In this paper, we continue the study of a left-distributive algebra of elementary embeddings from the collection of sets of rank less than λ to itself, as well as related finite left-distributive algebras (which can be defined without reference to large cardinals). In particular, we look at the critical points (least ordinals moved) of the elementary embeddings; simple statements about these or...

A computationally efficient method is proposed for computing the simplest normal forms of vector fields. A simple, explicit recursive formula is obtained for general differential equations. The most important feature of the approach is to obtain the “simplest” formula which reduces the computation demand to minimum. At each order of the normal form computation, the formula generates a set of al...

This work addresses the problem of verifying imperative programs that manipulate data structures, e.g., Rust programs. Data structures are usually modeled by Algebraic Types (ADTs) in verification conditions. Inductive invariants such often require recursively defined functions (RDFs) to represent abstractions structures. From logic perspective, this reduces solving Constrained Horn Clauses (CH...

A Space Free-Flying Robot (SFFR) includes an actuated base equipped with one or more manipulators to perform on-orbit missions. Distinct from fixed-based manipulators, the spacecraft (base) of a SFFR responds to dynamic reaction forces due to manipulator motions. In order to control such a system, it is essential to consider the dynamic coupling between the manipulators and the base. Explicit d...

An efficient method is presented for computing the normal form of general n-dimensional systems associated with 1:1 resonant double Hopf bifurcation. The approach combines the computations of center manifold and normal form in one unified procedure. The Jacobian of the system evaluated at an equilibrium contains non-semisimple eigenvalues. Explicit formulas are obtained for directly computing t...

This paper explores the algebraic matching approach for detection of vulnerabilities in binary codes. The algebraic programming system is used for implementing this method. It is anticipated that models of vulnerabilities and programs to be verified are presented as behavior algebra and action language specifications. The methods of algebraic matching are based on rewriting rules and techniques...

Engineering analysis often involves the accurate numerical solution of boundary value problems in discrete form. Hierarchical quadtree (or octree) grid generation offers an efficient method for the spatial discretisation of arbitrary-shaped two- (or three-) dimensional domains. It consists of recursive algebraic splitting of sub-domains into quadrants (or cubes), leading to an ordered hierarchi...

In this paper we argue that a large class of recursive contracts can be studied by means the conventional Negishi method. A planner is responsible for prescribing current actions along with distribution future utility values to all agents, so as maximize their weighted sum utilities. Under convexity method yields exact efficient frontier. Otherwise implementation re- quires contingent on public...