# Questions tagged [satisfiability]

Satisfiability (SAT) is the problem of determining whether there is a variable assignment that fulfills a given Boolean formula.

659 questions
Filter by
Sorted by
Tagged with
62 views

### Reference asking: phase transition in SAT

This is not a technical question, I hope this community has a room for such questions, but I will delete it in case this is inappropriate. It has been experimentally observed (e.g. here) that when ...
• 33
1 vote
758 views

### What are the differences between symbolic execution and SAT solvers?

My understanding is that symbolic execution only deals with specific paths and bad patterns, while SAT solvers, or satisfiability modulo theories in general, provide a much more robust analysis of the ...
237 views

### When does Gaussian elimination solve exact 1-in-3 SAT?

Terms: A literal is a variable or its negation. A clause is a set of literals. An exact 3-in-1 clause is satisfied if an assignment of values to variables results in exactly 1 ...
317 views

44 views

### Names of specific SAT variants

I enjoy reading research on satisfiability, but sometimes it's easier to find relevant information when you know the names of the variants. Example: All the clauses are width 3 and must have ...
81 views

### Turing reducibility of 2 versions of the satisfiability problem

I need help with this problem. There are 2 versions of the satisfiability problem: [1] decision version: determine whether an arbitrary formula f is satisfiable or not [2] search ...
75 views

### Reducibility of 2 boolean satisfiability problems

I beg some help with this problem. There are 2 boolean satisfiability problems. Problem $A$: Determining whether an arbitrary formula of size $n$ is $satisfiable$. Problem $B$: Determining ...
2k views

### Unique 3SAT to Unique 1-in-3SAT

Suppose I have a CNF formula with clauses of size 2 and 3. It has a unique satisfying assignment. It was made from a binary multiplication circuit where I multiplied two primes numbers A and B such ...
1 vote
161 views

### Unique 1-in-3 SAT

Suppose I have a CNF formula with clauses of size 2 and 3. It has a unique satisfying assignment. I know the value of each bit of the unique assignment because it was made from a binary ...
383 views

### Prove or Disprove, 3SAT ≤p 2SAT, then P = NP

I know that 3SAT is in NP and 2SAT is in P. And 2SAT can reduce to 3SAT just says 3SAT is strictly harder than 2SAT, so I don't think this proves P = NP, but it doesn't seem to disprove it either.
3k views

### What is wrong with this simple proof of P=NP?

Exactly 1 in 3 SAT ($X3SAT$) is a variation of the Boolean Satisfiabilty problem. Given an instance of clauses where each clause has three literals, is there a set of literals such that each clause ...
63 views

### Programming in Propositional Logic article notation question

I was reading this article about propositional logic and transforming problems to SAT. The author often uses the following notation (taken from Dominating set section): I don't understand what $[v,i]$...
370 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 ...
800 views

### Time complexities of state-of-the-art SAT solvers with respect to length of the formula

I am learning about DPLL and CDCL SAT solvers, and I know that they have time complexity exponential to the number of variables. If I am not mistaken, one of the reasons why most believe P does not ...
• 145
1 vote
682 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
430 views

### Definition of 2-CNF (a.k.a Krom) formula

In my lecturer's notes, the following definition for a 2-CNF wff is given: A 2-CNF formula, or Krom formula is a CNF formula F such that every clause has at most two literals. However, there is ...
123 views

### Clarification on "clause learning" in DPLL algorithm

I am struggling to understand the idea of conflict-driven clause learning, in particular, I can not understand why the clause we 'learned' is a substantially new (i.e. the clause database does not ...
• 687
23 views

### Flip Output of SAT problem [duplicate]

Why cant I Just create a TM A that runs a NTM B with a formula to compute the SAT Problem and Just Flip its Output. So when the Input NTM B Returns true (formula is satisfyable) the TM A Return false.
• 121
467 views

• 933
1 vote
477 views

### Integer programming to MAX-SAT translation

Reading A Comparison of Methods for Solving MAX-SAT Problems, I can see that a MAX-SAT problem can be translated to an integer programming (IP) problem. Definition of MAX-SAT [Wikipedia]: The ...
• 933