Talk:Boolean satisfiability problem

message: I noticed a typo in this section. Shouldn't it be UNAMBIGUOUS-SAT instead of UNAMBIGOUS-SAT?
KevinGoedecke (talk) 10:52, 11 August 2015 (UTC)
thread_title: Typo in "Extensions of SAT"

message: There is interesting work on the distribution of hard SAT problems, which seems like it should be discussed here.
I don't have time to add it now, but here is a link to the seminal paper:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.7362
Polytrope (talk) 17:11, 9 March 2011 (UTC)
thread_title:  Needs Discussion of Location of Hard SAT Problems 

message: It would be great to add some discussion on XOR-SAT  —Preceding unsigned comment added by 128.30.64.21 (talk) 23:45, 10 August 2010 (UTC)
thread_title:  Why No Discussion on XOR-SAT? 

message: Is the proper syntax for abbreviating 3-Satisfiability "3SAT" or "3-SAT" (hyphen or no hyphen)?  The page seems inconsistent with regards to this.
Sdoroudi (talk) 05:52, 1 June 2008 (UTC)
replies: text: I've seen paper titles using 3-SAT, 3SAT, and even 3Sat. In short, there is little agreement among researchers on this. Dcoetzee 08:55, 1 June 2008 (UTC)
replies: text: That said, is there anyway to standardize the article (we can put in somewhere an "also abbreviated as" or something like that, the first time the abbreviations are mentioned).  I don't much care which we go for, it would just be nice if the article is standardized. 131.215.170.228 (talk) 16:52, 1 June 2008 (UTC)
replies: text: Sorry forgot to sign Sdoroudi (talk) 16:52, 1 June 2008 (UTC)
thread_title: Proper Abbreviation Syntax

message: Why does the Satisfiability page redirect to this article? Someone not interested in computational complexity theory might be interested merely in a simple definition of satisfiability for propositional and predicate logic. Nortexoid 05:21, 23 May 2006 (UTC)
replies: text: Please feel free to turn that redirect into an article with these definitions. - Liberatore(T) 10:50, 23 May 2006 (UTC)
thread_title: Satisfiability

message: This page seems to be rather redundant and poorly organized to me (I'm quite familiar with the SAT problem).  Or maybe I'm just drunk right now...  67.142.130.30 07:18, 12 July 2006 (UTC)
thread_title: Organization

message: There is disagreement between this article and the CNF article on the number of literals in each clause of a k-CNF formula.  From Conjunctive Normal Form:
The k-SAT problem is the problem of finding a satisfying assignment to a boolean formula expressed in CNF such that each disjunction contains at most k variables.
From 3-SAT:
3-satisfiability is a special case of k-satisfiability (k-SAT) or simply satisfiability (SAT), when each clause contains exactly k = 3 literals.
Which is it? Should we choose one definition over the other, or should we provide both definitions to the reader? Moreover, must literals in each clause be unique? If yes, then this belongs in the article. Quaternion (talk) 03:08, 7 December 2007 (UTC)
replies: text: It's very easy to convert between forms. CRGreathouse (t | c) 02:22, 10 March 2011 (UTC)
thread_title: k-SAT: At most k literals or exactly k literals?

message: The problem of factorizing a number can be reduced to boolean satisfiablity. Essentially, we build a network of logic gates that perform a multiplication of two sets of inputs A[0..n] and B[0..n] (taken to be binary numbers A and B) and give a set of outputs C[0..n]. Each C is then expressed as a boolean function of the inputs A and B - admittedly, a pretty big one, but finite. We then specify a number by asserting or denying C. Thus, to find the factors of 10 we would assert C[3] & ~C[2] & C[1] & ~C[0]. We also assert that neither A nor B is 1. If we then can satisfy this in polynomial time, the solution for A[0..n] wil be a factor of C.  —Preceding unsigned comment added by 207.169.186.10 (talk) 05:50, 12 December 2007 (UTC)
thread_title:  Factorization 

message: This article is in direct contradiction with 2-SAT, which states:
:2-satisfiability (abbreviated as 2-SAT) is a special case of satisfiability if expressions are written in conjunctive normal form with 2 variables per clause (2-CNF).
whereas this article insists on DNF! Can someone please fix? linas (talk) 17:39, 31 March 2008 (UTC)
replies: text: As I said at Talk:2-satisfiability, it is not a contradiction. Sat in disjunctive normal form is trivial: each term gives a satisfying assignment. Sat in conjunctive normal form is, in general, hard, but 2-sat is an easier (though not as trivial as DNF) special case. —David Eppstein (talk) 17:52, 31 March 2008 (UTC)
replies: text: The paragraph discussing SAT for DNF expressions just seems to be under the wrong section heading.  I've moved it, which I think resolves the issue. Quaternion (talk) 17:57, 31 March 2008 (UTC)
thread_title:  Contradiction 

message: I agree with you, this may be confusing to newcomers, I think it is better to say "literals formed with variables" or better 
"literals formed with atom names" atoms should be enough but "atom names" may be more informative to newcomers. 
Also I think this notation is better:
:({l}_{1\,1}\vee{l}_{1\,2}\vee{l}_{1\,3})\wedge({l}_{2\,1}\vee{l}_{2\,2}\vee{l}_{2\,3})\wedge\ldots\wedge({l}_{m\,1}\vee{l}_{m\,2}\vee{l}_{m\,3})
:where each {l}_{i\,j}  is a literal, i.e. a proposition variable or its negation
But the one given in the article shows better in the screen.
I tried \mathcal{l} to display a calligraphic l, to avoid confusion with number one or capital i, but did not worked.
Anyway this is a superfluous change in notation as the other  is readable to anyone, but distinction between variables and literals should be clear and informative to newcomers as remarked by the previous user.  —Preceding unsigned comment added by Elias (talk • contribs) 22:15, 6 June 2009 (UTC)
thread_title:  Literals vs. Variables 

message: Judging by the lead there seems to be no problem.  Shouldn't the lead give at least a hint as to what the problem is?  Wikipedia expects an article's lead to summarize the article.  The concept of Boolean satisfiability on its own is a triviality. --Vaughan Pratt (talk) 06:33, 19 March 2011 (UTC)
replies: text: I added a paragraph.  Did it help? 75.57.242.120 (talk) 01:47, 20 March 2011 (UTC)

text: Reading through the article, the whole thing (while containing good material) badly needs reorganization and rewriting.  I'll see if I can mess with it in coming days/weeks/whatever, but expert help would be much appreciated.  75.57.242.120 (talk) 02:11, 20 March 2011 (UTC)
thread_title: Vacuous lead

message: We should add something about it.  This looks useful. 75.57.242.120 (talk) 01:32, 20 March 2011 (UTC)
thread_title:  random SAT 

message: I just deleted the following paragraph, putting it here in case I terribly misunderstood something:
(Context, kept:)
<BLOCKQUOTE>
Another reduction involves only four new variables and three clauses: R(¬x,a,b) ∧ R(b,y,c) ∧ R(c,d,¬z).
</BLOCKQUOTE>
(deleted:)
<BLOCKQUOTE>
To prove that R must exist, one first express R as product of maxterms, then show that
:x\lor y \lor z = (\neg x\lor a\lor b)\land(\neg y\lor c\lor d)\land(\neg z\lor e\lor f)\land(a\lor c\lor e)
The left side is evaluated true if and only if the right hand side is one-in-three 3SAT satisfied. The other variables are newly added variables that don't exist in any other expression. 
</BLOCKQUOTE>
(Context, kept:)
<BLOCKQUOTE>
The one-in-three 3SAT problem is often used in the literature as a known NP-complete problem in a reduction to show that other problems are NP-complete.
</BLOCKQUOTE>
My reasons for deleting:
* When proving that 3-SAT can be reduced to 1-in-3-SAT, the existence of R is assumed; there is no need to prove it.
* The equation is wrong: e.g. for x=y=z=FALSE and a=TRUE, the lhs and the rhs evaluates to FALSE and TRUE, respectively.
* I cannot see how the existence of R would follow from the equation.
Jochen Burghardt (talk) 18:30, 20 September 2013 (UTC)
thread_title:  Preserving paragraph deleted from [[Boolean satisfiability problem#Exactly-1 3-satisfiability]] 

message: The article mostly, but not always capitalizes the word "Boolean".
What is the reason to write "Boolean satisfibility problem" instead of "boolean satisfiability problem"?
I guess "boolean" could be considered like other adjectives like symmetric or digital.
Am I wrong?
91.17.148.168 (talk) 13:33, 3 March 2014 (UTC)
thread_title:  Capitalization of "Boolean satisfiability problem" ? 

message: In section Boolean satisfiability problem#3-satisfiability, on 13:50, 1 December 2010,  added the sentence:
The exponential time hypothesis is that no algorithm can solve 3-Sat in time \exp(o(n)).
E.g. on 12:32, 19 January 2014 (I didn't check the history in between), the sentence read:
The exponential time hypothesis is that no algorithm can solve 3-SAT faster than o(exp(n)).
On 18:15, 24 July 2014, 18.111.101.91 changed it to:
The exponential time hypothesis is that no algorithm can solve 3-SAT faster than exp(o(n)).
but I reverted it (see below for my thoughts). On 13:50, 6 October 2014,‎  changed it back to his original version (which I wasn't aware of up to now):
The exponential time hypothesis asserts that no algorithm can solve 3-SAT in time exp(o(n)).
So I see a need to discuss:
# "faster than" vs. "in time", and
# "exp(o(n))" vs. "o(exp(n))", and maybe
# whether to stick with the definition at exponential time hypothesis#Definition, which seems to amount to "every algorithm solving 3-SAT needs time O(2δn) for some δ>0", or, simpler, "O(cn) for some c>1".
As for 2., I still think that o should be the outermost operation, since it returns a set of functions; if exp is defined at all on the set o(n), it is defined elementwise, i.e. exp(o(n)) evaluates to o(exp(n)), unless I'm terribly wrong.
As for 1., I admit that, different to what I thought until yesterday, "faster than" may be too sharp; I'm confused by the unusual (to me) o instead of O.
For the latter reason, I'd like to suggest to use the O(cn) version from 3. - Jochen Burghardt (talk) 14:25, 6 October 2014 (UTC)
replies: text: Sorry, I wasn't aware of this edit conflict. exp(o(n)) is the correct term that should appear here, and o(exp(n)) is actually wrong: Note that the function 2^n is contained in o(exp(n))=o(e^n), but this is not what the exponential time hypothesis is about. Also cf. the article exponential time hypothesis. ylloh (talk) 15:40, 7 October 2014 (UTC)

text: Also note that the non-uniform version of the definition that is stated in exponential time hypothesis is usually just written as exp(o(n)) when the topic is discussed less formally. ylloh (talk)
Probably, your version (was and) is the right one, and the edit conflict was my fault. However, I still didn't fully understand your explanation: why is o(exp(n)) different from exp(o(n)), and why is the former term wrong? What is the definition of exp applied to a set of functions, viz. o(n)? - The article exponential time hypothesis#Definition primarily uses the big-O definition from Impagliazzo.Paturi.1999 (p.368), and then says that some sources use a slightly weaker notion, based on the little-o term 2o(n). I don't understand why that is weaker, but shouldn't we stick with the commonly used big-O definition? And: could you also comment on "faster than" vs. "in time"? - Jochen Burghardt (talk) 13:00, 9 October 2014 (UTC)
thread_title:  Exponential time hypothesis 

message: Hello fellow Wikipedians,
I have just modified  on Boolean satisfiability problem. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive http://web.archive.org/web/20070210083743/http://sat07.ecs.soton.ac.uk:80/ to http://sat07.ecs.soton.ac.uk/
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).
Cheers.—cyberbot IITalk to my owner:Online 14:08, 7 April 2016 (UTC)
thread_title:  External links modified 

message: Hello fellow Wikipedians,
I have just modified  on Boolean satisfiability problem. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20070208034716/http://www.sigda.org/newsletter/index.html to http://www.sigda.org/newsletter/index.html
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).
Cheers.—InternetArchiveBot (Report bug) 00:07, 6 November 2016 (UTC)
thread_title:  External links modified 

message: I have encountered the theme in practical sat solvers, but have never seen it expressed in theory.  It would seem to be a logical approach to showing NP=PSpace.Daniel pehoushek (talk) 22:34, 9 February 2017 (UTC)
thread_title:  Is adding a k-clause during satisfiability solving equivalent to deciding an (n-k) variable QBF? 

message: The current subsection is a great introduction, but IMO the topic deserves coverage as its own article including a table of SAT solvers and discussion of SAT conferences and competitions, etc. Caleb Stanford (talk) 21:42, 20 November 2021 (UTC)
replies: text: - Jochen Burghardt (talk) 18:43, 21 November 2021 (UTC)
thread_title:  [[SAT solver]] should be its own article 

message: The CNF paragraph makes reference to Horn clauses for seemingly no reason. As far as I can recall they are not relevant to the basic SAT problem (and HornSAT probably deserves it's own section or article). Should the reference to Horn clauses be removed? It looks quite out of place at the moment.
EditorPerson53 (talk) 13:52, 16 May 2022 (UTC)
replies: text: The intention is to have the necessary definitions collected in one section, viz. Boolean_satisfiability_problem#Definitions. Horn clauses occure in section Boolean_satisfiability_problem#Horn-satisfiability, and there the definition is used heavily. It is used also in Boolean_satisfiability_problem#Schaefer's_dichotomy_theorem. - Jochen Burghardt (talk) 17:46, 16 May 2022 (UTC)

text: The definition is needed for Boolean_satisfiability_problem#Horn-satisfiability and mentions in other sections. This article is in part an overview of the Boolean satisfiability problem and discusses a number of variants. Hence, I think a brief discussion of HORNSAT and the definition of a Horn clause is of due weight. -- {Talk} 17:55, 16 May 2022 (UTC)
thread_title:  Unnecessary references to Horn clauses?