Results 1  10
of
649
Lower bounds for splittings by linear combinations ∗
, 2014
"... A typical DPLL algorithm for the Boolean satisfiability problem splits the input problem into two by assigning the two possible values to a variable; then it simplifies the two resulting formulas. In this paper we consider an extension of the DPLL paradigm. Our algorithms can split by an arbitrary l ..."
Abstract
 Add to MetaCart
linear combination of variables modulo two. These algorithms quickly solve formulas that explicitly encode linear systems modulo two, which were used for proving exponential lower bounds for conventional DPLL algorithms. We prove exponential lower bounds on the running time of DPLL with splitting
Ranksparsity incoherence for matrix decomposition
, 2010
"... Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, and is intractable ..."
Abstract

Cited by 230 (21 self)
 Add to MetaCart
to solve in general. In this paper we consider a convex optimization formulation to splitting the specified matrix into its components, by minimizing a linear combination of the ℓ1 norm and the nuclear norm of the components. We develop a notion of ranksparsity incoherence, expressed as an uncertainty
Lemmas on Demand for Satisfiability Solvers
, 2002
"... We investigate the combination of propositional SAT checkers with constraint solvers for domainspecific theories such as linear arithmetic, arrays, lists and the combination thereof. Our procedure realizes a lazy approach to satisfiability checking of propositional constraint formulas by iterativel ..."
Abstract

Cited by 42 (5 self)
 Add to MetaCart
We investigate the combination of propositional SAT checkers with constraint solvers for domainspecific theories such as linear arithmetic, arrays, lists and the combination thereof. Our procedure realizes a lazy approach to satisfiability checking of propositional constraint formulas
The Complexity of Generalized Satisfiability for Linear Temporal Logic
"... In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NPcomplete or PSPACEcomplete, depending on the set of temporal operators used. If, in contrast, the set of propositional operators is restricted, the complexity may decrease. This ..."
Abstract

Cited by 20 (10 self)
 Add to MetaCart
In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NPcomplete or PSPACEcomplete, depending on the set of temporal operators used. If, in contrast, the set of propositional operators is restricted, the complexity may decrease
Sums of squares, satisfiability and maximum satisfiability
 In SAT 2005
, 2005
"... Recently the Mathematical Programming community showed a renewed interest in Hilbert’s Positivstellensatz. The reason for this is that global optimization of polynomials in IR[x1,..., xn] is N Phard, while the question whether a polynomial can be written as a sum of squares has tractable aspects. T ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
. This is due to the fact that Semidefinite Programming can be used to decide in polynomial time (up to a prescribed precision) whether a polynomial can be rewritten as a sum of squares of linear combinations of monomials coming from a specified set. We investigate this approach in the context of Satisfiability
UNSATISFIABLE LINEAR CNF FORMULAS ARE LARGE AND COMPLEX
, 2010
"... Abstract. We call a CNF formula linear if any two clauses have at most one variable in common. We show that there exist unsatisfiable linear kCNF formulas with at most 4k 2 4 k 4 k 8e 2 k 2 clauses is clauses, and on the other hand, any linear kCNF formula with at most satisfiable. The upper bound ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
has size at least 2 2 k 2 −1. This implies that small unsatisfiable linear kCNF formulas are hard instances for DavisPutnam style splitting algorithms. Second, if we require that the formula F have a strict resolution tree,..a a. i.e. every clause of F is used only once in the resolution tree
Two easy theories whose combination is hard
, 1977
"... We restrict attention to the validity problem for unquantified disjunctions of literals (possibly negated atomic formulae) over the domain of integers, or what is just as good, the satisfiability problem for unquantified conjunctions. When = is the only predicate symbol and all function symbols are ..."
Abstract

Cited by 41 (0 self)
 Add to MetaCart
We restrict attention to the validity problem for unquantified disjunctions of literals (possibly negated atomic formulae) over the domain of integers, or what is just as good, the satisfiability problem for unquantified conjunctions. When = is the only predicate symbol and all function symbols
Some 3CNF properties are hard to test
 In Proc. 35th ACM Symp. on Theory of Computing
, 2003
"... Abstract. For a Boolean formula ϕ on n variables, the associated property Pϕ is the collection of nbit strings that satisfy ϕ. We study the query complexity of tests that distinguish (with high probability) between strings in Pϕ and strings that are far from Pϕ in Hamming distance. We prove that th ..."
Abstract

Cited by 59 (10 self)
 Add to MetaCart
reading a constant fraction of the input, even when the input is very far from satisfying the formula that is associated with the property. A property is linear if its elements form a linear space. We provide sufficient conditions for linear properties to be hard to test, and in the course of the proof
Combining preorder and postorder resolution in a satisfiability solver
 Electronic Notes in Discrete Mathematics
, 2001
"... Recently, the classical backtrackingsearch satisability algorithm of Davis, Putnam, Loveland and Logemann (DPLL) has been enhanced in two distinct directions: with more advanced reasoning methods, or with con
ictdirected backjumping (CBJ). Previous methods used one idea or the other, but not bot ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
, but not both (except that CBJ has been combined with the unitclause rule). The diÆculty is that more advanced reasoning derives new clauses, but does not identify which backtrackable assumptions were relevant for the derivation. However CBJ needs this information. The lineartime decision procedure for binary
Efficient interpolant generation in satisfiability modulo theories,” in
 Proc. TACAS, ser. LNCS 4963.
, 2008
"... Abstract. The problem of computing Craig interpolants in SAT and SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of interest including that of equality and uninter ..."
Abstract

Cited by 42 (7 self)
 Add to MetaCart
and uninterpreted functions (EUF ), linear arithmetic over the rationals (LA(Q)), and their combinationand they are successfully used within model checking tools. For the theory of linear arithmetic over the integers (LA(Z)), however, the problem of finding an interpolant is more challenging, and the task
Results 1  10
of
649