Proving quantitative properties of programs, such as bounds on resource usage or information leakage, often leads to verification conditions that involve cardinalities of sets. Existing approaches for dealing with such verification conditions operate by checking cardinality bounds for given formulas. However, they cannot synthesize formulas that satisfy given cardinality constraints, which limi...

Safety verification of hybrid systems is a key technique in developing embedded systems that have a strong coupling with the physical environment. We propose an automated logical analytic method for verifying a class of hybrid automata. The problems are more general than those solved by the existing model checkers: our method can verify models with symbolic parameters and nonlinear equations as...

Automated synthesis of reactive systems from specifications has been a topic of research for decades. Recently, a variety of approaches have been proposed to extend synthesis of reactive systems from propositional specifications towards specifications over rich theories. We propose a novel, completely automated approach to program synthesis which reduces the problem to deciding the validity of ...

Separation logic-based abstraction mechanisms, enhanced with userdefined inductive predicates, represent a powerful, expressive means of specifying heap-based data structures with strong invariant properties. However, expressive power comes at a cost: the manipulation of such logics typically requires the unfolding of disjunctive predicates which may lead to expensive proof search. We address t...

This paper presents the estimation-inspection algorithm, a statistical algorithm for anomaly detection in process control networks. The algorithm determines if the payload of a network packet that is about to be processed by a control system is normal or abnormal based on the effect that the packet will have on a variable stored in control system memory. The estimation part of the algorithm use...

We obtain inductive and enumerative formulas for the multiplicities of weights spin module Clifford algebra a Levi subalgebra in complex semisimple Lie algebra. Our involve only matrices tableaux, our techniques combine linear algebra, theory, combinatorics. Moreover, this suggests relationship with nilpotent orbits. The case special $\mathfrak{sl}(n,{\mathbb C})$ is emphasized.

In this paper we investigate the Szegő-Radau and Szegő-Lobatto quadrature formulas on the unit circle. These are (n + m)-point formulas for which m nodes are fixed in advance, with m = 1 and m = 2 respectively, and which have a maximal domain of validity in the space of Laurent polynomials. That means that the free parameters (free nodes and positive weights) are chosen such that the quadrature...