We present a randomized DNA algorithm for k SAT based on the classical algorithm of Paturi et al For an n variable m clause instance of k SAT m n our algorithm nds a satisfying assignment assuming one exists with probability e in worst case time O k mn and space O k n log This makes it the most space e cient DNA k SAT algo rithm for k and k n log i e the clause size is small compared to the num...

this article is concerned with the question of how much the assured will be entitled to recover following an assured loss. it will be discussed which three elements are involved in this respect; first the loss of assured, second the amount of assuror obligation and third the contractual agreements of the parties in respect of the amount of assuror's payment.it should be noted that franchis...

In this paper, we present a new way to preprocess Boolean formulae in Conjunctive Normal Form (CNF). In contrast to most of the current pre-processing techniques, our approach aims at improving the filtering power of the original clauses while producing a small number of additional and relevant clauses. More precisely, an incomplete redundancy check is performed on each original clauses through...

We present a randomized DNA algorithm for k-SAT based on the classical algorithm of Paturi et al. [8]. For an n-variable, m-clause instance of k-SAT (m > n), our algorithm finds a satisfying assignment, assuming one exists, with probability 1−e−α, in worst-case time O(kmn) and space O(2(1− 1 k ). This makes it the most space-efficient DNA k-SAT algorithm for k > 3 and k < n/ logα (i.e. the clau...

literal: Let p be a proposition. Then p and -p are literals. clause: A clause is a disjunction of literals. Horn Clause: A Horn Clause is a clause in which there is at most one positive literal. definite clause: A definite clause is a Hom Clause in which there is exactly one positive literal. A definite clause such as can also be written as We call pi the head of the clause, and the conjunction...

This paper presents an analysis of sentences with the postverbal modal element DAK in Cantonese and Hakka. We argue that DAK is a verb, though in Cantonese and Hakka it is partly defective. It acquires different meanings depending on the position it occupies, which is either the position for modal verbs in the matrix clause or a modal position in the result denoting small clause. The analysis, ...

We analyze the efficiency of the random walk algorithm on random -CNF instances, and prove the first polynomial time upper bound for small clause density, less than . We complement this by proving exponential lower bounds for the running time of this algorithm on the planted-SAT distribution with large constant clause density. This is the first polynomial upper bound on the running time of a lo...

The structure of the monoid of autarkies for clause-sets is investigated (autarkies are generalizations of satisfying (truth) assignments). The notion of a \plain clause-set" is introduced, where every clause is usable by some resolution refutation, and it is shown that a clause-set is plain ii it has no non-trivial autarky. Every clause-set has a unique decomposition into a plain sub-clause-se...