Related papers: Reduction Operators and Completion of Rewriting Sy…
In this letter we develope an operator formalism for the $b-c$ systems with conformal weight $\lambda=1$ defined on a general closed and orientable Riemann surface. The advantage of our approach is that the Riemann surface is represented as…
We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection…
Lattices defined as modules over algebraic rings or orders have garnered interest recently, particularly in the fields of cryptography and coding theory. Whilst there exist many attempts to generalise the conditions for LLL reduction to…
We show how confluence criteria based on decreasing diagrams are generalized to ones composable with other criteria. For demonstration of the method, the confluence criteria of orthogonality, rule labeling, and critical pair systems for…
For the lambda-calculus with letrec we develop an optimisation, which is based on the contraction of a certain class of 'future' (also: virtual) redexes. In the implementation of functional programming languages it is common practice to…
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…
The present paper deals with complemented lattices where, however, a unary operation of complementation is not explicitly assumed. This means that an element can have several complements. The mapping $^+$ assigning to each element $a$ the…
Logically Constrained Term Rewriting Systems (LCTRSs) provide a general framework for term rewriting with constraints. We discuss a simple dependency pair approach to prove termination of LCTRSs. We see that existing techniques transfer to…
We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
The relationship between Term Graph Rewriting and Term Rewriting is well understood: a single term graph reduction may correspond to several term reductions, due to sharing. It is also known that if term graphs are allowed to contain…
We reduce the set of classic relational algebra operators to two binary operations: natural join and generalized union. We further demonstrate that this set of operators is relationally complete and honors lattice axioms.
For a complete lattice $L$ and a relational structure $\mathfrak{X}=(X,(R_i)_I)$, we introduce the convolution algebra $L^{\mathfrak{X}}$. This algebra consists of the lattice $L^X$ equipped with an additional $n_i$-ary operation $f_i$ for…
We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…
A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_\alpha$, the net $Tx_\alpha$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
This article is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…