We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N logN) algorithm for block sensitivity, an O(N logN) algorithm for ‘tree decomposition,’ and an O(N) algorithm for ‘quasisymmetry.’ These algorithms are based on new insights into the structure of Boolean functions that may be of independent interest. We also ...

Classical (or Boolean) type theory is the type theory that allows the type inference (σ → –)→ –⇒ σ (the type counterpart of double-negation elimination), where σ is any type and – is absurdity type. This paper first presents a denotational semantics for a simplified version of Parigot’s lambda-mu calculus, a premier example of classical type theory. In this semantics the domain of each type is ...

The fact that one can associate a finite monoid with universal properties to each language recognised by an automaton is central to the solution of many practical and theoretical problems in automata theory. It is particularly useful, via the advanced theory initiated by Eilenberg and Reiterman, in separating various complexity classes and, in some cases it leads to decidability of such classes...

Researchers have long been interested in nding simple axiomatizations of theories, including Boolean algebra. Boolean algebra can be axiomatized in many diierent ways using various sets of operations. The ordinary operations of Boolean algebra are disjunction (+), conjunction (), negation (0), zero (0), and one (1). One of the rst simple axiomatizations was presented by E. V. (Associativity) ((...

A voting rule in a Boolean algebra B is an upward closed subset that contains, for each element x ∈ B, exactly one of x and ¬x. We study several aspects of voting rules, with special attention to their relationship with ultrafilters. In particular, we study the set-theoretic hypothesis that all voting rules in the Boolean algebra of subsets of the natural numbers modulo finite sets are nearly u...

In this paper at the beginning, we make a short history of the logics, from the classical Boolean logic to the most general logic of today neutrosophic logic. We define the general logic space and give the definition of the neutrosophic logic. Then we introduce the indeterminate models in information fusion, which are due either to the existence of some indeterminate elements in the fusion spac...

A computably enumerable Boolean algebra B is effectively dense if for each x ∈ B we can effectively determine an F (x) ≤ x such that x 6= 0 implies 0 < F (x) < x. We give an interpretation of true arithmetic in the theory of the lattice of computably enumerable ideals of such a Boolean algebra. As an application, we also obtain an interpretation of true arithmetic in all theories of intervals o...

In sections 1 through 5, I develop in detail what I call the standard theory of worlds and propositions, and I discuss a number of purported objections. The theory consists of five theses. The first two theses, presented in section I, assert that the propositions form a Boolean algebra with respect to implication, and that the algebra is complete, respectively. In section 2, I introduce the not...

We investigate the combination of propositional SAT checkers with satisfiability procedures for domain-specific theories such as linear arithmetic, arrays, lists and the combination thereof. Our procedure realizes a lazy approach to satisfiability checking of Boolean constraint formulas by iteratively refining Boolean formulas based on lemmas generated on demand by the decision procedures.