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**publisher and metadata sources**).A Boolean formula in a conjunctive normal form is called a $(k,s)$ – formula if every clause contains exactly k variables and every variable occurs in at most s clauses. The $(k,s)$–${\text{SAT}}$… Continue Reading

Branching programs (b.p.'s) or decision diagrams are a general graph-based model of sequential computation. The b.p.'s of polynomial size are a nonuniform counterpart of LOG. Lower bounds for… Continue Reading

Abstract We present results from a case study comparing different multivariate classification methods. The input is a set of Monte Carlo data, generated and approximately triggered and pre-processed… Continue Reading

A polymeric composition having improved resistance to environmental flex cracking, solvent attack, abrasion and ozone attack comprises the blend of two different radial monoalkenyl arene-conjugated… Continue Reading

In this paper typical properties of large random Boolean AND/OR formulas are investigated. Such formulas with n variables are viewed as rooted binary trees chosen from the uniform distribution of all… Continue Reading

Abstract. It is known that if a Boolean function f in n variables has a DNF and a CNF of size
$ \le N $ then f also has a (deterministic) decision tree of size exp(O(log n log2N)). We show that this… Continue Reading

It is known that every DNF tautology with all monomials of length k contains a variable with at least Ω(2k/k) occurrences. It is not known, however, if this bound is tight, i.e. if there are… Continue Reading

Abstract We study the sequence of sets of Boolean formulas defined as follows: H 0 = {0, 1, x 1 , …, x n , ¬x 1 , …, ¬ x n }, H i+1 = {α(ϕ 1 , …, ϕ k ); ϕ j ∈ H i } , where α is a k-ary Boolean… Continue Reading

By (1, + k(n))-branching programs (b.p.'s) we mean those b.p.'s which during each of their computations are allowed to test at most k(n) input bits repeatedly. For a Boolean function computable… Continue Reading

It is known that if a Boolean function f in n variables has a DNF and a CNF of size ≤ N then f also has a (deterministic) decision tree of size exp(O(log n log2N)). We show that this simulation… Continue Reading