Two boolean functions f, g : {0, 1} → {0, 1} are isomorphic if they are identical up to relabeling of the input variables. We consider the problem of testing whether two functions are isomorphic or far from being isomorphic with as few queries as possible. In the setting where one of the functions is known in advance, we show that the non-adaptive query complexity of the isomorphism testing pro...

We extend our work on difference randomness. Each component of a difference test is a Boolean combination of two r.e. open sets; here we consider tests in which the k component is a Boolean combination of g(k) r.e. open sets for a given recursive function g. We use this method to produce an alternate characterization of weak Demuth randomness in terms of these tests and further show that a real...

Generally, when genetic programming (GP) is used for function synthesis any valuable experience gained by the system is lost from one problem to the next, even when the problems are closely related. With the aim of developing a system which retains beneficial experience from problem to problem, this paper introduces the novel Node-by-Node Growth Solver (NNGS) algorithm which features a componen...

‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

Quantum computing offers a promising emerging technology due to the potential theoretical capacity of solving many important problems with exponentially less complexity. Since most of the known quantum algorithms include Boolean components, the design of quantum computers is often conducted by a two-stage approach. In a first step, the Boolean component is realized in reversible logic and then ...

In several design methods for Pass-transistor Logic (PTL) circuits, Boolean functions are expressed as OBDDs in decomposed form and then the component OBDDs are directly mapped to PTL cells. The total size of OBDDs (number of nodes) corresponds to the circuit size. In this paper, we investigate a method for PTL synthesis based on exact minimization of Free BDDs (FBDDs). FBDDs are well-studied e...

This paper is concerned with the problem of Boolean approximation in the following sense: given a Boolean function class and an arbitrary Boolean function, what is the function’s best proxy in the class? Specifically, what is its strongest logical consequence (or envelope) in the class of affine Boolean functions. We prove various properties of affine Boolean functions and their representation ...