Related papers: Deciding Equations in the Time Warp Algebra
One of the key concepts in testing is that of adequate test sets. A test selection criterion decides which test sets are adequate. In this paper, a language schema for specifying a large class of test selection criteria is developed; the…
The $3x+1$ problem concerns the iteration of the map $T:\mathbb{Z}\to\mathbb{Z}$ defined by $T(x)=x/2$ for even $x$ and $T(x)=(3x+1)/2$ for odd $x$. We study the \emph{coefficient stopping time} dynamics of $T$ (in the sense of Terras) by…
A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but with predicate abstraction mechanism and equality is considered. The models of LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible constants)…
We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
We introduce a new setting, the category of $\omega$PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is general enough to assign meanings to most practical…
On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied…
Recent work has shown that not only decision trees (DTs) may not be interpretable but also proposed a polynomial-time algorithm for computing one PI-explanation of a DT. This paper shows that for a wide range of classifiers, globally…
A conformable time-scale fractional calculus of order $\alpha \in ]0,1]$ is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger time-scale calculus is obtained as a particular…
The Lie claw digraph controls Background Independence and thus the Problem of Time and indeed the Fundamental Nature of Physical Law. This has been established in the realms of Flat and Differential Geometry with varying amounts of extra…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
We demonstrate the first Recurrent Neural Network architecture for learning Signal Temporal Logic formulas, and present the first systematic comparison of formula inference methods. Legacy systems embed much expert knowledge which is not…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
This paper introduces a new method for the efficient computation of oscillatory multidimensional lattice sums in geometries with boundaries. Such sums are ubiquitous in both pure and applied mathematics, and have immediate applications in…
This paper extends prior work on the connections between logics from finite model theory and propositional/algebraic proof systems. We show that if all non-isomorphic graphs in a given graph class can be distinguished in the logic…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
We investigate the problem of computing tensor product multiplicities for complex semisimple Lie algebras. Even though computing these numbers is #P-hard in general, we show that if the rank of the Lie algebra is assumed fixed, then there…
We develop a computational approach to Metric Answer Set Programming (ASP) to allow for expressing quantitative temporal constrains, like durations and deadlines. A central challenge is to maintain scalability when dealing with fine-grained…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.