The idea of a finite collection of closed sets having " strongly regular intersection " at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically, we consider the case of two sets, one of which we assume to be suitably " regular " (special cases being convex sets, smooth manifolds, or feasible regions...

A map is a cell decomposition of a closed surface; it is regular if its automorphism group acts transitively on the flags, mutually incident vertex-edge-face triples. The main purpose of this paper is to establish, by elementary methods, the following result: for each positive integer w and for each pair of integers p ≥ 3 and q ≥ 3 satisfying 1/p + 1/q ≤ 1/2, there is an orientable regular map ...

The notion of delays arises naturally in many computational models, such as, in the design of circuits, control systems, and dataflow languages. In this work, we introduce automata with delay blocks (ADBs), extending finite state automata with variable time delay blocks, for deferring individual transition output symbols, in a discrete-time setting. We show that the ADB languages strictly subsu...

The motivation for this paper is the following: In [Fuc08] I showed that it is inconsistent with ZFC that the maximality principle for closed forcings holds at unboundedly many regular cardinals κ (even only allowing κ itself as a parameter in the maximality principle for <κ-closed forcings each time). So the question is whether it is consistent to have this principle at unboundedly many regula...

In order to study precisely the growth of timed languages, we associate to such a language a generating function. These functions (tightly related to volume and entropy of timed languages) satisfy compositionality properties and, for deterministic timed regular languages, can be characterized by integral equations. We provide procedures for closed-form computation of generating functions for so...

Using a calibration method we prove that, if Γ ⊂ Ω is a closed regular hypersurface and if the function g is discontinuous along Γ and regular outside, then the function uβ which solves { ∆uβ = β(uβ − g) in Ω \ Γ ∂νuβ = 0 on ∂Ω ∪ Γ is in turn discontinuous along Γ and it is the unique absolute minimizer of the nonhomogeneous Mumford-Shah functional

This article describes a canonical way to expand certain kind of (Z2)colored regular graphs into closed n-manifolds (by adding cells determined by the edgecolorings inductively), and shows that every closed combinatorial n-manifold can be obtained in this way. Simple equivalent conditions for a colored graph to admit such expansion is also found in the case when n ≤ 3.

A regular language L is power-closed if whenever x ∈ L, also x ∈ L for all k ≥ 1. We show that given a deterministic finite automaton A, it is PSPACE-complete to decide whether the language accepted by A is power-closed.

We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [20] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T1 spaces.

We consider lattices of regular sets of non negative integers, i.e. of sets definable in Presbuger arithmetic. We prove that if such a lattice is closed under decrement then it is also closed under many other functions: quotients by an integer, roots, etc.