# Questions tagged [sat]

SAT stands for the Boolean satisfiability problem.

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### Is there an algorithm for 3x3 sudokus without backtracking? [closed]

From what I can see on Wikipedia and the Internet at large, all sudoku solving algorithms (including human ones) employ some kind of EXPTIME backtracking search for some sudokus. Are there any SAT ...
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### At most how many satisfying assignments are there for a 2SAT with n variables?

It is not obvious but easy to see that, for some fixed set of satisfying assignments, there is no 2CNF that can satisfy the set of satisfying assignment exactly, when I discover this, I wonder at most ...
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### What are those deterministic algorithms for k-SAT that are not derandomization of random algorithms like PPSZ and Schöning's local search?

I am doing a survey on k-SAT where time complexity is in terms of n, i.e. the number of variables in a formula. As for the fast algorithms for k-SAT, we see biased-PPSZ, PPSZ, Schöning's local search,...
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### Reducing 3-XOR-SAT to HORN-SAT

In this question - XOR-SAT to Horn-SAT reduction, two algorithms are described for reducing any XOR-SAT formula to a HORN-SAT formula. My question is: say I limit the clauses of an XOR-SAT formula to ...
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### What is the complexity of checking equivalence of two boolean formulae without NOT symbol?

Suppose I have two boolean formulae (propositions) $P_1$, and $P_2$ (can be assumed to be in CNF) over the same variables and such that there are no "NOT" symbols used. I.e. only conjunction and ...
1 vote
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### Potentially stronger form of non-$ETH$

If we have a $2^{n^a}$ algorithm to $K$-$SAT$ where $a<1$ for all $K>2$ then $ETH$ fails and literature gives consequences. What are the consequences if $a=o(1)$?
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### Understanding non-equivalence of proof lengths according to proof systems

Here, in section 4.3, Fortnow says: But to prove P != NP we would need to show that tautologies cannot have short proofs in an arbitrary proof system. I am ...
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### Proof of SAT is complete for NP via first-order reductions

So I have been reading this: https://people.cs.umass.edu/~immerman/book/ch7.pdf I do not understand the proof of theorem 7.16, which says that SAT is complete for NP via first-order reductions. My ...
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### What is best known space requrement for solving SATISFIABILITY problem in exp time

I searched a lot for finding best space requirement algorithm for SATISFIABILITY problem but I didn't find any thing better than brute force that is in DSPACE(n). is there exists better bound? and ...
1 vote
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### Can MONOTONE WSAT be in solved in polynomial time?

In the weighted monotone satisfiability problem (MONOTONE WSAT), the input is an n-variable MONOTONE CNF Boolean formula (when there is no a clause with a negated variable) and an integer k, and the ...
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### Is there a standard format for Dependent QBF?

I know there is a standard input format DIMACS for a formula is in conjunctive normal form (CNF) and QDIMACS for quantified Boolean formulas. Is there a similar standard format for the Dependent-QBF (...
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### Seminal papers related to SMT theories (particularly QF_ABV)

I am working on an application using Quantifier-Free Bit-Vector/Array satisfiability which may or may not require mucking around with the internals of an SMT solver, and would like to understand what'...
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### Ways to think formally about Satisfiability Modulo Theories

Apologies if this is not a well-thought-out question, but I am interested in formalizing a problem which is ultimately described by a SMT formula in the theory of quantified arrays and linear ...
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### How hard is APPROXIMATE-#SAT?

It is well known that the problem of counting the satisfying assignments of SAT, namely the problem #SAT, is #P-complete. It is also suspected (somewhat less widely) that even deciding SAT should ...
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### a polynomial representation of boolean functions

I came up with this linear transformation to map boolean functions to polynomials and it seems to have some nice properties. I was wondering if there is any reference describing this (and/or similar) ...
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### How hard is gapped satisfiability?

It is well known that general satisfiability (of polynomially many clauses) is NP-hard, and in fact, it is conjectured that an algorithm deciding instances of SAT takes time nearly $2^n$ on $n$ ...
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### Sparsification Lemma for k-SAT and Exponential Time Hypothesis

According to R. Impagliazzo, R. Paturi and F. Zane, 2001 an instance of $k$-SAT is called sparse if $m = O(n)$ where $m$ denotes the number of clauses and $n$ the number of variables. The ...
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### Reduction from SAT to binary matrix subset problem

I'm trying to understand the answer by @Denis on this question, where he showed a way to reduce from SAT to the binary matrix column subset selection problem. The reason I'm having to post a new ...
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### Equality Constraints over Sets with Tree Automata

Tree Automata can be used to model sets of values of a Herbrand Universe, for example, to model possible values in a functional program. Systems of subtype constraints over set expressions have ...
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### How to benchmark #2-SAT counting algorithms?

Are there any libraries of #2-SAT instances that are hard to solve with state-of-the-art exact solvers (sharpSAT, cachet, ...)? Alternatively: are there practical ways to generate hard #2-SAT ...
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### Minimum Unsatisfiable Core

Recently in a course I'm taking, we have been learning about the DPLL(T) algorithm for SMT solving. The basic outline goes like this: ...
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