Questions tagged [2-sat]
The 2-sat tag has no usage guidance.
50
questions
0
votes
1
answer
25
views
reducing the word problem for dtm to sat / cnf-sat / 2-sat
word problem: given a language L through a deterministic turing machine, is the word w in the language L?
the problem should be decidable, since if there is a deterministic turing machine i can simply ...
- 11
1
vote
1
answer
150
views
Proof that 2-sat is P-hard?
i figured out this is what i want to know:
in Cook's theorem it is shown that SAT is NP-hard. he shows it by showing that sat is at least as difficult like the word problem for nondet. Polynomial Time ...
- 11
4
votes
1
answer
69
views
3-SAT with atmost 3 variables and variable occuring once per clause
I've stumbled across this problem on CSES
https://cses.fi/345/task/E/
and was wondering is it somehow reducible to 2-SAT with given constraints?
So, the problem states that you need to solve a 3-SAT ...
1
vote
0
answers
14
views
example of an NL-completeness reduction?
I'm looking for simple examples of nondeterministic log-space completeness reductions. In particular I seem unable to construct any nontrivial widget using 2-SAT clauses, which is known to be NL-...
- 2,296
1
vote
1
answer
47
views
Describe statement "Exactly k out of n variables should be true" in 2-SAT in time polynomial to n and k?
I have a list of $n$ variables, exactly $k$ of which should be true. Is it possible to encode this as a 2-SAT problem in time polynomial to $n$ and $k$?
3
votes
1
answer
97
views
Is 2-SAT over Linear Real Arithmetic in P or NP?
The general boolean satisfiability problem (SAT) is NP-complete, and thus can't be solved in polynomial time (assuming $P \neq NP$). But the special case of 2-SAT is in P, and can be solved in linear ...
- 133
2
votes
3
answers
169
views
Why can $2$-SAT be solvable efficiently, but $3$-SAT not?
I am aware that 2SAT is polynomial while 3SAT is not, but I am looking for an intuition why its so. After all, even in 2SAT we can attempt all possible truth functions and its $2^n$. So I am hoping ...
0
votes
0
answers
38
views
Is there a reduction from 2sat to bpm?
Given a 2SAT instance can we convert into bipartite perfect matching in parsimonious reduction?
- 2,822
2
votes
1
answer
21
views
Padding a 2SAT clause
In http://web.mit.edu/neboat/www/6.046-fa09/rec8.pdf, I see that they pad a 2SAT clause $(x\vee y)$ to make it a 3SAT clause by writing $(x\vee y\vee p) \wedge (x\vee y\vee \neg p)$. Why doesn't $(x\...
- 23
0
votes
1
answer
24
views
Doubt regarding the implications of a 2-SAT constraint
Consider an example 2-SAT instance with the constraint (x1 ∨ x2).
This CNF has these two implications:
¬x1→x2 and ¬x2→x1.
"They actually mean, if x1 is false then x2 must be true, and if ...
1
vote
1
answer
293
views
Showing resolution algorithm for 2SAT is polynomial time
I don't quite understand why the resolution algorithm completes in polynomial time for 2SAT but not 3SAT.
I'm looking at slide 42 of these slides for reference. It is clear that given two clauses of ...
- 13
0
votes
1
answer
43
views
Algorithm for assigning items to one of two sets (2-CNF?)
I have a set of items (A, B, C, D, ...) which I want to assign to one of two sets (set1, set2). Trying all possible assignments ...
- 13
0
votes
2
answers
65
views
Are different assignments allowed for the implication graph proof of 2-SAT being in P?
One proof for $2-SAT$ being in $P$ uses the implication graph, i.e. one creates 2 vertices per variable $a$, one for each possible literal ($a$ and $\neg a$). One then adds 2 arcs per clause $(a \lor ...
- 582
1
vote
1
answer
143
views
Complexity of specific cases of MAX2SAT
I know that MAX2SAT is NP-complete in general but I'm wondering about if certain restricted cases are known to be in P. Certainly the languages
$L_k:=\{ \phi \,|\, \phi\,\text{is an instance of 2SAT ...
- 1,601
1
vote
0
answers
89
views
2SAT problem testcase does not have any strongly connected components
My task is to solve the 2SAT problem.
I have read online that a good method to solve this problem would be to construct an implication graph, where each statement of the form ...
- 425
1
vote
1
answer
43
views
Polynomial time counter of solutions of 2SAT expression with pure literals
As per the title, is there any polynomial time algorithm to count the number of satisfying arguments for a 2SAT expression with pure literals? An even shallower case: Is there any such counter when ...
- 13
0
votes
1
answer
131
views
Maximum number of positive literals in 2SAT
MAX 2SAT is NP complete.
Instead of satisfying the maximum number of clauses, I have a fully satisfiable 2SAT formula and I want to have the maximum number of positive literals in the assignment (...
- 683
0
votes
0
answers
86
views
the correctness of 2-satisfiability problem algorithm by using implication graph
I learned finding a solution of 2-sat problem algorithm below.
The point are below
(1) when constructing the implication graph
(2) finding there is no occurrence of a variable x and its negation x' ...
- 11
2
votes
1
answer
155
views
MAX 2-SAT is polynomial time reducible to 2-SAT?
I know that 2-SAT is solvable in polynomial time and 2-SAT is NP-Hard.
I have issue about this statement:
MAX 2-SAT is polynomial-time reducible to 2-SAT. Can you explain to me how reduction looks ...
- 133
1
vote
1
answer
417
views
Use 2SAT to show that an implication graphs must have a cycle if it's not satisfiable
Using 2SAT and implication graphs, how could I prove the following properties of implication graphs:
Suppose there is a directed path between literals l1 and l2 in G_φ. Then there is also a directed ...
- 352
3
votes
1
answer
818
views
Expected length of a random walk on a line
I am given the following randomized algorithm for SAT,
Input: A satisfiable CNF-formula $\varphi$.
Output: An assignment $\rho$, such that $\rho \models \varphi$.
The algorithm works as follow:
...
- 4,073
3
votes
2
answers
398
views
How Tarjan algorithm work for the 2-SAT
Tarjan's algorithm for 2-SAT is based on the truth:
a 2-CNF formula is satisfiable if and only if there is no variable that belongs to the same strongly connected component as its negation.
But I ...
- 31
1
vote
0
answers
464
views
Min-Ones-2-SAT getting to vertex cover
In the Min-Ones-2-SAT problem, we are given a 2-CNF formula φ and an integer k, and the objective is to decide whether there exists a satisfying assignment for φ with at most k variables set to true....
- 111
3
votes
2
answers
1k
views
Give an NL-algorithm for complement of 2-SAT
Question1: What is the difference between 2SAT and the complement of 2SAT?
Question2: It is known that NL is contained in P, but what we know about P over NL? can be said that an algorithm that runs ...
- 101
8
votes
1
answer
596
views
Is a "local" version of 3-SAT NP-hard?
Below is my simplification of part of a larger research project on spatial Bayesian networks:
Say a variable is "$k$-local" in a string $C \in 3\text{-CNF}$ if there are fewer than $k$ clauses ...
- 319
0
votes
0
answers
77
views
2-sat and vertex cover [duplicate]
I've been recently dealing with the classical problem of finding the minimum vertex cover in a bipartite graph. The common approach is to set direction to all edges and run DFS from all vertices of ...
- 364
1
vote
0
answers
161
views
Can someone give me the resolution procedure for 2 SAT, which is O (nˆ2)
According to Wikipedia, Even, S .; Itai, A .; Shamir, A. cited it in "On the complexity of time table and multi-commodity flow problems".
The paper can be found here: http://www.cs.technion.ac.il/...
- 25
1
vote
1
answer
179
views
Counting models satisfying a boolean formula
I'm trying to implement the #2-SAT algorithm from the paper "Counting Satisfying Assignments in 2-SAT and 3-SAT" (Dahllöf, Jonsson and Wahlström, Theor. Comput. Sci. 332(1–3):265–...
- 129
1
vote
0
answers
28
views
Proof that MAX-2-SAT is NP-hard [duplicate]
According to Wikipedia, while the 2SAT problem is polynomial, its maximization variant MAX2SAT is NP-hard. But, they do not provide a reference for this claim. Is this obvious? If not, where can I ...
- 5,664
3
votes
1
answer
31
views
General structure of solutions to 3-SAT circuits
Certain special forms of the SAT problem have solution sets of a special form. For example, given any three solutions to a 2-SAT circuit, their bitwise median is also a solution. Likewise, given any ...
- 690
0
votes
1
answer
771
views
2SAT Problem using Implication Graph
I was doing a practice question. As you can see below there is an Implication graph. To check whether the problem is satisfiable, I checked whether there were any 'bad loops'. To do so, for each ...
- 21
2
votes
0
answers
60
views
Reducing a problem to 2-SAT
Given a matrix $A$ with entries $a_{ij} \in \{0,1\}$, the matrix $B$ is formed by $b_{ij}=a_{ij} + a_{i+1,j} + a_{i,j+1} + a_{i+1,j+1}$. $B$ has one row and one column less than $A$. The problem is ...
- 21
0
votes
1
answer
69
views
For which c, d is Gap2SAT[c, d] in P (such that 0<c<d<1)?
For which $c, d$ is $Gap2SAT[c, d]$ in $P$ (such that $0<c<d<1$)?
(I know if d=1 then for each c it will be in P, however with which c,d such that $0<c<d<1$ can I simply return ...
- 19
1
vote
1
answer
40
views
Is there an algorithm to find out if a truthtable can be represented as 2-sat, and if so find its 2-cnf?
I know that not all truthtables have a corresponding 2-cnf representation, but is there a way to find out if a given truthtable has a 2-cnf representation, and if so to find what that is?
- 57
1
vote
3
answers
135
views
NP-hardness of an extention of 2 sat
a 2 sat instance which is unsatisfiable and an integer k are given, decision problem is that: is it possible to delete k variables, also remove clauses contain them, in order to satisfy the 2-sat ...
- 125
5
votes
1
answer
587
views
Even, Itai & Shamir's limited backtracking algorithm for 2-SAT: is it really linear?
I have read in Wikipedia (and other sources) about the limited backtracking algorithm of Even, Itai & Shamir for solving 2-SAT problem in a linear time, but the approach doesn't seem to be linear, ...
- 219
2
votes
1
answer
47
views
2CNF with 3 variable occurences
If we do not allow unit clauses, can 2CNF containing 3 occurences per variable be unsatisfiable?
Every time I try to connect opposing variables to a cycle, I need to draw 4 edges for at least one ...
- 1,381
2
votes
1
answer
309
views
Is this case of weighted 2SAT NP-complete?
Weighted 2SAT asks if it is possible to satisfy the formula with at most $k$ variables set as positive/negative. Trivially, every instance must be in 2CNF. It is known to be $\mathsf{NP}$-complete.
...
- 1,381
1
vote
1
answer
79
views
How 2-QCNF algorithm works?
Suppose we have following 2-QCNF problem:
$$\forall x_1...\forall x_m\exists y_1...\exists y_k:\varphi(x_1,...,y_k)$$
where $\varphi$ is 2-CNF.
When the formula is false?
Rules that I found:
$\...
- 1,381
1
vote
1
answer
594
views
Is this possible to solve 4SAT in polynomial time? [closed]
I know and admit that this is long, but please read it slow and understand everything.
I think that this is one of the most interesting questions asked in computer science ever.
I don't expect for ...
4
votes
2
answers
783
views
2-SAT implication Understanding
Having a simple 2-SAT problem where the equation is simply: $a \lor b$
We have two implications:
$\lnot a \Rightarrow b$
$\lnot b \Rightarrow a$
Thus, in the graph we build we add edges similar to ...
- 41
1
vote
1
answer
91
views
2-clause satisfiability associated graph
A 2-clause is a clause with at most two propositions (clauses?) : $(p \wedge q,\neg p \wedge q, \neg p,...)$. I have to show that the folllowing problem is $\in$ P:
2-SAT:
Input : A conjunction $\Phi$...
2
votes
0
answers
272
views
Is Max-2SAT with exactly 3 occurrences per variable APX-hard?
The Max-2SAT problem asks if at least k clauses of a 2CNF formula can be satisfied.
The Max-2SAT(at-most-3) problem is the restriction in which every variable occurs in
at most 3 clauses (counting ...
- 520
3
votes
1
answer
321
views
Is SAT-Problem with XOR and AND NP-complete
Is this problem NP-complete?
I have many restrictions like this and want to find a feasible solution:
((a and b) xor (c and d)) = 1
with a,b,c,d are arbitrary literals. It looks similar to XOR-2SAT ...
- 31
4
votes
1
answer
1k
views
How to do last step of Krom's algorithm for solving 2SAT problems
I was making a program for solving 2 SAT problems, using Krom's algorithm. I did not found a lot of information searching in Google, so I used Wikipedia's description of Krom's algorithm to implement ...
- 143
0
votes
0
answers
122
views
How to check wether a 2SAT implication graph has a bad loop or not?
m doing a practise quiz which my professor has posted online, one of the questions im very confused about was this one.
...
- 111
5
votes
2
answers
761
views
Can you solve 2-sat problem when truth assignments of some variables are determined
I am trying to find a assignment to satisfy a 2-sat statement. Problem is some of the clauses are 0 or x or 1 or x. I think the <...
- 329
2
votes
1
answer
211
views
Schaefer's dichotomy theorem and reformulating 3-literal clauses
Does Schaefer's dichotomy theorem establish that a general 3-sat clause cannot be transformed into an equivalent set of 2-sat/Hornsat/affine clauses (using auxiliary variables) or just that this would ...
- 1,601
3
votes
0
answers
257
views
"Balancing" positive and negative literals in 2-sat
I saw in an answer to this post that it is possible to construct 3-sat clauses with extra variables such that the number of positive and negative literals for each variable are equal. Does anyone ...
- 1,601
14
votes
3
answers
3k
views
Is 2-SAT with XOR-relations NP-complete?
I'm wondering if there is a polynomial algorithm for "2-SAT with XOR-relations". Both 2-SAT and XOR-SAT are in P, but is its combination?
Example Input:
2-SAT part: ...
- 2,296