Synthesizing Conjunctive & Disjunctive Linear Invariants by K-means++ and SVM

The problem of synthesizing adequate inductive invariants lies at the heart of automated software verification. The state-of-the-art machine learning algorithms for synthesizing invariants have gradually shown its excellent performance. However, synthesizing disjunctive invariants is a difficult task. In this paper, we propose a method k++ Support Vector Machine (SVM) integrating k-means++ and SVM to synthesize conjunctive and disjunctive invariants. At first, given a program, we start with executing the program to collect program states. Next, k++SVM adopts k-means++ to cluster the positive samples and then applies SVM to distinguish each positive sample cluster from all negative samples to synthesize the candidate invariants. Finally, a set of theories founded on Hoare logic are adopted to check whether the candidate invariants are true invariants. If the candidate invariants fail the check, we should sample more states and repeat our algorithm. The experimental results show that k++SVM is compatible with the algorithms for Intersection Of Half-space (IOH) and more efficient than the tool of Interproc. Furthermore, it is shown that our method can synthesize conjunctive and disjunctive invariants automatically

Genomes of Animal Mitochondria have not Evolved According to Common Models of Substitution Probabilities

Common probabilistic models of substitutions of bases (Jukes-Cantor, Kimura 2-parameter, Tamura-Nei, F84, HKY, and the 6-parameter models used in linear invariants methods) must be rejected, at least for mitochondrial genomes of animals. They are rejected by a new test that is simple and lenient.

A Survey of Elementary Object Systems

This contribution presents the formalism of ElementaryObjectSystems (Eos). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. One central aim of this contribution is to compile all our previous works ded- icated to certain aspects of Eos together with recent yet unpublished results within one self-contained presentation. Since object nets in general are immediately Turing complete, we introduce the restricted class of elementary object nets which restrict the nesting of nets to the depth of two. In this work we study the relationship of Eos to existing Petri net formalisms. It turns out that Eos are more powerful than classical p/t nets which is demonstrated by the fact that e.g. reachability and liveness become undecidable problems for Eos. Despite these undecidability results other properties can be extended to Eos using a monotonicity argument similar to that for p/t nets. Also linear algebraic techniques, especially the theory of linear invariants and semiflows, can be extended in an appropriate way. The invariant calculus for Eos even enjoys the property of compositionality, i.e. invariants of the whole system can be composed of invariants of the object nets, which reduces the computational effort. To obtain a finer level of insight we also studied several classes like pure, minimal, or semi-bounded Eos. Among these variants the subclass of generalised state machines is worth mentioning since it combines the decidability of many theoretically interesting properties with a quite rich practical modelling expressiveness.

Linear invariants and the quantum dynamics of a nonstationary mesoscopic RLC circuit with a source

In this paper, we use Hermitian linear invariants and the Lewis and Riesenfeld invariant method to obtain the general solution of the Schrödinger equation for a mesoscopic RLC circuit with time-dependent resistance, inductance, capacitance and a power source and represent it in terms of an arbitrary weight function. In addition, we construct Gaussian wave packet solutions for this electromagnetic oscillation circuit and employ them to calculate the quantum fluctuations of the charge and the magnetic flux as well as the associated uncertainty product. We also show that the width of the Gaussian packet and the fluctuations do not depend on the external power.