We consider Dependency Quantified Boolean Formulas (DQBFs), a generalization of Quantified Boolean Formulas (QBFs), and demonstrate that DQBFs are a natural calculus to exactly express the realizability problem of incomplete combinational and sequential circuits with an arbitrary number of (combinational or bounded-memory) black boxes. In contrast to usual approaches for controller synthesis, r...

Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper and monic (or regular) triangular set is given. An improved zero decomposition algorithm which can be used to reduce the zero set of an equation system in ge...

Restricted Boolean networks are simplified Boolean networks that are required for either negative or positive regulations between genes. Higa et al. (BMC Proc 5:S5, 2011) proposed a three-rule algorithm to infer a restricted Boolean network from time-series data. However, the algorithm suffers from a major drawback, namely, it is very sensitive to noise. In this paper, we systematically analyze...

Algebraic attacks have received a lot of attention in studying security of symmetric ciphers. The function used in a symmetric cipher should have high algebraic immunity (AI) to resist algebraic attacks. In this paper we are interested in finding AI of Boolean power functions. We give an upper bound on the AI of any Boolean power function and a formula to find its corresponding low degree multi...

We investigate the relationship between the complexities of two models of randomized decision trees for read-once Boolean functions; namely, with the directional restriction and without it. A decision tree is directional if it reads a variable in a sub-formula, then it has to evaluate the sub-formula completely before reading another variable that appears in a different sub-formula. It was know...

This paper proposes a new set of propagation rules for quantified Boolean formulae based on literals and generated automatically thanks to quantified Boolean formulae certificates. Different decompositions by introduction of existentially quantified variables are discussed in order to construct complete systems. This set of rules is compared with already proposed quantified Boolean propagation ...

In this paper we study the problem of yielding robust performances from current state-of-the-art solvers for quantified Boolean formulas (QBFs). Building on top of existing QBF solvers, we implement a newmulti-engine solver which can inductively learn its solver selection strategy. Experimental results confirm that our solver is always more robust than each single engine, that it is stable with...

We propose in this article a unified framework for certificate and compilation for QBF. We provide a search-based algorithm to compute a certificate for the validity of a QBF and a search-based algorithm to compile a valid QBF in our unified framework.

This paper reports about the 2005 comparative evaluation of solvers for quantified Boolean formulas (QBFs), the third in a series of non-competitive events established with the aim of assessing the advancements in the field of QBF reasoning and related research. We evaluated thirteen solvers on a test set of more than three thousands QBFs, selected from instances submitted to the evaluation and...

A new tree-based representation for propositional formulas is introduced. This representation, the ∆-trees, allows a compact representation for well-formed formulas as well as a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of