we have a way to test whether a regular expression matches a string: convert the regular expression to an NFA and then run the NFA using the string as input. Hope this gives you a high level idea. in c to convert nfa to dfa does not handle null moves gist 10fec56cab1f8d0c33a9, yes it can be done it is usually done in 4 steps given regular expression step 1 write language valid and invalid strings step 2 draw dfa of given regular expression. At least two spaces are matched, but only if they occur directly after a period (. First, create the DFA in JFLAP. Definition of a Regular Expression R is a regular expression if it is: a for some a in the alphabet , standing for the language {a} ε. For fun, we. The conversion of a finite automaton to a regular expression is done through the state elimination method. But the problem is, when you get the regular expression with this grammar, you get a much more complex expression, not (a+b)*. · I'm learning to write a lexical analyzer generator (a clone of lex), based on regular expression to DFA direct translation algorithm described in "Dragon Book". So, it can convert Regular Expression into NFA. There is a path going from qi to q2 via q1. You need to figure out what are the operations represented by this expression, in which order they apply, and what are their operands. We will reduce the regular expression into smallest regular expressions and converting these to NFA and finally to DFA. Share Improve this answer Follow answered Jan 13, 2009 at 2:12 Norman Ramsey 197k 59 359 531. ١٢ جمادى الأولى ١٤٢٣ هـ. Here is an example explaining the process in detail. Lets take an regular expresion example: 0*(1(0+1))* Now convert above example in to regular language. Converting a regular expression to a DFA Ask Question Asked 7 years, 8 months ago Modified 7 years, 8 months ago Viewed 3k times 2 I've been trying to convert the regular expression to a non-deterministic finite automata (NFA) first using Thompson's construction, giving: , which looks correct. For fun, we. Repeat step 2 until the. Note: This method will construct NFA (with or without ε-transitions, depending on the expression) for the given regular expression, which can be further converted to DFA using NFA to DFA conversion. Pick an internal state (not the start state or the final state) to “rip out”. Although in general when the "Do It" button is selected JFLAP performs the indicated operation, here JFLAP instead provides a message that indicates its assumption that you already know how to accomplish the specified task. I've figured the regular expression to be: A (A+B+C+D)*D I'm stuck on converting it over to a DFA. This utility will double escape back slash. ) and before an uppercase letter. Sep 17, 2019 · 1 Need help creating a DFA. Apr 15, 2021 · The picture below shows the process of expressing the expression as NFA and then converting it to DFA. Using regular expressions (or regex) you can verify if Regular expressions are generally follow a similar pattern in most of the programming languages. Here’s another nice regex tester. Question: For the following DFA, find its equivalent regular expression? Step 1: We will first multiple final states into a single final state The resulting DFA after step 1 will be Step 2: Now, eliminate all the intermediary steps. Step 2 − Convert NFA with ε to NFA without ε. However, writing the algorithm is not such a good idea. $\endgroup$ –. The above answers shown some ways to achieve this. New features from 3. · The resultant regular expression is a(a+b)*+c which is a specification of the language recognized by the original DFA. Regex => NFA => DFA => Min-DFA Convert simple regular expressions to minimum deterministic finite automaton. in c to convert nfa to dfa does not handle null moves gist 10fec56cab1f8d0c33a9, yes it can be done it is usually done in 4 steps given regular expression step 1 write language valid and invalid strings step 2 draw dfa of given regular expression. 0 include several conversions from one representation to another. Here is an algorithm to do so. How to convert Regular expression to Finite Automata? · Step 1 − Construct a Transition diagram for a given RE by using Non-deterministic finite . Converting a regular expression to a DFA Ask Question Asked 7 years, 8 months ago Modified 7 years, 8 months ago Viewed 3k times 2 I've been trying to convert the regular expression to a non-deterministic finite automata (NFA) first using Thompson's construction, giving: , which looks correct. Regular Expression to NFA (Non-Deterministic Finite Automata) Visualize the Thompson-McNaughton-Yamada construction NFA for a given regular expression. ( Regex => NFA => DFA). Converting a regular expression to a DFA Ask Question Asked 7 years, 8 months ago Modified 7 years, 8 months ago Viewed 3k times 2 I've been trying to convert the regular expression to a non-deterministic finite automata (NFA) first using Thompson's construction, giving: , which looks correct. · Enter a regular expression into the input field below or click Generate random regex to have the app generate a simple regex randomly for you. · One of the properties of regex to NFA conversion is that of concatenation- when a regex describes a sequence, their states do as well. Our task consists in converting the given DFA to a regular expression, which accepts the same language L. Important states of NFA correspond to . JFLAP In addition to constructing and testing examples for these, JFLAP allows one to experiment with construction proofs from one form to another, such as converting an NFA to a DFA to a minimal state DFA to a regular expression or regular grammar. State Decomposition Method Theorem: Every language defined by a regular expression is also defined by a Finite Automata. A regex processor translates a regular. I've figured the regular expression to be: A (A+B+C+D)*D I'm stuck on converting it over to a DFA. RGPV 2020. Convert the NFA to an equivalent DFA in three possible ways: Step-by-step: the DFA is constructed in controlled increments All at once: completely convert the NFA to the DFA in one leap Animated: watch the conversion process take place automatically Technology. The alphabet recognised by the program is: letters [a-zA-Z] '$' -- this is used to symbolise lambda; paranthesis: '()' '*' -- the Kleene star '|' -- the 'OR' symbol; After writing your regular expresion you can run python. to a non-deterministic finite automata (NFA) first using Thompson's construction, giving: , which looks correct. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Regex => NFA => DFA => Min-DFA Convert simple regular expressions to minimum deterministic finite automaton. Jan 13, 2009 · You can code a DFA fairly straightforwardly using flex or re2c. State Decomposition Method Theorem: Every language defined by a regular expression is also defined by a Finite Automata. parser generators. Here is an example where we ignore the trap state q t. The subset construction algorithm is also applied to the resultant NFA, resulting in a language-equivalent deterministic finite-state automata (DFA). Why Regular Expressions Matter. Convert the NFA to an equivalent DFA in three possible ways: Step-by-step: the DFA is constructed in controlled increments All at once: completely convert the NFA to the DFA in one leap Animated: watch the conversion process take place automatically Technology. Definitely, you can construct a CFG that result in a given regular expression. The idea is to rip out one state at a time, while modifying the transitions to reflect the changes. 2 Algorithm for converting DFA/NFA to Regular Expression. At least two spaces are matched, but only if they occur directly after a period (. Converting a Regular Expression Directly to a DFA This is an optimization that can be used when generating a DFA from a regular expression to avoid creating an intermediate NFA and generate a non-minimized DFA directly from the regular expression string. · This online Regex Replace tool helps you to replace string using regular expression (Javascript RegExp) Yet another framework: stencil & svelte The next thing was the graphql schema definitions (https://sangria-graphql React Tearing GraphQL will continue to be more and more popular, so familiarize yourself. Output − NFA > accepting language denoted by R. Try it online!. Oct 21, 2017 · $\begingroup$ In general, the procedure is to draw a non-deterministic finite automaton from the regular expression, then convert to a DFA (where the states consist of set of states of the NDFA). Convert simple regular expressions to deterministic finite automaton. Actually, different CFG grammars can produce the same language. a regex that checks if the number of 1s is odd. The subset construction algorithm is also applied to the resultant NFA, resulting in a language-equivalent deterministic finite-state automata (DFA). We have now finished the series concerning the basics of lexical analysis. This method is used to get FA from the given regular expression. b) False. PRACTICE PROBLEMS BASED ON CONVERTING DFA TO REGULAR EXPRESSION- Problem-01: Find regular expression for the following DFA- Solution- Step-01: Initial state A has an incoming. How do you construct a DFA from a language that has a + sign? e. I've figured the regular expression to be: A (A+B+C+D)*D I'm stuck on converting it over to a DFA. RE with DFA Subject:. Regex => NFA Introduction Convert simple regular expressions to nondeterministic finite automaton. Arden’s Method is not capable of converting Ɛ-NFA. There is a good discussion on how to algorithmically convert a DFA to a regular expression, The final regular expression is: $$\left(\!, it into a set of . regular expression – Build NFA – Convert NFA to DFA using subset construction – Minimize resulting DFA Theorem: A language is recognized by a DFA (or NFA) if and only if it has a regular expression You need to know this fact but we won’t ask you anything about the “only if” direction from DFA/NFA to regular expression. Option (C) will have 10 as substring but 0* (10*)* may or may not. Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java, C#/. Questions to Think About 1. So they are not equivalent. DFA/NFA/eNFA to have the app generate a simple FSM randomly for you. 보기엔 쉬워보였지만, Regular Expression 에 대한 공부를 하고 최종적으로 DFA 를 만들기 위해서 Regex->e-NFA 과정이 필요하고. DFA to Regular Expression- The methods to convert DFA to regular expression are- Arden's Method and State Elimination Method. To indicate strings, the parameters to the literal notation do not use quotation marks while the parameters to the constructor. Click on the "Convert → Convert FA to RE" menu option, and this screen should come up: You can see that this is a fairly simple automaton, and that we are prompted for 4 new transitions. Introduction Convert simple regular expressions to deterministic finite automaton. txt file. Enter a FSM below and the application will convert and show the equivalent regular expression. May 5, 2015 · Converting a regular expression to a DFA Ask Question Asked 7 years, 8 months ago Modified 7 years, 8 months ago Viewed 3k times 2 I've been trying to convert the regular expression to a non-deterministic finite automata (NFA) first using Thompson's construction, giving: , which looks correct. Answer each step separately. 1 Answer Sorted by: 2 You need to figure out what are the operations represented by this expression, in which order they apply, and what are their operands. We have an Answer from Expert View Expert Answer Expert Answer We have an Answer from Expert Buy This Answer $5 Place Order We Provide Services Across The Globe Order Now Go To Answered Questions. 2 Algorithm for converting DFA/NFA to Regular Expression Suppose we want to find an equivalent regular expression for some DFA or NFA. The converted regular expression is (0+ 1)* 100 (0+10). In a normal NFA or DFA, every character in the string causes a single transition in the machine, and each transition in the machine "consumes" one character. ) and before an uppercase letter. Step 3: In Q', find the possible set of states for each input symbol. This post originated from Lab 1 of course Compilers: Principles that I'm currently taking, in which we were required to write a flex program . The subset/powerset construction algorithm converts an NFA to a DFA. tv nihon, nadamoo scanner driver
here is the example: enter image description here. . Regular expression to dfa converter
Some basic RA . The Thompson-McNaughton-Yamada construction (aka Thompson construction) algorithm converts regular expressions into graphs. Here I am writing Regular Expression for complement directly: (00 + 1)* 0 (^ + 1 (1 + 0)*) where ^ is null symbol. An ε-NFA is like an NFA, except that we are allowed to include "epsilon transitions". Step2: Whatever the machine DFA or NFA we follow the same procedure to find regular expression. Underlying Theory. I am then using subset construction to create the DFA from the NFA, shown here. Lets take an regular expresion example: 0*(1(0+1))* Now convert above example in to regular language. Step 2 − Convert NFA with ε to NFA without ε. Click on the “Convert → Convert FA to RE” menu option, and this screen should come up: You can see that this is a fairly simple automaton, and that we are prompted for 4 new transitions. RGPV 2020. 2 Algorithm for converting DFA/NFA to Regular Expression Suppose we want to find an equivalent regular expression for some DFA or NFA. The GNFA method is a procedure to convert any given NFA to an equivalent regular expression. Sorted by: 2. We have defined regular expressions, the two sub-types of FAs and we have seen how we can convert between the two, as well as expressing a regular expression as both an NFA and a DFA. To indicate strings, the parameters to the literal notation do not use quotation marks while the parameters to the constructor. · We will concatenate three expressions "1", " (0 + 1)*" and "0". Unlike DFA engines, when traditional NFA engines perform pattern matching, their processing order is driven by the regular expression pattern. In the expression tree, you'd get a node for the star operator, and an a node for the symbol the operator acts upon. Now I can successfully convert a regular expression to DFA, but I got stuck when there is multiple rules, for example:. Feb 5, 2016 · A regular expression works on the same principal, it only describes which inputs you accept, it does not describe which are rejected. The RegExp constructor creates a regular expression object for matching text with a pattern. 0* (1 (0+1))*. What I have so far automata. Utility – To construct DFA from a given regular expression, we can first construct an NFA for the given expression and then convert this NFA to DFA by a subset construction method. 0* (1 (0+1))*. But to avoid this two-step procedure, the other way round is to directly construct a DFA for the given expression. Definitely, you can construct a CFG that result in a given regular expression. Left recursion Try to eliminate left recursion. AUTOMATON CONVERSION. There is a path going from qi to q2 via q1. Repeat the process for every state; Begin the process from start state. 1 Need help creating a DFA. The subset/powerset construction algorithm converts an NFA to a DFA. Empty set transitions can be omitted. One can specify all token types using regular expressions. Hope this gives you a high level idea. 우선 첫번째로, 입력받은 >Regular</b> <b>Expression</b>를 e-NFA로. The conversions are nondeterministic finite automaton (NFA) to deterministic finite automaton (DFA), DFA to minimum state DFA, NFA to regular grammar, regular grammar to. (note that you cannot remove those edges and the sink state in the DFA, because, as stated above, a DFA must decide an answer on each input, even if it loops in a sink state. The conversion of a finite automaton to a regular expression is done through the state elimination method. Shares: 299. 4 Case Study: The Up: 2 Lexical Analysis Previous: 2. Feb 22, 2022 · Utility – To construct DFA from a given regular expression, we can first construct an NFA for the given expression and then convert this NFA to DFA by a subset construction method. Can someone explain the correct way to convert to a NFA and then to DFA. Uses augmented regular expression r#. ) and before an uppercase letter. This method is used to obtain FA from the given regular expression. The State elimination . O O ABC CD O A O AC - we use state - Elimination method to convert the DFA to gegular expression This method Step - 1: has initial state new incoming edges, create a new initial state I final state on states has outgoing edges. create a new final state - so, here final states has outgoing states So it converted as : CS Scanned with CamScanner. This utility only parses stuff in between /regex/. Finite State Machine simulator for Deterministic Finite Automata, Non-Deterministic Finite Automata, and Push-Down Automata. some helpful links: From here and through my profile you can find some more helpful answers on FA. But to avoid this two-step procedure, the other way round is to directly construct a DFA for the given expression. e-NFA->DFA에 대한 과정을 구현하면서 꽤나 애먹었다. In this video you learn how to design NFA for the Regular Expression(0+1)* (00+11)(0+1)* and then covert it into DFA. Add a new start state with a λ transition to the old start state. This post originated from Lab 1 of course Compilers: Principles that I'm currently taking, in which we were required to write a flex program . Apr 15, 2021 · The picture below shows the process of expressing the expression as NFA and then converting it to DFA. Convert DFA to a Regular . Supported grammars r = (s) r = st r = s|t r = s* r = s+ r = s? r = ϵ (Copy this character to input if needed) Examples (a|b)* (a*|b*)* ((ϵ|a)b*)* (a|b)*abb(a|b)* Input: Convert ×Invalid Grammar URL:. Visual NFA to DFA Converter https://joeylemon. You'd type up an NFA as below. Introduction Convert simple regular expressions to deterministic finite automaton. Hope this gives you a high level idea. Jan 13, 2009 · You can code a DFA fairly straightforwardly using flex or re2c. In other regex languages you can do that inside the regex language , but not with a regex. JFLAP is software for experimenting with formal languages topics including nondeterministic finite automata, nondeterministic pushdown automata, multi-tape Turing machines, several types of grammars, parsing, and L-systems. At least two spaces are matched, but only if they occur directly after a period (. You can see it in your diagram for the nfa, too. Note : Sometimes, it is not easy to convert regular expression to DFA. There exists an algorithmic way to convert a DFA into an equivalent regular expression as is stated here. It is to accept any string starting with A and ending with D. We will reduce the regular expression into smallest regular expressions and converting these to NFA and finally to DFA. some helpful links: From here and through my profile you can find some more helpful answers on FA. /regex_to_dfa " (a|b)*abb" Number of states: 4. We will discuss the rules & steps used in the. After we remove the ε transitions from the NDFA, we get the following −. Convert DFA to a Regular . Besides, dot script transition is provided so that you can make diagrams with Graphiz. Convert the NFA to an equivalent DFA in three possible ways: Step-by-step: the DFA is constructed in controlled increments All at once: completely convert the NFA to the DFA in one leap Animated: watch the conversion process take place automatically Technology. e-NFA->DFA에 대한 과정을 구현하면서 꽤나 애먹었다. This is how to convert regex (REGular EXpression) to DFA by creating and using syntax tree in Java language. The steps in this method are given below:- Step 1: Make a transition diagram for a given regular expression, using NFA with ε moves. Answer: a. C-> aC | bC. Note: This method will construct NFA (with or without ε-transitions, depending on the expression) for the given regular expression, which can be further converted to DFA using NFA to DFA conversion. (note that you cannot remove those edges and the sink state in the DFA, because, as stated above, a DFA must decide an answer on each input, even if it loops in a sink state. In the former articles, we have been introduced to both Regular Expressions and Finite Automata's. regular expression – Build NFA – Convert NFA to DFA using subset construction – Minimize resulting DFA Theorem: A language is recognized by a DFA (or NFA) if and only if it has a regular expression You need to know this fact but we won’t ask you anything about the “only if” direction from DFA/NFA to regular expression. · The picture below shows the process of expressing the expression as NFA and then converting it to DFA. string as a regular expression,. But to avoid this two-step procedure, the other way round is to directly construct a DFA for the given expression. Converting a Regular Expression Directly to a DFA. conversions of regular expressions to NFA, and DFA to regular expressions. . karely ruiz porn