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A Note on Satisfying Truth-Value Assignments of Boolean Formulas

Zbigniew Stachniak
2004 International Conference on Theory and Applications of Satisfiability Testing  
We show that every 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.  ... 
dblp:conf/sat/Stachniak04 fatcat:ji3ysqbkcnhldk7e2uvv42zpha

Enforcing Confidentiality and Data Visibility Constraints: An OBDD Approach [chapter]

Valentina Ciriani, Sabrina De Capitani di Vimercati, Sara Foresti, Giovanni Livraga, Pierangela Samarati
2011 Lecture Notes in Computer Science  
We propose 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  ... 
doi:10.1007/978-3-642-22348-8_6 fatcat:xux3eoux2bepfbzpokdkvcumoy

Short Note on P vs NP [article]

Frank Vega
2022 Zenodo  
Under the assumption 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] .  ... 
doi:10.5281/zenodo.6042255 fatcat:qwj4muudbvcbrmv7mamzhgel4u

A Solution of the P versus NP Problem

Frank Vega
2019 Zenodo  
$P$ versus $NP$ is considered as 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.  ... 
doi:10.5281/zenodo.3242873 fatcat:fa7zsrnj35c65hao2aopnpgpzi

An OBDD approach to enforce confidentiality and visibility constraints in data publishing*

Valentina Ciriani, Sabrina De Capitani di Vimercati, Sara Foresti, Giovanni Livraga, Pierangela Samarati, Yingjiu Li
2012 Journal of Computer Security  
In this paper, we make 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.  ... 
doi:10.3233/jcs-2012-0449 fatcat:gug5f2yvrbb6xdfp3u5etcsg6m

A Solution of the P versus NP Problem

Frank Vega
2019 Zenodo  
$P$ versus $NP$ is considered as 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.  ... 
doi:10.5281/zenodo.3242872 fatcat:m7w5qsd255d3rjgjo7pzgfodem

A Solution of the P versus NP Problem

Frank Vega
2019 Zenodo  
$P$ versus $NP$ is considered as 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.  ... 
doi:10.5281/zenodo.3243510 fatcat:dhyilijvtrdxzoaiq4nft7xmtu

The inverse satisfiability problem [chapter]

Dimitris Kavvadias, Martha Sideri
1996 Lecture Notes in Computer Science  
We study the complexity 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  ... 
doi:10.1007/3-540-61332-3_158 fatcat:4lgwlsov5bhyjfjk6ufvuopnzu

Solving SMT Problems with a Costly Decision Procedure by Finding Minimum Satisfying Assignments of Boolean Formulas [chapter]

Martin Babka, Tomáš Balyo, Jaroslav Keznikl
2014 Studies in Computational Intelligence  
Unfortunately most 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.  ... 
doi:10.1007/978-3-319-00948-3_15 fatcat:5d6pkkvds5g6bij22kc26vrsua

The Problem of Judgment Aggregation in the Framework of Boolean-Valued Models [chapter]

Daniel Eckert, Frederik Herzberg
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.  ... 
doi:10.1007/978-3-319-09764-0_9 fatcat:agybn7tadbg5dlsptxfu6wlo24

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

Y. Sagiv, C. Delobel, D. S. Parker, Ronald Fagin
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.  ... 
doi:10.1145/31846.31853 fatcat:3flpgx6o2ja35cbgukuqurwf7e

L versus parity-L

Frank Vega
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.  ... 
doi:10.5281/zenodo.3805353 fatcat:6z3dtmkj4vcafjj3buotcsyxva

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

Frank Vega
2021 Zenodo  
Given 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.  ... 
doi:10.5281/zenodo.4527665 fatcat:7jfzv375cbag5pt2aumskzygoq

On truth-table reducibility to SAT

Samuel R. Buss, Louise Hay
1991 Information and Computation  
In addition, we prove that 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".  ... 
doi:10.1016/0890-5401(91)90075-d fatcat:rgymrlwjirbwrhdhdiclwayrga

Fuzzy Maximum Satisfiability [article]

Mohamed El Halaby, Areeg Abdalla
2016 arXiv   pre-print
The MaxSAT problem for 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 ∨.  ... 
arXiv:1602.02211v1 fatcat:una3l47hancfxm3kjl5ntemyia
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