Related papers: Algebraic Laws for True Concurrency
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
Integrable difference equations commonly have more low-order conservation laws than occur for nonintegrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in…
We develop Algebraic Phase Theory (APT), an axiomatic framework for extracting intrinsic algebraic structure from phase based analytic data. From minimal admissible phase input we prove a general phase extraction theorem that yields…
Process algebra has been successful in many ways; but we don't yet see the lineaments of a fundamental theory. Some fleeting glimpses are sought from Petri Nets, physics and geometry.
In various subjects, there exist compact and consistent relationships between input and output parameters. Discovering the relationships, or namely compact laws, in a data set is of great interest in many fields, such as physics, chemistry,…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution…
In this note, we introduce a class of algebras that are in some sense related to conformal algebras. This class (called TC-algebras) includes Weyl algebras and some of their (associative and Lie) subalgebras. By a conformal algebra we…
A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence…
The two major systems of formal verification are model checking and algebraic model-based testing. Model checking is based on some form of temporal logic such as linear temporal logic (LTL) or computation tree logic (CTL). One powerful and…
In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic…
In this paper we define the algebraic entropy test for face-centered quad equations, which are equations defined on vertices of a quadrilateral plus an additional interior vertex. This notion of algebraic entropy is applied to a recently…
An Independent Parallelism Theorem is proven in the theory of adhesive HLR categories. It shows the bijective correspondence between sequential independent and parallel independent direct derivations in the Weak Double-Pushout framework,…
In this paper, we revisit the problem of classifying real algebraic and semialgebraic sets by their topological types, focusing on establishing the effectiveness of bounds rather than deriving new quantitative estimates. Building on Hardt's…
Previous papers give accounts of quests for satisfactory formalizations of the classical informal notion of an algorithm and the contemporary informal notion of an interactive algoritm. In this paper, an attempt is made to generalize the…
Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…
Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.
In recent years, a large class of nuclear $C^\ast$-algebras have been classified, modulo an assumption on the Universal Coefficient Theorem (UCT). We think this assumption is redundant and propose a strategy for proving it. Indeed,…
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
We consider several ways of decomposing models into parts of bounded size forming a congruence over a base, and show that admitting any such decomposition is equivalent to mutual algebraicity at the level of theories. We also show that a…