Abductive reasoning involves determining a parsimonious set of explanations that can account for a set of observations. In the Boolean minimization problem, the designer attempts to express a Boolean formula as a sum of products or product of sums expression of the smallest size that satisfies the desired function. In this paper, we show that independent abduction problem can be encoded as an i...

We present a semantics for Probabilistic Description Logics that is based on the distribution semantics for Probabilistic Logic Programming. The semantics, called DISPONTE, allows to express assertional probabilistic statements. We also present two systems for computing the probability of queries to probabilistic knowledge bases: BUNDLE and TRILL. BUNDLE is based on the Pellet reasoner while TR...

In [4] Wolfram asserts to have found minimal Boolean formulas for (what he denotes) rules of one-dimensional, two-state, nearest neighbor cellular automata (CA) or simply elementary rules. These formulas are minimal in the sense that they “use the minimum possible number of operators” over basis Ω1 = {0,1,¬,∧,∨,⊕}. Provided that elementary rules can be interpreted as 3-input Boolean functions a...

The conceptions of χ-value and K-rotation symmetric Boolean functions are introduced by Cusick. K-rotation symmetric Boolean functions are a special rotation symmetric functions, which are invariant under the k − th power of ρ. In this paper, we discuss cubic 2-value 2-rotation symmetric Boolean function with 2n variables, which denoted by F2n(x2n). We give the recursive formula of weight of F2...

We show lower bounds of Ω( √ n) and Ω(n) on the randomized and quantum communication complexity, respectively, of all nvariable read-once Boolean formulas. Our results complement the recent lower bound ofΩ(n/8) by Leonardos and Saks [LS09] andΩ(n/2 log ) by Jayram, Kopparty and Raghavendra [JKR09] for randomized communication complexity of read-once Boolean formulas with depth d. We obtain our ...

This paper describes a new Boolean satisfiability based formulation to generate robust tests for path delay faults in combinational circuits. Conditions to detect a target path delay fault are represented by a Boolean formula. Unlike the technique described in [30], which extracts the formula for each path delay fault, the proposed formulation needs to extract the formula only once for each cir...

Boolean concepts are concepts whose membership is determined by a Boolean function, such as that expressed by a formula of propositional logic. Certain Boolean concepts have been much studied in the psychological literature, in particular with regard to their ease of learning. But research attention has been somewhat uneven, with a great deal of attention paid to certain concepts and little to ...

Circuit size, branching program size, and formula size of Boolean functions, denoted by C(f), BP(f), and L(f), are the most important complexity measures for Boolean functions. Often also the formula size L (f) over the restricted basis f_;^;:g is considered. It is well-known that C(f) 3BP(f), BP(f) L (f), L (f) L(f)2, and C(f) L(f) 1. These estimates are optimal. But the inequality BP(f) L(f)2...

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In partic...