My field of research is Theoretical Computer Science. My focus has been in the classical and quantum complexity of Boolean functions (including property testing, sensitivity and block sensitivity of Boolean functions and quantum database search), in electronic commerce, in graph algorithms and in coding theory. I have designed effective algorithms as well as proved lower bounds for the complexi...

We characterize the forbidden projections of unate Boolean functions. Forbidden projections are analogous to forbidden graph minors. Unate functions have been studied in switching theory and in computational learning theory.

This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.

The Appell-type polynomial family corresponding to the simplest non-commutative derivative operator turns out to be connected with the Boolean probability theory, the simplest of the three universal non-commutative probability theories (the other two being free and tensor/classical probability). The basic properties of the Boolean Appell polynomials are described. In particular, their generatin...

The research of Boolean index sets of graphs is one of the most important graph theories in the graph theory . Boolean index sets of graphs are to use the vertex sets and the edge sets of graphs to study the characteristics of various graphs and their inherent characteristics through corresponding the mapping function to 2 Z . It’s theory can be applied to information engineering, communication...

We show how the abstract theory of (complete, boolean) lattices can be for-malised as a theory in the HOL theorem prover. The abstract lattice theory can be instantiated for concrete cases, providing immediate instantiations of many useful results. In particular, we treat the abstract theory of function lattices as an instantiation of the abstract lattice theory.

The aim of this note is to demonstrate that Kaplansky–Hilbert lattices and injective Banach lattices may be produced from each other by means of the well known convexification procedure. This is done via the Boolean valued analysis approach. The subject gives a good opportunity to discuss also the relationship between the Kantorovich’s heuristic principle and the Boolean value transfer principl...

Abstract We study satisfiability modulo the theory of finite fields and give a decision procedure for this theory. implement our prime inside cvc5 SMT solver. Using theory, we construct queries that encode translation validation various zero knowledge proof compilers applied to Boolean computations. evaluate on these benchmarks. Our experiments show implementation is superior previous approache...

In hard real-time systems, where system complexity meets stringent timing constraints, the task of system-level synthesis has become more and more challenging. As a remedy, we introduce an SMT-based system synthesis approach where the Boolean solver determines a static binding of computational tasks to computing resources and a routing of messages over the interconnection network while the theo...