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Questions tagged [sat-solvers]

Questions regarding solver programs for the boolean satisfiability problem.

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2 votes
1 answer
99 views

Find a list of actions that result in desired state

I have a problem that I need to solve, and I'm looking for which area of computer science (algorithms. etc) would be appropriate to solve this problem. In the system we have a list of actions that a ...
0 votes
0 answers
37 views

Seeking CNF Encoding with Exponential Lower Bound in Propagation Redundancy [migrated]

I'm exploring the possibility of encoding a proposition in CNF that might have an exponential lower bound for the number of steps needed to prove it unsatisfiable using propagation redundancy. While ...
0 votes
0 answers
14 views

Finding a common variable value among all SAT solutions

Let $F$ be a boolean formula on $n$ variables $x_1, \cdots, x_n$. $\textbf{SAT}(F)$ asks whether there exists an assignment of truth values to variables under which $F$ is true. I'm curious about ...
1 vote
0 answers
13 views

Are there ASICs optimized to solve the SAT problem?

Are there ASICs (application-specific integrated circuits) optimized to solve the SAT problem, such as by the DPLL algorithm?
2 votes
1 answer
148 views

SAT solvers for counting the number of solutions

Are there existing SAT solver libraries that can count the number of solutions of a boolean formula? Can you give examples? I mean implementations more efficient than the naive approach, i.e. each ...
1 vote
0 answers
90 views

Sat solvers with backdoor set

I have large cnf with thousands of variables, but with known compact backdoor set. I think this set can be used by CDCL solvers to choose assignment variables to simplify formula much faster, but I ...
1 vote
1 answer
323 views

How fast can we make generalized k-SAT?

Suppose a generalized version of k-SAT where the usual clauses (disjunctions of literals) are generalized to arbitrary Boolean functions of k variables. (For example, $(x \oplus (y \land z)), ((x \...
1 vote
1 answer
165 views

How to find the learned clause from a UIP cut

I would guess that this question is going to make some people wonder how I haven't already found a solution looking through papers -- but I do not see a clear algorithm. In implementing CDCL, I read ...
5 votes
3 answers
2k views

Are there any open source SAT solvers with UNSAT core extraction algorithm built in?

Just like the title says. I need to use a SAT solver on a series of CNF formulas but not only do I need an answer of the type satisfiable/unsatisfiable but also some subset of clauses whose ...
1 vote
1 answer
45 views

Showing SAT is auto-reducible

I am trying to wrap my head around the concepts of auto-reducibility and having access to an Oracle. The way I understand is that a language is auto-reducible iff there is a Turing Machine $M^{L}(x)=1$...
1 vote
1 answer
104 views

Specialized SAT solver (?)

(Context) Given two byte arrays of length 16, say $L$ and $H$, one can define a mapping $M$ from the set of all bytes to itself in the following way. If $0 \le b \lt 256$ is a byte, let $\text{lo}(b)$ ...
3 votes
1 answer
100 views

Could SAT solvers be significantly more efficient if they allowed for non-CNF formula?

SAT Solvers focus on CNF formulas. For many implications it is much mroe natural to use implications and conjunctions to encode problems, and when converting to CNFs, information is lost, and the ...
0 votes
0 answers
13 views

Reference request for Unit Clause Based SAT Reduction Rules

I tested my XSAT solver using the 4 pigeons in 3 holes problem converted to XSAT. The pigeon hole instance I give below had 108 variables and 88 clauses after being converted to monotone XSAT. My ...
0 votes
0 answers
17 views

Complexity Class of the Problem: Existence of Unsatisfying Interpretations in Boolean Formulas

What is the complexity class of the problem if there exist two different interpretations that do not satisfy a given Boolean formula? I believe the problem of existence of an interpretation that does ...
1 vote
2 answers
176 views

Can an optimization algorithm be "universal"?

I am wondering if a Bayesian Optimization framework (e.g. Google's Vizier) can be used in lieu of a traditional solver like Gurobi or CPLEX. In trying to answer this question, I realized that I don'...
0 votes
1 answer
58 views

What's the relation between DPLL and BDDs?

BDDs are a way of representing Boolean formulas. DPLL is an algorithm to determine satisfiability of Boolean formulas. My understanding is that the two are used for SAT solving. How are they combined?
1 vote
1 answer
54 views

CDCL SAT solvers and don't cares

Modern CDCL SAT solvers often can return partial assignments where missing literals mean that the value of that variable is not important for the satisfaction of the formula (i.e. it is a don't care). ...
4 votes
0 answers
56 views

Benchmark of SAT solvers on random k-SAT instances at satisfiability threshold

I am looking for a solid reference (peer-reviewed publication) on the design and/or benchmarking of SAT solvers for random k-SAT ($4 \leq k \leq 8$) operating at satisfiability threshold. The majority ...
2 votes
0 answers
62 views

Modified DPLL for 3-SAT by reducing to 2-SAT

In Boolean Satisfiability of CNF formulae we have $k$-SAT where each clause has at most $k$ literals. It is well known that $k$-SAT is polynomial time reducible to $3$-SAT. It is also well known that $...
1 vote
4 answers
2k views

Is this possible to solve 3SAT in O(n^24) time and O(1) space?

Assume that n is the number variables of the given 3CNF formula (n≥3) and all clauses in the given 3CNF formula are different. That means that for each clause, each literal can be either positive ...
12 votes
4 answers
2k views

Are there competitions for integer programming?

Are there competitions for integer programming like there are for SAT and MAXSAT?
-1 votes
1 answer
47 views

Can you help me find some examples of 3co-SAT for 4 variables?

I've been studying the examples of 3co-SAT recently. It's easy to find an example of one variable. $(x_1\lor x_1\lor x_1)\land (\overline{x_1}\lor \overline{x_1}\lor \overline{x_1})$ Examples of 2 ...
0 votes
1 answer
444 views

Time-complexity of evaluating a CNF formula

Given a Boolean formula over $n$ variables in CNF and a partial assignment to it, all the algorithms I can think of to evaluate the assignment run in time $\Theta(n^2)$. Is it possible to do it in $O(...
2 votes
2 answers
140 views

what does **input** mean for the $3SAT$ question? Is it the number of variables $n$ or the number of clauses $m$

We know that $3SAT \in NP$, and the definition of $NP$ is as follows: $NP$ is the class of languages that have polynomial time verifiers. But I have a question: what does input mean for the $3SAT$ ...
1 vote
1 answer
202 views

MAX-SAT 2-Approximation algorithm

I have the two following questions: I know SAT -> MAX-SAT but how can I show that if MAX-SAT is solved in polynomial time then SAT is solved in polynomial time as well?(I guess using approximation ...
20 votes
3 answers
1k views

Recipe book for SAT encodings?

SAT solvers are getting more and more efficient in solving large instances and are being used as back-ends in various contexts. Every time one wants to use them to solve a problem in a specific domain,...
1 vote
1 answer
82 views

prove that if $SAT\notin Size(2^{n/100})$ then CorrectSATSolver$\in P$

I need to prove that if $SAT\notin Size(2^{n/100})$ then CorrectSATSolver$\in P$. Where CorrectSATSolver $= \{C | C(\varphi) = 1 \iff \varphi$ is satisfiable$\}$. In other words, CorrectSATSolver ...
4 votes
1 answer
735 views

What are efficient approaches to implement unit propagation in DPLL-based SAT solvers?

I'm trying to decompose deduction steps of DPLL algorithm -- unit propagation and pure literal elimination -- for parallelization. However, I want a baseline and asymptotic analysis to compare to my ...
2 votes
0 answers
73 views

Quantum Boolean SAT algorithm?

Is there a quantum SAT algorithm, a quantum analogue of the DPLL or CDCL algorithms? Note: I'm not looking for the quantum analogue of the Boolean satisfiability problem (though that would be ...
2 votes
1 answer
118 views

How to determine if clause will change the satisfiability of the 3SAT formula?

I have satisfiable 3SAT formula like: (x1 or x2 or x3) and (not x1 or x2 or not x3) and some clause which is not in this formula ...
3 votes
1 answer
78 views

Stalmarck's method: x ≡ x → z, does z have to be true?

I have been researching Ståmarck's method 1. In the paper cited here, some rules are given. Rules are made of triplets (x, y, z) such that: y $\to$ z $\equiv$ x where x, y and z are booleans which ...
2 votes
0 answers
42 views

Non-trivial reduction form SAT to $3$-SAT

Looking for any idea for reduction from $SAT \leq 3-SAT$ where $SAT$ is known to have $d$ variables at most in each clause. I am looking for a reduction in which the resulting formula will not depend ...
6 votes
1 answer
207 views

Why is this SAT problem hard and what can I do about it?

For a graph theory problem I need to solve hundreds of millions of CNF problems that typically have around 200 variables and 15,000 clauses no larger than 10. By default I use glucose, which usually ...
2 votes
2 answers
751 views

Is any sudoku solver an SAT solver?

I have recently created a sudoku solver using C#, which outputs the solution to a sudoku after a reasonable amount of time in many cases. I have used the basic sudoku SAT-reduction (i.e. x111 meaning ...
1 vote
1 answer
160 views

Three dimensional matching expressed as SAT

The posting in the website Embedding SATISFIABILITY into 3-DIMENSIONAL MATCHING seeks $3SAT$ as a $3$ dimensional matching instance. I am looking to solve the converse problem. How to solve three ...
6 votes
3 answers
336 views

Detection of redundant boolean constraints

I'm trying to solve a constraint programming problem using a SAT solver. I have set of constraints in the form of propositional logic statements, which are converted to CNF using Tseitin ...
0 votes
0 answers
59 views

SAT solvers that can compute prime implicants and/or minimization

I'm looking into computing the prime implicants of a Boolean function. I have found many different algorithms in the literature, many of them relying on SAT solvers. However, I have not been able to ...
1 vote
0 answers
154 views

Which features can be considered for neural network based SAT solving?

I'm trying to implement SAT solver, based on backtracking algorithm and BCP. This SAT solver is trying to pick one literal from each clause, from 3-CNF SAT instances. I've implemented a neural network ...
1 vote
1 answer
246 views

Proving using a SAT solver that KB entails D

Suppose you're given this KB: $$KB = (A, A ⇒ B, A ⇒ C, B ∧ C ⇒ D)$$ How would you show using a SAT solver that $KB \vDash D$?
11 votes
1 answer
909 views

Can top SAT-solvers factor easy numbers?

Modern SAT-solvers are very good at solving many real-world examples of SAT instances. However, we know how to generate hard ones: for instance use a reduction from factoring to SAT and give the RSA ...
1 vote
0 answers
65 views

How often can a learned clause cause this solver to backtrack?

The is an improvement to the X3SAT solver I described in What is wrong with this simple proof of P=NP? I have fixed the flaw found in that solver. Now, I want to know how often the solver described ...
2 votes
1 answer
68 views

Solving largely monotone SAT formulas

I just wonder if solving largely monotone SAT formulas (meaning most clauses do not contain negated literals, but some do) is in any way easier than general SAT formulas? In other words, are there ...
33 votes
3 answers
7k views

Encoding 1-out-of-n constraint for SAT solvers

I'm using a SAT solver to encode a problem, and as part of the SAT instance, I have boolean variables $x_1,x_2,\dots,x_n$ where it is intended that exactly one of these should be true and the rest ...
1 vote
2 answers
538 views

Is there any algorithm for 3SAT problem that is fast and relatively easy to implement?

Here is the description for 3SAT satisfiability problem. I already know about the DPLL algorithm, but it's implementation is pretty complex. I would like some algorithm that is relatively simpler but ...
1 vote
1 answer
975 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 ...
3 votes
1 answer
51 views

How to leverage the fact that I'm solving 1000's of very similar SMT instances?

I have a core SMT solver problem consisting of 100,000 bit-vector array clauses, and one 10000-dimensional bit-vector array. Then, my program takes as input k << 100,000 new clauses, and adds ...
0 votes
2 answers
438 views

Constrain certain variables in CNF to unique satisfying assignments

[Reposted because the original question was deleted by the poster.] I'm looking for a way to add additional clauses (and maybe additional variables) to an already existing SAT instance so that ...
2 votes
1 answer
624 views

How to choose between UC and PL when using the DPLL algorithm?

We know DPLL algorithm is backtracking + unit propagation + pure literal rule. I have an example. There is one example to solve following Satisfiability problem with DPLL. if assign of "0" to ...
3 votes
1 answer
141 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 ...
4 votes
2 answers
470 views

Is it feasible to solve this subset cover problem with SAT solver?

The problem is to find $\mathcal{S}$, a minimal collect of subsets of $\{1,\dots, 17\}$ such that the two conditions are satisfied: if $S \subseteq \mathcal{S}$ then $|S|=6$; for any $A \subseteq \{1,...