Talk:Boolean satisfiability problem

Because of their length, the previous discussions on this page have been archived. If further archiving is needed, see Wikipedia:How to archive a talk page.

Previous discussions:

• Archive 1 (from creation to 18/10/2005)

Needs Discussion of Location of Hard SAT Problems

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)

Why No Discussion on XOR-SAT?

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) There is a "hidden" reason every discussion is deleted: there is no constructive formula from OR-SAT in polynomial space able to represent a XOR-SAT. That contradicts the theorem of Cook which expects how the configuration would be. I would recommend you my own links, but I am sure this will be deleted too.

Combine this Page with "Satisfiability and validity"

This page addresses the same topic, but in more detail. Suggest merging "Satisfiability and validity" into this by making it the introduction.

Proper Abbreviation Syntax

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)

I've seen paper titles using 3-SAT,[1][2] 3SAT,[3] and even 3Sat.[4] In short, there is little agreement among researchers on this. Dcoetzee 08:55, 1 June 2008 (UTC)

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)

Sorry forgot to sign Sdoroudi (talk) 16:52, 1 June 2008 (UTC)

Satisfiability

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)

Please feel free to turn that redirect into an article with these definitions. - Liberatore(T) 10:50, 23 May 2006 (UTC)

Organization

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)

As an expert on Satisfiability, I agree that the page would benefit from some reorganisation and revisions targeted to improving clarity and accuracy of the information provided. I may have time to do this myself in a while, but perhaps the problems have been resolved by then ... Hh 00:20, 27 November 2006 (UTC)

k-SAT: At most k literals or exactly k literals?

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)

It's very easy to convert between forms. CRGreathouse (t | c) 02:22, 10 March 2011 (UTC)

Factorization

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)

Contradiction

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)

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)

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)

Literals versus Variables

The description of the example for 3-Satisfiability includes the following sentence:

E has two clauses (denoted by parentheses), four literals (x1, x2, x3, x4), and k=3 (three literals per clause).

but in the example, there is also the literal not(x2) and not(x3). As far as I know, a literal is a variable or the negation of a variable in propositional logic, and a term or the negation of a term in predicate logic. Therefore, it should read "... four variables (x1, x2, x3, x4) ..." or "... five literals (x1, x2, not(x2), not(x3), x4) ...". The distinction between literals and variables (or atoms in predicate logic) is an important one, and this example description is confusing for newcomers to logic.

If you all agree, I will change the description, or somebody else, who is positive, might do. —Preceding unsigned comment added by 141.84.9.33 (talk) 17:09, 26 February 2009 (UTC)

Literals vs. Variables

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)

Vacuous lead

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)

I added a paragraph. Did it help? 75.57.242.120 (talk) 01:47, 20 March 2011 (UTC)

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)

random SAT

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