Consider the problem of deciding whether a Boolean formula f is self-dual, i.e. f is logically equivalent to its dual formula f d , deened by f d (x) = f(x). This problem is a well-studied problem in several areas like theory of coteries, database theory, hypergraph theory or computational learning theory. In this paper we exhibit polynomial time algorithms for testing self-duality for several ...

We study the query complexity of testing for properties defined by read once formulas, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in , doubly exponential in the arity, and...

We show a connection between the deMorgan formula size of a Boolean function and the noise stability of the function. Using this connection, we show that the Fourier spectrum of any balanced Boolean function computed by a deMorgan formula of size s is concentrated on coefficients of degree up to O( √ s). These results have several applications that apply to any function f that can be computed b...

We study the query complexity of testing for properties defined by read once formulas, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in ǫ, doubly exponential in the arity, an...

Relating the PSPACE reasoning power of Boolean Programs and Quantified Boolean Formulas Alan Skelley Master of Science Graduate Department of Computer Science University of Toronto 2000 We present a new propositional proof system based on a recent new characterization of polynomial space (PSPACE) called Boolean Programs, due to Cook and Soltys. We show that this new system, BPLK, is polynomiall...

Low degree annihilators for Boolean functions are of great interest in cryptology because of algebraic attacks on LFSR-based stream ciphers. Several polynomial algorithms for construction of low degree annihilators are introduced in this paper. The existence of such algorithms is studied for the following forms of the function representation: algebraic normal form (ANF), disjunctive normal form...

This paper describes a constraint-based invariant generation technique for proving the validity of safety assertions over the domain of predicate abstraction in an interprocedural setting. The key idea of the technique is to represent each invariant in bounded DNF form by means of boolean indicator variables, one for each predicate p and each disjunct d denoting whether p is present in d or not...

Let A be any universal algebra. We say formula A is explicitly expressible on algebra A via system of formulas Σ, if A can be obtained on A of variables and formulas of Σ by means of superpositions. We say a system of formulas Σ is complete in A, if any formula is expressible via Σ. We say a system Σ is precomplete as to expressibility on A if Σ is not complete on A, but for any formula F , whi...

In this paper we explain the design and preliminary implementation of a solver for the positive satisfiability problem of concepts in a fuzzy description logic over the infinite-valued product logic. The same solver also works for 1-satisfiability in quasi-witnessed models. The solver works by first performing a direct reduction of the problem to a satisfiability problem of a quantifier free bo...

We obtain a sharp estimate of the speed convergence in Boolean central limit theorem for measures with finite sixth moment. The main tool is quantitative version Stieltjes-Perron inversion formula.