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ON SATISFIABILITY TREES

2016
*
International Journal of Applied Mathematics
*

Clausal

doi:10.12732/ijam.v29i5.5
fatcat:5oikf2gogzbntaelybob7t624u
*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. ...##
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On the Tractability of Un/Satisfiability
[article]

2020
*
arXiv
*
pre-print

Therefore, the formula is

arXiv:1408.5282v10
fatcat:x2tmlxbbezfthh6ai3mwqws2ja
*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 . ...##
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On Supergraphs Satisfying CMSO Properties
[article]

2021
*
arXiv
*
pre-print

The algorithmic metatheorem described above sheds new light

arXiv:2001.00758v5
fatcat:hbr46cmdnfdu7nky3653ohyuga
*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*. ...##
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Satisfiability on Mixed Instances

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

doi:10.1145/2840728.2840768
dblp:conf/innovations/ChenS16
fatcat:pkhlcnd75beernitffblimhuvm
*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*. ...##
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Semidefinite Optimization Approaches for Satisfiability and Maximum-Satisfiability Problems

2005
*
Journal on Satisfiability, Boolean Modeling and Computation
*

This paper surveys some of the results obtained in the application of semidefinite programming to

doi:10.3233/sat190001
fatcat:m2roi6zd6nb5hjiupljnb5teti
*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. ...##
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On operators satisfying an inequality

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

doi:10.1186/1029-242x-2012-244
fatcat:inkvbevssrbdbpy7mxjypvil4y
*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. ...##
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On the random satisfiable process
[article]

2008
*
arXiv
*
pre-print

., x_n, and starting from the empty formula, go over the clauses

arXiv:0807.4326v1
fatcat:wua6zgqm6fdydgki2kwd4aauz4
*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. ...##
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On languages satisfying Ogden's lemma

1978
*
RAIRO Informatique théorique
*

REMARK 3 : The languages B P are built exactly

doi:10.1051/ita/1978120302011
fatcat:6ebmwvgegfev5hg6oq5cqyuklm
*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] . ...##
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On manifolds satisfying w21=0

1971
*
Topology
*

Let V and V* be dualjinite dimensional rector spaces ocerZ2 andj : V -+ VW a map

doi:10.1016/0040-9383(71)90031-0
fatcat:m5lubr3bxrcfzbyfva56dre2h4
*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. ...##
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On the Hardness of PCTL Satisfiability
[article]

2015
*
arXiv
*
pre-print

We present an exponential-time algorithm for the

arXiv:1506.02483v3
fatcat:l47flsf5qzdbfh3v6twvtmmv4i
*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 . ...##
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On the unique satisfiability problem

1982
*
Information and Control
*

UNIQUE SAT is the problem of deciding whether a given Boolean formula has exactly

doi:10.1016/s0019-9958(82)90439-9
fatcat:b6i4m3iq25a4zn4hgb2jblqpnm
*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. ...##
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On an unsatisfiability-satisfiability prover

1989
*
Publications of the Research Institute for Mathematical Sciences
*

The

doi:10.2977/prims/1195173764
fatcat:dtxcudaz4jc6rh7esov4uhtadq
*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*. ...##
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On the Random Satisfiable Process

2009
*
Combinatorics, probability & computing
*

. , x n , and starting from the empty formula, go over the clauses

doi:10.1017/s0963548309990356
fatcat:trlt4wgoofat5bgtrmyoa3xtam
*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. ...##
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On languages satisfying "interchange Lemma"

1993
*
RAIRO - Theoretical Informatics and Applications
*

ACKNOWLEDGEMENTS I wish to thanks for the suggestions

doi:10.1051/ita/1993270100711
fatcat:itmu7hlp3zas7psmlctq7uudgi
*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. ...##
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Bounds on the quantum satisfiability threshold
[article]

2014
*
arXiv
*
pre-print

Our use of differential equation to establish upper bounds

arXiv:0907.1297v3
fatcat:h4gpypasrjcq5du5utsobe6uqi
*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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