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A Note on Satisfying Truth-Value Assignments of Boolean Formulas

2004
*
International Conference on Theory and Applications of Satisfiability Testing
*

We show that every

dblp:conf/sat/Stachniak04
fatcat:ji3ysqbkcnhldk7e2uvv42zpha
*satisfiable**Boolean**formula*has at least*one*bounded*assignment*. ... We also discuss*a*possible application*of*bounded*truth*-*value**assignments*in local search and other methods for solving*Boolean**satisfiability*problems. ... The notions*of**a**truth*-*value**assignment*and*of**a**satisfying**truth*-*value**assignment**of**a**Boolean**formula*are defined in the usual way. ...##
###
Enforcing Confidentiality and Data Visibility Constraints: An OBDD Approach
[chapter]

2011
*
Lecture Notes in Computer Science
*

We propose

doi:10.1007/978-3-642-22348-8_6
fatcat:xux3eoux2bepfbzpokdkvcumoy
*a*modeling*of*constraints and*of*the data fragmentation problem based*on**Boolean**formulas*and Ordered Binary Decision Diagrams (OBDDs). ... Exploiting OBDDs, we efficiently manipulate*Boolean**formulas*, thus easily computing data fragments that*satisfy*the constraints. ... Acknowledgments This work was supported in part by the EU within the 7FP project "PrimeLife" under grant agreement 216483, by the Italian Ministry*of*Research within the PRIN 2008 project "PEPPER" (2008SY2PH4 ...##
###
Short Note on P vs NP
[article]

2022
*
Zenodo
*

Under the assumption

doi:10.5281/zenodo.6042255
fatcat:qwj4muudbvcbrmv7mamzhgel4u
*of*certain hypothesis, we show that $P \neq NP$. In this way, we provide another possible tool to prove the $P$ versus $NP$ problem. ...*A**truth**assignment*for*a**Boolean**formula*ϕ is*a*set*of**values*for the variables in ϕ.*A**satisfying**truth**assignment*is*a**truth**assignment*that causes ϕ to be evaluated as true. ...*A**Boolean**formula*with*a**satisfying**truth**assignment*is*satisfiable*. The problem SAT asks whether*a*given*Boolean**formula*is*satisfiable*[2] . ...##
###
A Solution of the P versus NP Problem

2019
*
Zenodo
*

$P$ versus $NP$ is considered as

doi:10.5281/zenodo.3242873
fatcat:fa7zsrnj35c65hao2aopnpgpzi
*one**of*the most important open problems in computer science. This consists in knowing the answer*of*the following question: Is $P$ equal to $NP$? ...*A*precise statement*of*the $P$ versus $NP$ problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find*a*proof for this problem have failed. ...*A**truth**assignment*for*a**Boolean**formula*φ is*a*set*of**values*for the variables in φ.*A**satisfying**truth**assignment*is*a**truth**assignment*that causes φ to be evaluated as true. ...##
###
An OBDD approach to enforce confidentiality and visibility constraints in data publishing*

2012
*
Journal of Computer Security
*

In this paper, we make

doi:10.3233/jcs-2012-0449
fatcat:gug5f2yvrbb6xdfp3u5etcsg6m
*a*step towards private data publication by proposing*a*solution based*on*the release*of*vertical views (fragments) over*a*relational table that*satisfy*confidentiality and visibility ... We translate the problem*of*computing*a*fragmentation composed*of*the minimum number*of*fragments into the problem*of*computing*a*maximum weighted clique over*a*fragmentation graph. ...*A**truth**assignment*to the*Boolean*variables in*a**formula*corresponds to*a*path from the root to*one**of*the two leaf nodes*of*the OBDD*of*the*formula*. ...##
###
A Solution of the P versus NP Problem

2019
*
Zenodo
*

$P$ versus $NP$ is considered as

doi:10.5281/zenodo.3242872
fatcat:m7w5qsd255d3rjgjo7pzgfodem
*one**of*the most important open problems in computer science. This consists in knowing the answer*of*the following question: Is $P$ equal to $NP$? ...*A*precise statement*of*the $P$ versus $NP$ problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find*a*proof for this problem have failed. ...*A**truth**assignment*for*a**Boolean**formula*φ is*a*set*of**values*for the variables in φ.*A**satisfying**truth**assignment*is*a**truth**assignment*that causes φ to be evaluated as true. ...##
###
A Solution of the P versus NP Problem

2019
*
Zenodo
*

$P$ versus $NP$ is considered as

doi:10.5281/zenodo.3243510
fatcat:dhyilijvtrdxzoaiq4nft7xmtu
*one**of*the most important open problems in computer science. This consists in knowing the answer*of*the following question: Is $P$ equal to $NP$? ...*A*precise statement*of*the $P$ versus $NP$ problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find*a*proof for this problem have failed. ...*A**truth**assignment*for*a**Boolean**formula*φ is*a*set*of**values*for the variables in φ.*A**satisfying**truth**assignment*is*a**truth**assignment*that causes φ to be evaluated as true. ...##
###
The inverse satisfiability problem
[chapter]

1996
*
Lecture Notes in Computer Science
*

We study the complexity

doi:10.1007/3-540-61332-3_158
fatcat:4lgwlsov5bhyjfjk6ufvuopnzu
*of*telling whether*a*set*of*bit-vectors represents the set*of*all*satisfying**truth**assignments**of**a**Boolean*expression*of**a*certain type. ... We also prove*a*dichotomy theorem analogous to the classical*one*by Schaefer, stating that, unless P=NP, the problem can be solved in polynomial time if and only if the clauses allowed are all Horn, or ... Therefore, the*Boolean*vector m = m 1 · · · m n is an encoding*of**a**satisfying**assignment*to the variables for*formula*ψ: string m i is an encoding*of*the*truth**value**assigned*to the variable x i for each ...##
###
Solving SMT Problems with a Costly Decision Procedure by Finding Minimum Satisfying Assignments of Boolean Formulas
[chapter]

2014
*
Studies in Computational Intelligence
*

Unfortunately most

doi:10.1007/978-3-319-00948-3_15
fatcat:5d6pkkvds5g6bij22kc26vrsua
*of*the modern state-*of*-the-art SAT solvers always output*a*complete*assignment**of*variables for*satisfiable**formulas*even if they can be*satisfied*by*assigning**truth**values*to only*a*... An SMT-solving procedure can be implemented by using*a*SAT solver to find*a**satisfying**assignment**of*the propositional skeleton*of*the predicate*formula*and then deciding the feasibility*of*the*assignment*... This work was also partially supported by the Grant Agency*of*the Czech Republic project GACR P202/10/J042. ...##
###
The Problem of Judgment Aggregation in the Framework of Boolean-Valued Models
[chapter]

2014
*
Lecture Notes in Computer Science
*

*A*framework for

*boolean*-

*valued*judgment aggregation is described. The simple (im)possibility results in this paper highlight the role

*of*the set

*of*

*truth*

*values*and its algebraic structure. ... and the algebra

*of*

*truth*

*values*. ... Acknowledgements We wish to thank Achim Jung for helpful comments

*on*an earlier version

*of*this paper. ...

##
###
Correction to "An equivalence between relational database dependencies and a fragment of propositional logic"

1987
*
Journal of the ACM
*

*A*

*Boolean*dependency u is

*satisfied*by

*a*relation r if u (i.e., the corresponding

*Boolean*

*formula*)

*satisfies*every

*truth*

*assignment*

*of*cy(r). ... For each pair

*of*distinct tuples

*of*r, the set

*a*(r) contains the

*truth*

*assignment*that maps an attribute

*A*to true if the two tuples are equal

*on*

*A*, and to false if the two tuples have different

*values*... We thank Joel Berman and Wim Blok for pointing out the error in the original version

*of*Theorem 15 and for the observation that the original version is correct for positive

*Boolean*dependencies [ 11. ...

##
###
L versus parity-L

2020
*
Zenodo
*

*A*major complexity classes are L and ⊕L.

*A*logarithmic space Turing machine has

*a*read-only input tape,

*a*write-only output tape, and some read/write work tapes. ... Whether L = ⊕L is

*a*fundamental question that it is as important as it is unresolved. We prove there is

*a*complete problem for ⊕L that can be logarithmic space reduced to

*a*problem in L. ... We could affirm this, because

*of*the clause (x ⊕ j⊕ x ⊕ j) is always

*satisfied*for any

*truth*

*assignment*, where is the N OT

*Boolean*function. ...

##
###
Algebraic Polynomial Sum Solver Over $\{0, 1\}$

2021
*
Zenodo
*

Given

doi:10.5281/zenodo.4527665
fatcat:7jfzv375cbag5pt2aumskzygoq
*a*polynomial $P(x_{1}, x_{2}, \ldots, x_{n})$ which is the sum*of*terms, where each term is*a*product*of*two distinct variables, then the problem $APSS$ consists in calculating the total sum*value*...*of*$\sum_{\forall U_{i}} P(u_{1}, u_{2}, \ldots, u_{n})$, for all the possible*assignments*$U_{i} = \{u_{1}, u_{2}, ... u_{n}\}$ to the variables such that $u_{j} \in \{0, 1\}$. ...*A**Boolean**formula*with some*satisfying**truth**assignment*is*satisfiable*and without any*satisfying**truth**assignment*is unsatisfiable. ...##
###
On truth-table reducibility to SAT

1991
*
Information and Computation
*

In addition, we prove that

doi:10.1016/0890-5401(91)90075-d
fatcat:rgymrlwjirbwrhdhdiclwayrga
*a*constant number*of*rounds*of*parallel queries to SAT is equivalent to*one*round*of*parallel queries. ... We show that polynomial time*truth*-table reducibility via*Boolean*circuits to SAT is the same as logspace*truth*-table reducibility via*Boolean**formulas*to SAT and the same as logspace Turing reducibility ...*A**truth**assignment*α is*a*mapping from {x i : 0 < i} to {0, 1} where α(x i ) = 1 iff x i is*assigned**truth**value*"True". ...##
###
Fuzzy Maximum Satisfiability
[article]

2016
*
arXiv
*
pre-print

The MaxSAT problem for

arXiv:1602.02211v1
fatcat:una3l47hancfxm3kjl5ntemyia
*a*set*of**formulae*Φ is the problem*of*finding an*assignment*to the variables in Φ that*satisfies*the maximum number*of**formulae*. ... Like its*Boolean*counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness. ...*Boolean*Logic and SAT*A**Boolean*variable x can take*one**of*two possible*values*: 1 or 0.*A*literal l is*a*variable x or its negation ¬x.*A*disjunction C is*a*group*of*r literals joined by ∨. ...
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