Related papers: O-Minimal Invariants for Discrete-Time Dynamical S…
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…
The automatic generation of loop invariants is a fundamental challenge in software verification. While this task is undecidable in general, it is decidable for certain restricted classes of programs. This work focuses on invariant…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
The article is dedicated towards the study of fractional order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions…
Interval temporal logics provide a general framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. In this paper, we identify all fragments…
We investigate questions related to the minimal degree of invariants of finitely generated diagonalizable groups. These questions were raised in connection to security of a public key cryptosystem based on invariants of diagonalizable…
We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
The higher-dimensional version of Kannan and Lipton's Orbit Problem asks whether it is decidable if a target subspace can be reached from a starting point under repeated application of a linear transformation. Similarly, the continuous…
The paper introduces a class of distances for linear behaviors over finite time horizons. These distances allow for comparisons between finite-horizon linear behaviors represented by matrices of possibly different dimensions. They remain…
It is established the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional laplacian, nonlinearities with critical exponential growth and potentials this is which may change sign. The…
We address the following decision problem. Given a numeration system $U$ and a $U$-recognizable set $X\subseteq\mathbb{N}$, i.e. the set of its greedy $U$-representations is recognized by a finite automaton, decide whether or not $X$ is…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Detecting non-termination is crucial for ensuring program correctness and security, such as preventing denial-of-service attacks. While termination analysis has been studied for many years, existing methods have limited scalability and are…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
We study some model-theoretic notions in NIP by means of spectral topology. In the o-minimal setting we relate the o-minimal spectrum with other topological spaces such as the real spectrum and the space of infinitesimal types of Peterzil…
We investigate a class of fourth-order differential systems with instantaneous and non-instantaneous impulses. Our technical approach is mainly based on a variant of Clark's theorem without the global assumptions. Under locally subquadratic…
We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique…