The Adams spectral sequence was invented by J.F.Adams [1] almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive ...

In this paper we give a compositional (or inductive) construction of monitoring automata for LTL formulas. Our construction is similar in spirit to the compositional construction of Kesten and Pnueli [5]. We introduce the notion of hierarchical Büchi automata and phrase our constructions in the framework of these automata. We give detailed constructions for all the principal LTL operators inclu...

In many applications, it is impractical—if not even impossible—to obtain data to fit a known cubature formula (CF). Instead, experimental often acquired at equidistant or scattered locations. this work, stable (in the sense of nonnegative only weights) high-order CFs are developed for purpose. These based on approach allow number points N be larger than basis functions K which integrated exactl...

The Adams spectral sequence was invented by J.F.Adams [1] almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive ...

The Adams spectral sequence was invented by J.F.Adams [1] almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive ...

The logical system AF2μ, an extension of second-order predicate calculus with monotone inductive definitions, is presented. Some properties of this system are shown including that it is a good system for extracting programs from proofs by means of a realizability interpretation in the style of Krivine-Parigot, where the realizers are terms of the Curry-system of λ-calculus and the realizability...

We present a simple, yet flexible parameter synthesis approach for Cyber-Physical Systems (CPS). The user defines the behavior of a CPS, a set of (un)safe states, and a generic template for an invariant using Satisfiability Modulo Theories (SMT) formulas. Counterexample-Guided Inductive Synthesis (CEGIS) is then used to compute values for open parameters and a concrete invariant to prove that a...