Related papers: Strictifying and taming directed paths in Higher D…

Higher Dimensional Automata (HDA) are higher dimensional relatives to transition systems in concurrency theory taking into account to which degree various actions commute. Mathematically, they take the form of labelled cubical complexes. It…

In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy…

It has been observed that the very important motion planning problem of robotics mathematically speaking boils down to the problem of finding a section to the path-space fibration, raising the notion of topological complexity, as introduced…

In order to gain a better understanding of the state space of programs, with the aim of making their verification more tractable, models based on directed topological spaces have been introduced, allowing to take in account equivalence…

State-space reduction techniques, used primarily in model-checkers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not…

This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…

A path-following control algorithm enables a system's trajectories under its guidance to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence…

Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…

Timed automata are a common formalism for the verification of concurrent systems subject to timing constraints. They extend finite-state automata with clocks, that constrain the system behavior in locations, and to take transitions. While…

Offline optimal planning of trajectories for redundant robots along prescribed task space paths is usually broken down into two consecutive processes: first, the task space path is inverted to obtain a joint space path, then, the latter is…

Directed topology is a refinement of standard topology, where spaces may have non-reversible paths. It has been put forward as a candidate approach to the analysis of concurrent processes. Recently, a wealth of different frameworks for,…

We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…

Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic…

A popular method for solving reachability in timed automata proceeds by enumerating reachable sets of valuations represented as zones. A na\"ive enumeration of zones does not terminate. Various termination mechanisms have been studied over…

Navigating mobile robots through environments shared with humans is challenging. From the perspective of the robot, humans are dynamic obstacles that must be avoided. These obstacles make the collision-free space nonconvex, which leads to…

Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…

When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…

The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the…

This paper focuses on the analysis of real-time non preemptive multiprocessor scheduling with precedence and several latency constraints. It aims to specify a schedulability condition which enables a designer to check a priori -without…

Topological spaces - such as classifying spaces, configuration spaces and spacetimes - often admit extra temporal structure. Qualitative invariants on such directed spaces often are more informative yet more difficult to calculate than…