Stumped - why is this grammar ambiguous?

G : S β†’ aSA | Ξ»
A β†’ ba | Ξ»

This is driving me crazy. What are the two different derivations that will yield the same string? I am not seeing it, have been staring at it for hours. Thanks for any help.

πŸ‘︎ 9
πŸ’¬︎
πŸ‘€︎ u/wyzapped
πŸ“…︎ Sep 30 2019
🚨︎ report
This troll calling me an idiot for not understanding his sentence when the grammar was ambiguous
πŸ‘︎ 5
πŸ’¬︎
πŸ‘€︎ u/thetechie02
πŸ“…︎ Jul 23 2019
🚨︎ report
ELI5: How can there be no algorithm for certain things (like determining whether a context-free grammar is ambiguous) yet us humans can do it?
πŸ‘︎ 6
πŸ’¬︎
πŸ‘€︎ u/nanoman1
πŸ“…︎ Nov 01 2018
🚨︎ report
[WP] The person inscribing curses for grave robbers committed several typos, used ambiguous grammar and had atrocious handwriting to boot
πŸ‘︎ 17
πŸ’¬︎
πŸ‘€︎ u/Hrtzy
πŸ“…︎ Mar 30 2018
🚨︎ report
lark-parser 0.7 - the Earley implementation now creates a Shared Packed Parse Forest (SPPF), for optimal performance when parsing ambiguous grammars github.com/lark-parser/la…
πŸ‘︎ 7
πŸ’¬︎
πŸ‘€︎ u/erez27
πŸ“…︎ Mar 31 2019
🚨︎ report
Microsoft Word's ambiguous grammar imgur.com/XGrAPI7
πŸ‘︎ 153
πŸ’¬︎
πŸ‘€︎ u/greatdane4
πŸ“…︎ Sep 11 2013
🚨︎ report
An Interactive Guide to Ambiguous Grammar mcsweeneys.net/articles/a…
πŸ‘︎ 123
πŸ’¬︎
πŸ‘€︎ u/Libralily
πŸ“…︎ Sep 03 2015
🚨︎ report
An interactive guide to ambiguous grammar mcsweeneys.net/articles/a…
πŸ‘︎ 13
πŸ’¬︎
πŸ‘€︎ u/budalicious
πŸ“…︎ Jul 08 2016
🚨︎ report
[WP] The person inscribing curses for grave robbers committed several typos, used ambiguous grammar and had atrocious handwriting to boot

"Alright, here it is."

Jennings gestured to the marble arch, beyond which lay a dusty mausoleum. He looked anxiously at Brenner a moment, then at Thompson.

Thompson was clearly uneasy, but doing her best to hide it. Some of her anxiety was probably left over from the Chamber of the Tarantula, Jennings thought. He hadn't fared much better, the first time he came through.

Thompson stepped carefully through the archway, her eyes scanning the pool of illumination created by her lantern. In the center of the room was a dais, upon which lay a stone tomb.

Jennings and Brenner followed quickly behind her. "There, you see?" Jennings said, pointing to the markings inscribed on the tomb's top.

Slowly, Thompson drew nearer. She leaned down and blew about an inch of dust out of the engraved letters, then held her lantern high to study them.

"It's...really strange that it's written in English," she began, half to herself.

Brenner shot a look at Jennings. "I told you!"

Jennings glared back. "The Egyptians were very advanced! Maybe they figured out English early on!"

Brenner crossed his arms. "And then decided to use that instead of their own language?"

"Boys...please." Both men fell silent, with Jennings visibly sulking.

Thompson's eyes danced across the letters, moving her lips but not speaking. Seconds of silence stretched into minutes. Brenner shifted uneasily. Jennings' curiosity clearly overpowered his irritation, as he took a step nearer. "So?"

"So...I mean, I'm not an expert in ancient Egyptian law, but...this is how I understand it. I think...I think you're fine, honestly. Personally, I would say why risk it - but professionally...I don't see any issues here. This is...yeah, you're golden."

Jennings and Brenner beamed at each other. Thompson took a step back as the men got out crowbars and began prying at the lid. After a few minutes of grunting and straining, they managed to get it off.

The lantern light shone gold on the ceiling and walls around them, reflecting the dazzling treasures within. A moment later, the shadows in the corners all seemed to get sucked into the center of the room, coalescing into a dark form hovering above the tomb.

"Defilers of the tomb, who heeded not the warning of the Pharaoh, your actions have condemned you! Forces from the Beyond will now chain you to this room...forevermore!"

Jennings and Brenner looked at each other again, then at Thompson. They each stepped aside so that she could approach.

"Just so w

... keep reading on reddit ➑

πŸ‘︎ 5
πŸ’¬︎
πŸ‘€︎ u/adlaiking
πŸ“…︎ Apr 12 2018
🚨︎ report
Ambiguous (to me) grammar question

> ... c'est quasi le mΓͺme de ceux qui dΓ©couvrent peu Γ  peu la vΓ©ritΓ© dans les sciences, que de ceux qui, commenΓ§ant Γ  devenir riches, ont moins de peine Γ  faire de grandes acquisitions, qu'ils n'ont eu auparavant, Γ©tant plus pauvres, Γ  en faire de beaucoup moindres.

This sentence strings together several constructions which I have a weak grasp on and the effect is that I don't understand the point of the science/wealth analogy.

avoir de peine - peine can be difficulty as in "exertion", difficulty as in "anguish", or idiomatically, grief (avoir de peine, to grieve).

commencer Γ  - as I understand it, this can either mean "having first become rich, then..." or else "at the point where they were just becoming rich..."

faire de grandes acquisitions - As far as I can tell, this can refer either to expanding a business empire (i.e., becoming more rich) or spending money on consumer goods (i.e., becoming less rich).

Long story short, I can't tell whether the point of the parable is that people who are a little bit rich are less satisfied with their standard of living than poor people, or whether they find it easier to improve their financial position than poor people.

Thanks for any help you can offer, either on the overall meaning of the sentence or on parsing the individual components.

πŸ‘︎ 4
πŸ’¬︎
πŸ‘€︎ u/siecle
πŸ“…︎ Sep 20 2013
🚨︎ report
This grammar is ambiguous and causing some conflicts the SLR(1) parser I'm trying to build. I have no idea why. It's worth 10% of the semester mark, please help me pass.

I tried to left-factorize it so that it wouldn't reject a string as soon as it encounters a semi colon in the string. But it still does. I know left-factorization doesn't get rid of ambiguity so the grammar is still ambiguous. It's quite a big grammar, and I see no obvious signs of ambiguity. I just know that they're there because of the conflicts.

P'' -> P'$

P' -> P

P -> C | C;D

D -> R | RD

R -> pu{P}

C -> I | I;C

I -> h | O | A | R | Z

O -> i(V) | z(V)

Y -> u

V -> S | N

S -> u

N -> u

A -> S=s | S=S | N=X

X -> N | b | L

L -> d(X,X) | s(X,X) | m(X,X)

R -> f(B)t{C} | f(B)t{C}1{C}

B -> e(V,V) | (N<N) | (N>N) | nB | a(B,B) | o(B,B)

Z -> w(B){C} | r(N=0;N<N;N=a(N,1)){C}

I'm feeling pretty hopeless at this point and if you could point me in the right direction I would be so grateful.

πŸ‘︎ 7
πŸ’¬︎
πŸ‘€︎ u/redititititit
πŸ“…︎ Apr 01 2017
🚨︎ report
Inconsistent/ambiguous grammar rule(s) in this problem?

I was studying a Kaplan practice test for the SAT to help tutor a student, and I noticed an inconsistent grammar rule:

'it' is only used for inanimate objects, and 'they' is only used for people.

This was the explanation for why a sentence similar to this one is considered grammatically incorrect:

The United Nations made progress in their agenda today. (incorrect)

The United Nations made progress in its agenda today. (correct)

However, I received inconsistent answers with my peers who are or have studied English, and they say one or both of the following are correct:

Here are 50 french fries; eat it slowly.

Here are 50 french fries; eat them slowly.

Any clue if this is inconsistent, or is it just the practice test? I find it surprising that a nation-wide standardized test would dogmatically determine what is right in an ambiguous grammar rule.

πŸ‘︎ 3
πŸ’¬︎
πŸ‘€︎ u/Arrow_of_Ace
πŸ“…︎ Apr 24 2016
🚨︎ report
Removing ambiguity in grammar

Hi all, I'm writing a c compiler from scratch for learning purpose. I'm facing an issue with few ambiguous non-terminals that generates the same FIRST set. The problem is the ambiguity lies in different non-terminal derivation rather than in a non-terminal single derivation. For example, consider the following grammar,

  1. E -> T | ( F)
  2. T -> S
  3. S -> ( D )

In the above case, the FIRST set of both productions in the 1st non-terminal contain "(" symbol. In such cases, how can I remove the ambiguity. The problem with using left factoring in my case is that it will break the other productions on the grammar. How can I solve this problem? Any help would be appreciated and Thanks in advance :)

Edit: This is my first time writing a compiler, and I'm building an LL(1) parser. So If I'm missing something please let me know :)

πŸ‘︎ 6
πŸ’¬︎
πŸ‘€︎ u/RajendraCh0la
πŸ“…︎ Jan 16 2022
🚨︎ report
What are some examples of ambiguity in Finnish grammar?

What are some examples of ambiguity in Finnish grammar?

I.e. cases where it's not entirely clear what rules should apply.

πŸ‘︎ 4
πŸ’¬︎
πŸ‘€︎ u/mavavilj
πŸ“…︎ Jan 18 2022
🚨︎ report
An Interactive Guide to Ambiguous Grammar mcsweeneys.net/articles/a…
πŸ‘︎ 7
πŸ’¬︎
πŸ“…︎ Sep 03 2015
🚨︎ report
How can CYK be able to recognize ambiguous grammars?

Hi, I have a general doubt about CYK algorithms and it is what enables it to recognize ambiguous grammars unlike other parsing algorithms. Also, are there any tools for generating syntatic analizers that use this algorithm? Thank You.

πŸ‘︎ 4
πŸ’¬︎
πŸ‘€︎ u/rick94sm
πŸ“…︎ Nov 23 2015
🚨︎ report
An Interactive Guide to Ambiguous Grammar mcsweeneys.net/articles/a…
πŸ‘︎ 8
πŸ’¬︎
πŸ“…︎ Sep 03 2015
🚨︎ report
Ambiguous grammar and police shootings. mcsweeneys.net/articles/a…
πŸ‘︎ 3
πŸ’¬︎
πŸ‘€︎ u/mackload1
πŸ“…︎ Sep 03 2015
🚨︎ report
An Interactive Guide to Ambiguous Grammar mcsweeneys.net/articles/a…
πŸ‘︎ 6
πŸ’¬︎
πŸ‘€︎ u/gAlienLifeform
πŸ“…︎ Sep 03 2015
🚨︎ report
An interactive guide to ambiguous grammar mcsweeneys.net/articles/a…
πŸ‘︎ 3
πŸ’¬︎
πŸ‘€︎ u/Epistaxis
πŸ“…︎ Sep 23 2015
🚨︎ report
Grammar (Antlr) ... How to solve this kind of ambiguity

Hi all,

does anybody have experience with Antlr specifically or with lexers and parsers in general?

Maybe it is even a reasonable common sense exercise.

I started from this grammar: https://github.com/antlr/grammars-v4/tree/master/pgn

I had two issues that I wanted to address. I downloaded games from lichess.org, which all contain intervening commentary followed by an integer with a black move indicator: https://chess.stackexchange.com/questions/3975/how-to-write-the-first-move-of-a-pgn-that-starts-with-blacks

That wasn't supported.

Then I saw a feature request which complained that the san moves are not taken apart further. After thinking about that I wanted that feature too and wrote a san move grammar first with a parser that converts the codes to natural language and tried to integrate it.

It works well with the lichess.org format, but not with the unit test cases of the repository. I started seeing moves like "White pawn moves to square a4 and promotes to King". The issue is that all spaces are ignored and code like "47. a3 Kc7" matches the promotion rule for the white player.

Two ways I see to fix it is

  1. have separate Parsers and take the san move apart with a parser in a parser
  2. rewrite the grammar to get the lexer to keep track of the separator spaces

... but I feel like I am so close and I might be missing something. Is there a way to tell the antlr lexer that it should not be greedy in the promotion case?

Any other smart way to make sure the ambiguity is resolved?

I think this is the most relevant part of my modified grammar:

element
 : full_move
 | half_move
 | NUMERIC_ANNOTATION_GLYPH
 ;

full_move
 : white_move black_move
 ;

half_move
 : white_move
 ;

white_move
 : WHITE_MOVE_STARTER (san_move | CASTLING_KINGSIDE | CASTLING_QUEENSIDE) SUFFIX_ANNOTATION? BRACE_COMMENT?
 ;

black_move
 : BLACK_MOVE_STARTER? (san_move | CASTLING_KINGSIDE | CASTLING_QUEENSIDE) SUFFIX_ANNOTATION? BRACE_COMMENT?
 ;

san_move
 : piece? coords? CAPTURE? to_specifier move_event*
 ;

move_event
 : promotion
 | CHECK
 | DOUBLE_CHECK
 | EN_PASSANT
 | DRAW_OFFER
 ;

to_specifier
 : coords
 ;
... keep reading on reddit ➑

πŸ‘︎ 2
πŸ’¬︎
πŸ‘€︎ u/Signature1980
πŸ“…︎ Sep 20 2021
🚨︎ report
My translation vs the subtitles, being confidently incorrect about grammar, and understanding with ambiguity

First, I'm not looking for answers, just other people's opinions on these thoughts. Second, a quick summary of where I'm at: I'm probably at an intermediate level with Japanese. On a good day I can comfortably watch and understand an entire anime episode, and on bad days I rely mostly on the audiovisual component to get me there. I can use the monolingual dictionary about 50% of the time, maybe more.

Immersion is extremely good at acquiring vocab and phrasal vocabulary for me. But I struggle with grammar. I'm watching and I make a card out of a sentence, but what about when I am wrong, but think I understand it? How am I supposed to dislodge the incorrect meaning or realize there's a grammatical nuance that changes the meaning? Relying on noticing that my interpretation becomes less correct as the context evolves?

Related but somewhat different is that sometimes I'll snag a card, but after watching, when finishing the card, I notice I have that word from some obscure sentence long ago, I didn't catch that it was a word I knew in-context, or I'll just reading it again I understand it. In the first case I have been opting to keep those cards, but not the other cases. For the other cases I think this is just a problem of comprehension at the speed of native language, right?

Anyway, I probably shouldn't, but sometimes (rarely?) when I think I understand something I'll switch to the English subs to confirm, and I'm usually right or in the ballpark, but there's something in the subs that isn't consistent with my understanding. Like seeing the translation "crystallizes" my interpretation of the Japanese because now I know the meaning the Japanese should have. The languages of course don't have perfect translations, and I've been putting this into the "understanding with ambiguity is natural" bucket. I sort of want someone to tell me that actually that's how I understand English and I didn't notice that over time my certainty in my understanding went up and that'll happen with Japanese, too.

Recently I experienced just plain not comprehending a card I strictly fully understood: γ€Œζ€γ£γ¦γ¦γ‚‚γ€€γ‚‚γ†θ¨€γ„γΎγ›γ‚“γ€ and I just didn't get it until I consulted the subs. I think the answer is "immersion will sort that out," but unlike with vocabulary, the mechanism by which I will find the correct answer is unclear. That feeling is frustrating because I should understand it, but sometimes simple sentences like this seem to have some kind of probability to whether I'll actually ge

... keep reading on reddit ➑

πŸ‘︎ 5
πŸ’¬︎
πŸ‘€︎ u/cerrosafe
πŸ“…︎ Aug 25 2020
🚨︎ report
What are the known ambiguities in C language grammar? cs.stackexchange.com/q/12…
πŸ‘︎ 5
πŸ’¬︎
πŸ‘€︎ u/foadsf
πŸ“…︎ Jun 20 2020
🚨︎ report
Is there a book on the limitations and problems of language, like on ambiguity and why this makes grammar necessary?

This question is inspired by a quote in, This explains everything, "to communicate about things not in the here-and-now, you need more. Effectively planning future joint activities needs pretty well all of grammatical structure, particularly if the planning involves more than two peopleβ€”with even more demands made on the grammar if the plan requires coordination among groups not all present at the same place or time."

πŸ‘︎ 7
πŸ’¬︎
πŸ“…︎ Jun 27 2020
🚨︎ report
GitHub - TheLartians/Parser: A fast C++17 parsing expression grammar (PEG) parser generator supporting left-recursion and grammar ambiguity github.com/TheLartians/Pa…
πŸ‘︎ 15
πŸ’¬︎
πŸ‘€︎ u/TheLartians
πŸ“…︎ Apr 12 2019
🚨︎ report
Proper algorithm for resolving ambiguity in grammars via enforcing associativity and precedence rules cs.stackexchange.com/ques…
πŸ‘︎ 10
πŸ’¬︎
πŸ‘€︎ u/real_pinocchio
πŸ“…︎ Nov 23 2019
🚨︎ report
Globasa Grammar Adjustment Proposal: "tas" - indirect object ("cel" remains a preposition of destination only) in order to not inherit the ambiguity of the English word "to". /r/Globasa/comments/gusud…
πŸ‘︎ 5
πŸ’¬︎
πŸ‘€︎ u/seweli
πŸ“…︎ Jun 03 2020
🚨︎ report
Unambiguous JavaScript Grammar - "The Script and Module goal of ECMA262 have a grammatical ambiguity where some code can run in both goals, having the exact same source text, but produce different results". github.com/bmeck/Unambigu…
πŸ‘︎ 62
πŸ’¬︎
πŸ‘€︎ u/fagnerbrack
πŸ“…︎ Jul 03 2016
🚨︎ report
The faulty grammar and the ambiguity of it makes me think this prompt was unintended in Shadow Raid. cloud-4.steampowered.com/…
πŸ‘︎ 38
πŸ’¬︎
πŸ‘€︎ u/PreciseAlien
πŸ“…︎ Jul 31 2014
🚨︎ report
Arkansas attorney general rejects marijuana proposal -- Rutledge wrote in an opinion released Monday that the proposal is being rejected because of ambiguities in the text. Rutledge also noted that the proposal contains errors of grammar, punctuation and spelling. arkansasonline.com/news/2…
πŸ‘︎ 18
πŸ’¬︎
πŸ‘€︎ u/BlankVerse
πŸ“…︎ Oct 27 2015
🚨︎ report
Unambiguous JavaScript Grammar - "The Script and Module goal of ECMA262 have a grammatical ambiguity where some code can run in both goals, having the exact same source text, but produce different results". github.com/bmeck/Unambigu…
πŸ‘︎ 6
πŸ’¬︎
πŸ‘€︎ u/fagnerbrack
πŸ“…︎ Jul 03 2016
🚨︎ report
How to remove ambiguity from the Go programming language grammar?

Hi. I'm making a simple Go compiler using JFlex and CUP, but the grammar is very ambiguous. I've been able to remove some ambiguities so far, but I've been trying for like 3 days straight and can't for the life of my remove the ambiguity from Expression because it's full of recursion.

I know there isn't an algorithm to remove ambiguities, but I really need help and don't know what to do anymore. Do you guys have any tips? Maybe someone has Go's grammar without ambiguities? Idk, anything really...
Here's the spec in EBNF: https://golang.org/ref/spec#Expression

Thanks!

πŸ‘︎ 3
πŸ’¬︎
πŸ‘€︎ u/matheuspot
πŸ“…︎ May 20 2018
🚨︎ report
UPDATE: So a guy has mislead me and i mirrored his own shitty behaviour knowing it would hurt him.

Part 1. https://www.reddit.com/r/pettyrevenge/comments/rm1whj/so_a_guy_has_mislead_me_and_i_mirrored_his_own/?utm_source=share&utm_medium=ios_app&utm_name=iossmf

i didn’t expect this to blow up, thank you for all the comments guys!

This is an update regarding me going to see the guy again. So he has practically begged me into meeting him again to talk since I seem β€œto be confused about us”. INTERESTING. I was contemplating whether it’s actually worth it to give any time of day but the inner asshole has successfully won so I went. I won’t lie I had a plan of what i’ll say in case he starts to lie and manipulate again but then it turned out even better… long-story short, he started telling me how we still should see each other; how β€œcasual” is a very ambiguous term and it doesn’t mean i’m not important to him but then i interrupted his bullshit and proceeded to THANK HIM. I said I’m thankful that he,unlike me, found the strength to be honest about the fact that we’re clearly incompatible and shouldn’t waste each others time. I said I was afraid to tell him that all along because i didn’t want to hurt his feelings but i’m so glad he had the guts to bring it up so we can finally move on to see other people that we actually enjoy spending time with. I said I was very relieved the first time he said that despite being confused. His reaction was priceless, I might as well have splashed my coffee into his face, it was so sour. Best fucking lie for revenge of my life, it felt good.

He has now sent me a loooong text about how he feels everything was a huge miscommunication and that β€œwe” (lol) deserve another chance.

Edit: grammar

πŸ‘︎ 8k
πŸ’¬︎
πŸ‘€︎ u/necreativnenko
πŸ“…︎ Dec 30 2021
🚨︎ report
Is it difficult to be "comprehensible" in a language? Is this merely about following the grammar?

Is it difficult to be "comprehensible" in a language? Is this merely about following the grammar?

This puzzles me.

I find that I can follow language quite well even if it's not entirely grammatical.

πŸ‘︎ 2
πŸ’¬︎
πŸ‘€︎ u/mavavilj
πŸ“…︎ Jan 28 2022
🚨︎ report
A program which searches for ambiguities in context-free grammars github.com/stepchowfun/cf…
πŸ‘︎ 11
πŸ’¬︎
πŸ‘€︎ u/stepstep
πŸ“…︎ Jan 04 2017
🚨︎ report
Context free grammars and Ambiguity questions

I'm learning about context free grammars right now and had a couple questions.

  1. Is there any unambiguous grammar for the language a^i b^j c^k, where i=j or c=k? I could make an ambiguous one pretty easily but I haven't been able to come up with an unambiguous one.

2). Are there any general tips for making a grammar unambiguous? I know there's no exact algorithm, but maybe just some rules of thumb for specific special cases? (maybe like if there are multiple epsilons, or if there's a kleene star in the regexp)

Thanks!

πŸ‘︎ 10
πŸ’¬︎
πŸ‘€︎ u/MacawsInMacau
πŸ“…︎ Nov 30 2017
🚨︎ report
Which of these two sentences is correct?

I love your and Michael’s dogs.

I love you and Michael’s dogs.

Or is neither correct? If so, what is the correct way to say it?

πŸ‘︎ 11
πŸ’¬︎
πŸ‘€︎ u/GLuxious
πŸ“…︎ Dec 26 2021
🚨︎ report
I Popped a Blood Vessel Writing This Post. It's Shit.

I am not a financial advisor and this is not financial advice.

I've been seeing numerous posts about GME going to the hundreds of thousands or millions within a couple of days or a week or two, and I wanted to clarify some basic stuff for the new autistic apes.

Just because GME, for example, goes to $500, it does not mean SHF get margin called, let alone close their position. Each SHF have different price points on when they get margin called. There are a lot of factors that need to be considered, such as their leverage, position amount, and assets used as collateral.

Now let's say that a SHF does get margin called, it would take 5 days before the broker/clearing house takes over and force buy. In that 5 business days, if the price point goes below their margin requirements, that SHF is saved by the bell. It would take another margin call and another 5 business day before the liquation.

As this affects all SHF in certain stocks, we can assume, they are all colluding together. A simple powerhouse like SIG can do many things to drop the price. I won't go into details on what they can do, as there is a lot of DD on deep itm puts/calls, shorting the ETFs with large volume of GME, or future swaps, and etc. This is simply to explain the basic that many don't seem to understand.

Rostin Behnam postponed bank swaps until 2023. They think you'll forget and not care.

Now let's say that these SHF are not colluding or cheating, but rather they went by the books. If a SHF does get margin called and in 5 business days, the broker/clearing house takes over, it does not mean the price will jump immediately. I'll use Credit Suisse and Archegos as the example as it relates with GME.

Archegos lost their excess margin (cushion) of 900 million in the initial GME January run-up, and after March 22nd, ViacomCBS crashed, which happened to be Archegos majority holding. Credit Suisse margin called them and a day later, they were forced closed.

First, GME went to $500 a share and due to the excess margin limits Archegos had, they did not get margin called. I am re-iterating this since you retards think every SHF will get margin called at $500. Second, when they closed their position, the price did not spike. Why? Probably other short institutions spread the baggage amongst each other. They're not going to buy in the lit exchange immediately. That

... keep reading on reddit ➑

πŸ‘︎ 5k
πŸ’¬︎
πŸ‘€︎ u/theshinster112
πŸ“…︎ Dec 22 2021
🚨︎ report

Please note that this site uses cookies to personalise content and adverts, to provide social media features, and to analyse web traffic. Click here for more information.