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### ON SATISFIABILITY TREES

M. Mareti\'c
2016 International Journal of Applied Mathematics
Clausal satisfiability trees are defined as a class of satisfiability trees suited for formulas in clausal form. Issues related to size of clausal satisfiability trees are investigated.  ...  We define a satisfiability tree in the context of classical propositional logic.  ...  Tableau as a Satisfiability Tree Here we have the opportunity to describe the tableau method's rules for analysis of α and β formulas as operations on satisfiability trees.  ...

### On the Tractability of Un/Satisfiability [article]

Latif Salum
2020 arXiv   pre-print
Therefore, the formula is satisfiable iff the scope of every literal is satisfied.  ...  C k is satisfied by definition iff exactly one of r i , r j , or r u is true. Note that (r i ∨ r j ∨ r u ) in a 3SAT formula is satisfied iff at least one of them is true.  ...  XX:6 On the Tractability of Un/Satisfiability Definition 26. L ψ = {i ∈ L | r i ∈ ψ s } and L φ = {i ∈ L | r i ∈ C k in φ s } due to ϕ s = ψ s ∧ φ s .  ...

### On Supergraphs Satisfying CMSO Properties [article]

Mateus de Oliveira Oliveira
2021 arXiv   pre-print
The algorithmic metatheorem described above sheds new light on certain unresolved questions within the framework of graph completion algorithms.  ...  t satisfies ψ.  ...  Now one can check by induction on the height of positions that for each s ∈ [t] and each position p ∈ Pos( T), the five conditions C1-C5 of Definition 5.1 are satisfied.  ...

### Satisfiability on Mixed Instances

Ruiwen Chen, Rahul Santhanam
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16
We use the perspective of compositional mixing to show the first non-trivial algorithm for satisfiability of quantified Boolean formulas, where there is no depth restriction on the formula.  ...  desire to find a unifying framework for known satisfiability algorithms.  ...  Clearly, φ is satisfiable iff at least one of φ and φ are satisfiable.  ...

### Semidefinite Optimization Approaches for Satisfiability and Maximum-Satisfiability Problems

Miguel F. Anjos
2005 Journal on Satisfiability, Boolean Modeling and Computation
This paper surveys some of the results obtained in the application of semidefinite programming to satisfiability and maximum-satisfiability problems.  ...  detail include the ground-breaking approximation algorithm of Goemans and Williamson for MAX-2-SAT, the Gap relaxation of de Klerk, van Maaren and Warners, and strengthenings of the Gap relaxation based on  ...  The focus of this paper is on recent progress in the application of SDP to satisfiability (SAT) and maximum-satisfiability (MAX-SAT) problems.  ...

### On operators satisfying an inequality

Salah Mecheri
2012 Journal of Inequalities and Applications
Let d A,B ∈ B(B(H)) denote either the generalized derivation δ A,B = L A -R B or the elementary operator A,B = L A R B -I, where L A and R B are the left and right multiplication operators defined on B  ...  G, we have f (z) ≡  on G.  ...  T, T * satisfies generalized Weyl's theorem if and only if T satisfies generalized Weyl's theorem if and only if T satisfies Weyl's theorem if and only if T * satisfies Weyl's theorem.  ...

### On the random satisfiable process [article]

Michael Krivelevich, Benny Sudakov, Dan Vilenchik
2008 arXiv   pre-print
., x_n, and starting from the empty formula, go over the clauses one by one, including each new clause as you go along if after its addition the formula remains satisfiable.  ...  Specifically, we show that typically all satisfying assignments are essentially clustered in one cluster, and all but e^-Ω(m/n) n of the variables take the same value in all satisfying assignments.  ...  By Proposition 8, ψ 1 coincides with ϕ (the satisfying assignment w.r.t. which H is defined) on H.  ...

### On languages satisfying Ogden's lemma

L. Boasson, S. Horváth
1978 RAIRO Informatique théorique
REMARK 3 : The languages B P are built exactly on the same principle as the non-regular language of [1] satisfying the pumping lemma of regular sets. Moreover, B P does satisfy this lemma.  ...  -We show that varions types ofnon-context-free languages satisfying Ogden's lemma can very easily be constructed. A simple answer is then given to a question of [6] and [7] .  ...

### On manifolds satisfying w21=0

J.L. Dupont, G. Lusztig
1971 Topology
Let V and V* be dualjinite dimensional rector spaces ocerZ2 andj : V -+ VW a map satisfying j* = . J. T/!en there exist u E Y such that (c, j(x)) = (x, j(x)) for x E V, and rank j = (v, j(v)) mod. 2.  ...  It follows that one has also %* = ^ly, @ V as graded vector spaces.  ...

### On the Hardness of PCTL Satisfiability [article]

Souymodip Chakraborty, Joost-Pieter Katoen
2015 arXiv   pre-print
We present an exponential-time algorithm for the satisfiability of a bounded, negation-closed fragment of PCTL, and show that the satisfiability problem for this fragment is EXPTIME-hard.  ...  This paper shows that the satisfiability problem for probabilistic CTL (PCTL, for short) is undecidable.  ...  Every state σ of M f D satisfies f 0 . Hence, by construction of f 0 , there exists exactly one state s ∈ S (of the MDP D) such that M f D , σ ⊧ ψ s .  ...

### On the unique satisfiability problem

Andreas Blass, Yuri Gurevich
1982 Information and Control
UNIQUE SAT is the problem of deciding whether a given Boolean formula has exactly one satisfying truth assignment.  ...  Given a Boolean formula, is it true that it has exactly one satisfying truth assignment? We are interested in the complexity of U N I Q U E SAT relative to many-one polynomial time reductions.  ...  Since X satisfies (i)-(iii), M xu8 has no accepting computation on input 0 n, so we have a contradiction. Thus, M is defeated.  ...

### On an unsatisfiability-satisfiability prover

Chiharu Hosono
1989 Publications of the Research Institute for Mathematical Sciences
The satisfiability and the unsatisfiability are naturally defined. If a clause C contains both L and ~L, then C is said to be a tautology.  ...  One is shown in § 6 that is the class of formulas whose clausal form is satisfiable in some finite domain.  ...  a set of clause is satisfiable, then it is in fact satisfiable.  ...

### On the Random Satisfiable Process

MICHAEL KRIVELEVICH, BENNY SUDAKOV, DAN VILENCHIK
2009 Combinatorics, probability & computing
. , x n , and starting from the empty formula, go over the clauses one by one, including each new clause as you go along if, after its addition, the formula remains satisfiable.  ...  Specifically, we show that typically all satisfying assignments are essentially clustered in one cluster, and all but e −Ω(m/n) n of the variables take the same value in all satisfying assignments.  ...  A second implication of this is an upper bound on the number of possible satisfying assignments, and on the distance between every such two.  ...

### On languages satisfying "interchange Lemma"

Victor Mitrana
1993 RAIRO - Theoretical Informatics and Applications
ACKNOWLEDGEMENTS I wish to thanks for the suggestions on parts of the first version of the text given to us by the referee.  ...  A SHORT COMPARISON WITH OTHER ITERATION CONDITION ON FORMAL LANGUAGES We dénote OG-the family of languages satisfying Ogden's lemma, [7] BH-the family of languages satisfying Bar Hillel's lemma, SO -  ...  property P, then F is undecidable on if.  ...

### Bounds on the quantum satisfiability threshold [article]

Sergey Bravyi, Cristopher Moore, Alexander Russell
2014 arXiv   pre-print
Our use of differential equation to establish upper bounds on a satisfiability threshold appears to be novel, and our techniques may apply to various classical problems as well.  ...  For larger k, we show that the quantum threshold is a constant factor smaller than the classical one.  ...  In the next lemma we determine the rank of its satisfying space when adorned with separable clause vectors, which is an upper bound on its rank in the generic case.  ...
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